BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN METHOD:PUBLISH X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT SUMMARY:Francesco Gavazzo - Term Relation Algebras and the Algebraization of Language Metatheory DTSTART:20260625T103000 DTEND:20260625T114500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-06-25/sessions/353/ CATEGORIES: DESCRIPTION:Many semantic aspects of a formal language can be defined as s tructural\npredicates on its abstract syntax\, and much of its metatheory can be\nunderstood through the 'logical' properties of these predicates. T ypical\nexamples include results such as congruence of bisimilarity\, type safety\,\nconfluence of evaluation\, and termination of reduction. While several general\ntheories have been proposed to study some of these proper ties — notable\nexamples include mathematical operational semantics and categorical rewriting\n— a theory accounting for all of them\, uniformly and abstractly\, independently\nof specific languages and syntactic struc tures\, is still missing.\n\nIn a recent line of research\, I have propose d to develop such a theory in the\nform of an algebra of structural predic ates\, extending traditional logical\nalgebras with operations akin to the structural definitions of predicates\,\nsuch as structural recursion and substitution. This talk gives an introduction\nto such algebras in their r elational form — Term Relation Algebras (TRAs) —\nand to their applica tions to the metatheory of programming languages and\nformal systems.\n\nT he first part of the talk introduces TRAs from an 'algebraic logic'\npersp ective. TRAs arise as algebras of relations on term structures\,\ninternal izing such structure through logical operations on relations.\nRemarkably\ , not only is this 'logical internalization' possible on virtually\nall te rm structures — first- and second-order terms\, nominal terms\, string\n diagrams\, and so on — but it yields\, in all these cases\, essentially the same\nalgebras. TRAs axiomatize these algebras abstractly\, with no r eference to any\nunderlying term structure.\n\nThe second part shifts to a pplications of TRAs to language metatheory\, showing\nhow many of the sema ntic notions and properties mentioned above can be studied\nalgebraically within TRAs. The payoff of the algebraization is generality\nand unificat ion: on the one hand\, metatheorems that are otherwise reproved\nsystem b y system are proved once and for all as algebraic properties (mostly\nqua si-equations) in the framework of TRAs\; on the other hand\, the algebraic \nlens reveals how conceptually different metatheorems\, such as confluenc e of\nreduction and congruence of bisimilarity\, are actually deeply relat ed. \n\nTime permitting\, the last part of the talk is devoted to some in formal\ncomparisons between TRAs and 'proof-theoretic' approaches to langu age\nmetatheory. URL:https://chocola.ens-lyon.fr/events/meeting-2026-06-25/sessions/353/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno da Rocha Paiva - Internalising effectful forcing in System T DTSTART:20260528T151500 DTEND:20260528T161500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-05-28/sessions/351/ CATEGORIES: DESCRIPTION:Gödel first introduced System T in his dialectica interpretat ion to prove\nconsistency of arithmetic. As a higher-order analogue of pri mitive recursive\nfunctions\, computability in System T has been studied e xtensively. For example\,\nit is known that all functions F : (ℕ → ℕ ) → ℕ are continuous\, in the sense that\ntheir output must only rely on a finite amount of their input. Moreover\, it can\neven be shown if F i s a System T function\, then the amount of input that\nrequired to compute F(α) can itself be computed via a function m : (ℕ → ℕ) → ℕ\nin System T. While the former result has a succinct semantic proof using a m odel\nbased in dialogue trees\, the latter result seemed out of reach. In this talk we\nwill see how to rephrase this model as a syntactic translati on using\nChurch-encodings of dialogue trees\, allowing us to prove that t he stronger\nresult about moduli of continuity. URL:https://chocola.ens-lyon.fr/events/meeting-2026-05-28/sessions/351/ END:VEVENT BEGIN:VEVENT SUMMARY:Nuria Brede - On a generic approach to constructive reverse mathem atics DTSTART:20260528T134500 DTEND:20260528T144500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-05-28/sessions/350/ CATEGORIES: DESCRIPTION:In joint work with Hugo Herbelin\n\, we studied different choice\nand bar induction principles f rom a "generic" perspective: We showed\nhow weak Kőnig's lemma\, the fan theorem\, bar induction\, dependent\nchoice\, the Boolean prime ideal theo rem and general choice have common\ncontrapositive generalisations. In the talk\, I will revisit this work\nand put it into perspective of an ongoin g classification and\nformalisation effort to constructively relate variou s logical\nprinciples which are classically equivalent to choice axioms. URL:https://chocola.ens-lyon.fr/events/meeting-2026-05-28/sessions/350/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam van Gool - Ultraconvergence spaces DTSTART:20260528T103000 DTEND:20260528T114500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-05-28/sessions/352/ CATEGORIES: DESCRIPTION:We introduce the concept of *ultraconvergence space*: a catego ry equipped with\nadditional structure that captures "how objects converge along\nultrafilter-indexed families of objects". The main instance of int erest is the\ncategory of points of any Grothendieck topos\, which can be endowed with such\nan ultraconvergence structure in a canonical way. When viewed through a\nlogical lens\, the ultraconvergence space canonically a ssociated to a geometric\ntheory is its category of models\, equipped with additional structure that\ncaptures "how models map to ultraproducts of m odels". Our main theorem is a\nrepresentation result: if a topos has enou gh points\, then it is equivalent to\na category of étale spaces over the canonical ultraconvergence space of its\npoints. This theorem simultaneou sly generalizes both M. Barr's 1970\n"Relational algebras" representing to pological spaces via the ultrafilter\nmonad\, and M. Makkai's 1987 "Stone duality for first-order logic" between\ncoherent toposes and ultracategor ies.\n\nThis is joint work with Jérémie Marquès and Umberto Tarantino\, recently\nappeared in Journal of Pure and Applied Algebra 2026 \n()\, also see \n . URL:https://chocola.ens-lyon.fr/events/meeting-2026-05-28/sessions/352/ END:VEVENT BEGIN:VEVENT SUMMARY:Thiago Felicissimo - Definitional Proof Irrelevance Made Accessibl e DTSTART:20260430T151500 DTEND:20260430T161500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-04-30/sessions/348/ CATEGORIES: DESCRIPTION:A universe of propositions equipped with definitional proof \n irrelevance constitutes a convenient medium to express properties and \npr oofs in type-theoretic proof assistants such as Lean\, Rocq\, and Agda. \n However\, allowing accessibility predicates—used to establish semantic \ ntermination arguments—to inhabit such a universe yields undecidable \nt ypechecking\, hampering the predictability and foundational bases of a \np roof assistant. To effectively reconcile definitional proof irrelevance \n and accessibility predicates with both theoretical foundations and \npract icality in mind\, we describe a type theory that extends the \nCalculus of Inductive Constructions featuring observational equality in \na universe of strict propositions\, and two variants for handling the \nelimination p rinciple of accessibility predicates: one variant \nsafeguards decidabilit y by sticking to propositional unfolding\, and the \nother variant favors flexibility with definitional unfolding\, at the \nexpense of a potentiall y diverging typechecking procedure. Crucially\, \nthe metatheory of this d ual approach establishes that any proof made in \nthe definitional variant of the theory can be translated into a proof of \nthe same statement in t he propositional variant\, all while preserving \nthe decidability of the latter. Moreover\, we prove the two variants to \nbe consistent and to sat isfy forms of canonicity\, ensuring that programs \ncan indeed be properly evaluated. We present an implementation in Rocq \nand compare it with exi sting approaches. Overall\, this work introduces \nan effective technique that informs the design of proof assistants with \nstrict propositions\, e nabling local computation with accessibility \npredicates without compromi sing the ambient type theory. \n\nThis is joint \nwork with Yann Leray\, L oïc Pujet\, Nicolas Tabareau\, Éric Tanter and Théo \nWinterhalter.\n\n See [https://hal.science/hal-05474391](https://hal.science/hal-05474391) URL:https://chocola.ens-lyon.fr/events/meeting-2026-04-30/sessions/348/ END:VEVENT BEGIN:VEVENT SUMMARY:Niyousha Najmaei - From Semantics to Syntax: A Type Theory for Com prehension Categories DTSTART:20260430T134500 DTEND:20260430T144500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-04-30/sessions/347/ CATEGORIES: DESCRIPTION:Recent models of intensional type theory have been constructed in algebraic weak factorization systems (AWFSs). AWFSs give rise to compr ehension categories that feature non-trivial morphisms between types\; the se morphisms are not used in the standard interpretation of Martin-Löf ty pe theory in comprehension categories.\nWe develop a type theory that inte rnalizes morphisms between types\, reflecting this semantic feature back i nto syntax. Our type theory comes with Π-\, Σ-\, and identity types. We discuss how it can be viewed as an extension of Martin-Löf type theory wi th coercive subtyping\, as sketched by Coraglia and Emmenegger. We further more define semantic structure that interprets our type theory and prove a soundness result. Finally\, we exhibit many examples of the semantic stru cture\, yielding a plethora of interpretations. \n\nThis is joint work wit h Niels van der Weide\, Benedikt Ahrens\, and Paige Randall North.\n\nPape r available at [https://arxiv.org/abs/2503.10868](https://arxiv.org/abs/25 03.10868) URL:https://chocola.ens-lyon.fr/events/meeting-2026-04-30/sessions/347/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Castellan - Social studies of science as inspiration for res earch in PL DTSTART:20260430T103000 DTEND:20260430T114500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-04-30/sessions/349/ CATEGORIES: DESCRIPTION:In this talk\, I will present the field of Science and Technol ogy Studies (STS). Born in the 1970s at the crossroad between epistemology \, sociology and history\, the field proposes to enrich traditional philos ophy of science by including the scientists as humans and members of socie ty in the analysis. The goal of the talk is to illustrate how this field c an provide us reflexivity on our own research and its interaction with soc iety.\n\nI will introduce the starting point of STS by briefly addressing the well-known problem of science neutrality. I will draw three areas of S TS to illustrate how a change of perspective may alter the way of we do re search and generate interesting research questions in computer science tha t may be more aligned with our values. Examples will be drawn from Botasco pia\, an interdisciplinary research between computer scientists\, biologis ts and social scientists\, using plant identification as a place to experi ment different relationships between humans\, nature and technology. URL:https://chocola.ens-lyon.fr/events/meeting-2026-04-30/sessions/349/ END:VEVENT BEGIN:VEVENT SUMMARY:Steve Zdancewic - Vellvm: Formal Verification of LLVM IR Code DTSTART:20260402T151500 DTEND:20260402T161500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-04-02/sessions/346/ CATEGORIES: DESCRIPTION:LLVM is an industrial-strength compiler that's used for everyt hing from iOS\ndevelopment to academic research.  However\, like any piec e of complicated\nsoftware\, LLVM IR itself has a complex specification\, making it hard to fully\nunderstand\, and its implementation has bugs\, wh ich can cause potentially\ncatastrophic mis-compilation errors. These prop erties make the LLVM framework\na\nsweet spot for bug-finding and verifica tion technologies--any improvements to\nit\nare amplified across its many applications.\n\nThis talk will survey the Vellvm (Verified LLVM) project\ , which aims to define\na\nformal\, mathematical specification for a large \, useful subset of LLVM.  Vellvm\nis implemented in the Rocq interactive theorem prover\, which can be used for\ndeveloping machine-checkable prop erties about LLVM IR programs and compiler\noptimization passes.  Along t he way\, we'll explore some subtleties of LLVM IR\nsemantics and see how V ellvm models them in a modular way by composing\n"monadic\ninterpreters" b uilt on top of a data structure called _interaction trees_.\nWe'll also se e some applications of Vellvm for verified compiler construction. URL:https://chocola.ens-lyon.fr/events/meeting-2026-04-02/sessions/346/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephanie Weirich - Tracking how dependently typed functions use t heir arguments DTSTART:20260402T134500 DTEND:20260402T144500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-04-02/sessions/345/ CATEGORIES: DESCRIPTION:Dependent types increase the expressiveness of programming lan guages by\nallowing the result types of functions to depend on the values of their\narguments. However\, many of these arguments are purely specific ational: they\nare there to provide information to the type checker\, but otherwise have no\nruntime significance. Such arguments can be identified through various\nmechanisms\, such as usage analysis (counting how many ti mes functions use\ntheir parameters) or dependency analysis (tracking whic h results depend on\nwhich inputs).\n\nIn this talk\, I will show how depe ndent type systems can integrate such\nanalyses and make use of this infor mation. In particular\, I will provide an\noverview of the Dependent Calcu lus of Indistinguishability (DCOI)\, a system\nthat uses dependency tracki ng to identify specificational arguments so that\nthey may be erased at ru ntime and ignored during conversion.\n\nThis is joint work with Yiyun Liu\ , Jonathan Chan\, and Jessica Shi. URL:https://chocola.ens-lyon.fr/events/meeting-2026-04-02/sessions/345/ END:VEVENT BEGIN:VEVENT SUMMARY:Mariangiola Dezani - Intersection Type Galore DTSTART:20260402T103000 DTEND:20260402T114500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-04-02/sessions/344/ CATEGORIES: DESCRIPTION:The first part of the talk reviews in full generality intersec tion type\ntheories and filter models\, i.e. lambda-calculus models\, gen erated by them. \n\nThe second part of the talk gives an overview of how v arious authors exploited\nintersection types in different developments and applications.\n\nFinally some new results dealing with the interpretation of unsolvable \nlambda-terms in filter models will be discussed. URL:https://chocola.ens-lyon.fr/events/meeting-2026-04-02/sessions/344/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Barbarossa - Computational interpretations of logic : the c ase of Dialectica DTSTART:20260312T151500 DTEND:20260312T161500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-03-12/sessions/343/ CATEGORIES: DESCRIPTION:I will first recall some computational interpretations of logi c\, with a focus\non Gödel's Dialectica -- which plays a central role in concrete applications\nof proof theory to mainstream mathematics via the s o-called "proof mining"\nprogram.\n\nThen I will discuss some content from a recent joint work with Thomas Powell\n(University of Bath): we present Dialectica as a collection of rules inspired\nby Hoare logic \; in this wa y\, Dialectica is viewed as a specification system\nfor "procedural" progr ams that come with a forward and backward direction\, and\nthis viewpoint naturally captures the dynamics of extracted realisers from\nproofs. We al so define a big-step semantics for (a fragment of) this system\,\nthat sho ws that Dialectica performs a generalised backpropagation. URL:https://chocola.ens-lyon.fr/events/meeting-2026-03-12/sessions/343/ END:VEVENT BEGIN:VEVENT SUMMARY:Éléonore Mangel - Classical notions of computation and the Haseg awa-Thielecke theorem DTSTART:20260312T134500 DTEND:20260312T144500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-03-12/sessions/342/ CATEGORIES: DESCRIPTION:In the spirit of the Curry-Howard correspondence between proof s and programs\, we define and study a syntax and semantics for classical logic equipped with a computationally involutive negation\, using a polari sed effect calculus\, the linear classical L-calculus. A main challenge in designing a denotational semantics for the calculus is to accommodate bot h call-by-value and call-by-name evaluation strategies\, which leads to a failure of associativity of composition. In order to tackle this issue\, w e define a notion of adjunction between graph morphisms on non-associative categories\, which we use to formulate polarized and non-associative noti ons of symmetric monoidal closed duploid and of dialogue duploid. We show that they provide a direct style counterpart to adjunction models: linear effect adjunctions for the (linear) call-by-push-value calculus and dialog ue chiralities for linear continuations\, respectively. In particular\, we show that the syntax of the linear classical L-calculus can be interprete d in any dialogue duploid\, and that it defines in fact a syntactic dialog ue duploid. As an application\, we establish\, by semantic as well as synt actic means\, the Hasegawa-Thielecke theorem\, which states that the notio ns of central map and of thunkable map coincide in any dialogue duploid (i n particular\, for any double negation monad on a symmetric monoidal categ ory). \n\nThis is joint work with Paul-André Melliès and Guillaume Munch -Maccagnoni URL:https://chocola.ens-lyon.fr/events/meeting-2026-03-12/sessions/342/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Krivine - Reversible Computations are Computations DTSTART:20260312T103000 DTEND:20260312T114500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-03-12/sessions/341/ CATEGORIES: DESCRIPTION:Causality serves as an abstract notion of time for concurrent systems. A\ncomputation is causal\, or simply valid\, if each observation of a computation\nevent is preceded by the observation of its causes. The present work\nestablishes that this simple requirement is equally relevant when the\noccurrence of an event is invertible. We propose a conservative extension of\ncausal models for concurrency that accommodates reversible computations. We\nfirst model reversible computations using a symmetric re siduation operation in\nthe general model of configuration structures. We show that stable\nconfiguration structures\, which correspond to prime alg ebraic domains\, remain\nstable under the action of this residuation. We t hen derive a semantics of\nreversible computations for prime event structu res\, which is shown to coincide\nwith a switch operation that dualizes co nflict and causality.\n\nThis is joint work with Clément Aubert\, August a University. USA.\n\n\nReference \n[https://www.coalg.org/calco-mfps-2025 /pre-proceedings/MFPS25-29.pdf](https://www.coalg.org/calco-mfps-2025/pre- proceedings/MFPS25-29.pdf) URL:https://chocola.ens-lyon.fr/events/meeting-2026-03-12/sessions/341/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphaëlle Crubillé - Interpreting De Finetti's Theorem in the Ca tegory of Integrable Cones DTSTART:20260205T151500 DTEND:20260205T161500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-02-05/sessions/340/ CATEGORIES: DESCRIPTION:We establish a connection between two results in the literatur e \non probabilistic semantics: a formulation of De Finetti's theorem in t he \nlanguage of category theory due to Jacobs and Staton\, and the generi c \nconstruction of the free exponential of Linear Logic by Melliès et al \, \nthat has been instantiated in the model of probabilistic coherence \n spaces by Crubillé et al. The structural proximity of these two \nconstru ctions is manifest\, but making this connection formal requires \ntechnica l developements on the relationship between the category of \nstochastic k ernels and the category of integrable cones\, two well-known \ncategories in probabilistic semantics.  We then use this connection to \ngive a char acterisation of the total elements of the probabilistic \ncoherence space !Bool. URL:https://chocola.ens-lyon.fr/events/meeting-2026-02-05/sessions/340/ END:VEVENT BEGIN:VEVENT SUMMARY:Jui-Hsuan Wu (Ray) - Non-Wellfounded Derivations for Intersection Subtyping with Fixpoints DTSTART:20260205T134500 DTEND:20260205T144500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-02-05/sessions/339/ CATEGORIES: DESCRIPTION:Subtyping is a key ingredient of many intersection type system s. In the case\nof the BCD system\, B. Pierce gave a transitivity-free pre sentation of\nsubtyping. This alternative presentation provides better str uctural properties\nfor the analysis of this relation and leads to a simpl e decision algorithm.\n\nIn this talk\, I will show how this transitivity- free approach can be extended\nbeyond BCD to a broad class of intersection type systems. The extensions we\nconsider allow imposing some pre-order a s well as fixpoint equations on atoms.\nThis includes in particular the ca se of various intersection type systems\ncompatible with eta-equality (Sco tt\, Park\, etc).\n\nI will then establish the equivalence between these t ransitivity-free systems\nand their traditional BCD-style presentations us ing cut-elimination techniques\nfrom proof theory. The presence of fixpoin ts requires moving beyond standard\nfinite derivations\, leading to the us e of non-wellfounded derivations. In the\ncontext of the structural analys is of intersection subtyping\, this happens to\nbe the first use of infini tary derivations.\n\nThis is joint work with Olivier Laurent. URL:https://chocola.ens-lyon.fr/events/meeting-2026-02-05/sessions/339/ END:VEVENT BEGIN:VEVENT SUMMARY:Morgan Rogers - What is a monoid? DTSTART:20260205T103000 DTEND:20260205T114500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/meeting-2026-02-05/sessions/338/ CATEGORIES: DESCRIPTION:In many situations one encounters an entity that resembles a m onoid. It consists of a carrier and two operations that resemble a unit an d a multiplication\, subject to three equations that resemble associativit y and left and right unital laws. The question then arises whether this en tity is\, in fact\, a monoid in a suitable sense.\n\nCategory theorists ha ve answered this question by providing a notion of monoid in a monoidal ca tegory\, or more generally in a multicategory. While these encompass many examples\, there remain cases which do not fit into these frameworks\, suc h as the notion of relative monad and the modelling of call-by-push-value sequencing. In each of these examples\, the leftmost and/or the rightmost factor of a multiplication or associativity law seems to be distinguished. \n\nTo include such examples\, we generalize the multicategorical framewor k in two stages.\n\nFirstly\, we move to the framework of a left-skew mult icategory (due to Bourke and Lack)\, which generalizes both multicategory and left-skew monoidal category. The notion of monoid in this framework en compasses examples where only the leftmost factor is distinguished\, such as the notion of relative monad.\n\nSecondly\, we consider monoids in the novel framework of a bi-skew multicategory. This encompasses examples wher e both the leftmost and the rightmost factor are distinguished\, such as t he notion of a category on a span\, and the modelling of call-by-push-valu e sequencing.\n\nIn the bi-skew framework (which is the most general)\, we give a coherence result saying that a monoid corresponds to an unbiased m onoid\, i.e. a map from the terminal bi-skew multicategory. \n\nThis is jo int work with Paul Blain Levy URL:https://chocola.ens-lyon.fr/events/meeting-2026-02-05/sessions/338/ END:VEVENT BEGIN:VEVENT SUMMARY:Julie Cailler - Deskolemization: From Tableaux to Machine-Checkabl e Proofs DTSTART:20251211T151500 DTEND:20251211T161500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-12-11/sessions/337/ CATEGORIES: DESCRIPTION:Bridging the gap between automated and interactive theorem pro vers remains one\nof the major challenges in formal reasoning. Automated t heorem provers can\ngenerate proofs very efficiently\, but their internal proof representations are\nusually not readily translatable into proofs ch eckable by interactive theorem\nprovers. Techniques such as the analytic t ableau method are\, in principle\,\nwell suited to produce proofs that can be certified\, but things get more\ncomplicated when we use more advanced proof-search strategies — e.g.\,\nSkolemization — that transform the structure of the proof.\n\nIn this talk\, we will discuss how this problem can be addressed through\ndeskolemization\, the process of reconstructing the logical structure of\ntableau proofs that rely on different Skolemiza tion strategies. We will\npresent a generic deskolemization framework\, im plemented in the Goéland\nprover\, and show how the resulting proofs can be exported and verified in\nsystems such as Rocq\, Lambdapi\, SC-TPTP and Lisa. URL:https://chocola.ens-lyon.fr/events/seminaire-2025-12-11/sessions/337/ END:VEVENT BEGIN:VEVENT SUMMARY:Kostia Chardonnet - Compiling Quantum λ-Terms into Circuits via t he Geometry of Interaction DTSTART:20251211T134500 DTEND:20251211T144500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-12-11/sessions/336/ CATEGORIES: DESCRIPTION:We present an algorithm turning any term of a linear quantum λ-calculus into a quantum circuit. The essential ingredient behind the pr oposed algorithm is Girard's geometry of interaction\, which\, differently from its well-known uses from the literature\, is here leveraged to perfo rm as much of the classical computation as possible\, while producing a ci rcuit that\, when executed\, performs all the quantum operations in the un derlying λ-term. Noticeably\, we identify a class of terms which can be c ompiled without an exponential blowup\, which is encountered when using\np lain operational semantics. URL:https://chocola.ens-lyon.fr/events/seminaire-2025-12-11/sessions/336/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Paquet - Monads and algebras for efficient inference in proba bilistic programming DTSTART:20251211T103000 DTEND:20251211T114500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-12-11/sessions/332/ CATEGORIES: DESCRIPTION:Computing the output distribution of a discrete probabilistic program (a\nprocess known as exact inference) can be very slow if implemen ted naively. A\ncommon solution is to use efficient representations of pro bability\ndistributions as trees of random variables.\n\nWe have developed a new semantic model for probabilistic programming that\ncaptures this ki nd of optimization. The model is compositional\, making it easy\nto explai n why the optimization is correct with respect to the standard\nsemantics of probabilistic programming.\n\nIn this talk\, I will explain the constru ction in detail. The key idea is to\ndecompose the probabilistic effect in to two effects: name generation (for\ncreating new random variables) and r ead-only state (for branching on sampled\nvalues). The main technical chal lenge is to correctly combine the monadic\nsemantics of call-by-value for the first effect with call-by-name for the\nsecond.\n\nThis is based on a joint work with Aurore Alcolei\, Simon Castellan\, and Tom\nHirschowitz. URL:https://chocola.ens-lyon.fr/events/seminaire-2025-12-11/sessions/332/ END:VEVENT BEGIN:VEVENT SUMMARY:Joshua Wrigley - Day algebras DTSTART:20251120T151500 DTEND:20251120T161500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-11-13/sessions/335/ CATEGORIES: DESCRIPTION:Many logics used in computer science manipulate propositions a bout \nsystems in different states.\n\nThere are resource dependent logics \, where the resources in a state can \nbe ‘shared’ or ‘not shared ’. Accordingly\, there are two conjunctions \nfor propositions – one for when the conjunction can be proved when \nsharing resources\, and one for non-shared resources.\n\nThen there are temporal logics for reasoning about systems evolving \nthrough discrete time\, where our logical calcul us is augmented with \nconnectives about what will happen in the future\, after a discrete time \njump.\n\nSeparation logic was developed to reason about programs running in the \nstandard execution model involving pointer s and heaps (i.e. mutable data \nstructures). Heaps can be combined\, but only if they are ‘disjoint’\, so \nas to avoid an extra condition of consistency on their intersection \nwhich helps with reasoning at scale. Separation logic introduces a \n‘separating conjunction’ that expresse s that the propositions involved \nare satisfied on disjoint parts of the heap.\n\nIn all these examples\, structure on the set of states is being l ifted to \nthe propositions about those states. In this talk\, we will di scuss how \nthat lifting is calculated by using a generalisation of a clas sical \ncategory-theoretic construction: Day convolution. This ‘extensi on \nconstruction’ lifts all (partial) algebraic structure on the set of \nstates to logical operations on the propositions about those states. \ nMoreover\, the extended operations are automatically residuated\, meaning \nthey admit a notion of implication.\n\nThis is joint work with Edmund R obinson.\n\nRelevant paper: Edmund Robinson and Joshua Wrigley. "Day algeb ras." \n[arXiv:2504.06200](https://arxiv.org/abs/2504.06200) (2025). URL:https://chocola.ens-lyon.fr/events/seminaire-2025-11-13/sessions/335/ END:VEVENT BEGIN:VEVENT SUMMARY:Aymeric Walch - A compositional approach to Taylor expansion DTSTART:20251120T134500 DTEND:20251120T144500 DTSTAMP:20260612T104319Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-11-13/sessions/334/ CATEGORIES: DESCRIPTION:The combination of the theory of differential calculus with th e\ntheory of programming languages is an active field of research\, with t he\ndevelopment of automated differentiation and of the differential lambd a\ncalculus. It is well known that differentiation can be turned into a\nc ompositional operation\, using the tangent bundle construction\, also call ed\ndual numbers in automated differentiation.\n\nIn this talk\, we explai n how Taylor expansion at any order can be similarly\nturned into a compos itional operation\, using an idea similar to that of jet\nbundles that app ear in differential geometry.\n\nWe will then discuss how category theory is a nice framework to describe those\nideas. Formally\, Taylor expansion is captured as a functor\, and the axioms of\ndifferential calculus boil d own to naturality equations that turns this\nfunctor into a monad. This ca tegorical structure is similar to the structure\nof higher order dual numb ers that have found recent applications in automated\ndifferentiation.\n \ nThe first half of this talk does not require prior knowledge on category\ ntheory. URL:https://chocola.ens-lyon.fr/events/seminaire-2025-11-13/sessions/334/ END:VEVENT BEGIN:VEVENT SUMMARY:Sonia Marin - Intuitionistic modal logics and their justifications DTSTART:20251120T103000 DTEND:20251120T114500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-11-13/sessions/333/ CATEGORIES: DESCRIPTION:Justification logic is an explication of modal logic: boxes ar e replaced with\nproof terms formally through realisation theorems. In int uitionistic modal\nlogic\, boxes and diamonds are decoupled and not De Mor gan dual. We propose\njustification counterparts to some intuitionistic mo dal logics by making\ndiamonds explicit and introducing new terms called s atisfiers. In this talk\,\nwe will hopefully introduce enough background i nformation to eventually \npresent an axiomatisation of these justificatio n logics with a syntactic\nrealisation procedure using cut-free (nested) s equent systems for\nintuitionistic modal logics. \n\n(This is joint work w ith Paaras Padhiar\, building\nup on other works with Anupam Das and with Roman Kuznets and Lutz\nStraßburger.) URL:https://chocola.ens-lyon.fr/events/seminaire-2025-11-13/sessions/333/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesca Guffanti - Quantifier-free formulas and quantifier alter nation depth in doctrines. DTSTART:20251016T151500 DTEND:20251016T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-10-16/sessions/331/ CATEGORIES: DESCRIPTION:This talk aims to describe a first step toward a doctrinal app roach to\nquantifier-free formulas and quantifier alternation depth modulo a first-order\ntheory.\n\nThe set of quantifier-free formulas modulo a fi rst-order theory is axiomatized\nby what we call a quantifier-free fragmen t of a Boolean doctrine with\nquantifiers. Rather than being an intrinsic notion\, a quantifier-free fragment\nis an additional structure on a Boole an doctrine with quantifiers. Under a\nsmallness assumption\, the structur es occurring as quantifier-free fragments of\nsome Boolean doctrines with quantifiers are precisely the Boolean doctrines\n(without quantifiers). To obtain this characterization\, we use the fact that\nevery Boolean doctri ne over a small base category admits a quantifier\ncompletion\, of which i t is a quantifier-free fragment.\n\nFurthermore\, the stratification by qu antifier alternation depth of first-order\nformulas motivates the introduc tion of quantifier alternation stratified\nBoolean doctrines. While quanti fier-free fragments are defined in relation to\nan “ambient” Boolean d octrine with quantifiers\, a quantifier alternation\nstratified Boolean do ctrine requires no such ambient doctrine. Indeed\, it\nconsists of a seque nce of Boolean doctrines (without quantifiers) with\nconnecting axioms. Su ch sequences are in one-to-one correspondence with pairs\nconsisting of a Boolean doctrine with quantifiers and a quantifier-free\nfragment of it.\n \nThis talk is based on a joint work with Marco Abbadini [1]. \n\n[1] M. A bbadini\, F. Guffanti. Quantifier-free formulas and quantifier\nalternatio n depth in doctrines. Journal of Pure and Applied Algebra\, Volume\n229\, Issue 8\, 2025. URL:https://chocola.ens-lyon.fr/events/seminaire-2025-10-16/sessions/331/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafaël Bocquet - Relative induction principles for the syntax of dependent type theory DTSTART:20251016T134500 DTEND:20251016T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-10-16/sessions/330/ CATEGORIES: DESCRIPTION:In algebraic approaches to the syntax and semantics of depende nt type\ntheory\, the syntax is characterized as the initial object of a\n category of models. Then the universal property of the initial model\ncorr esponds to an induction principle over the syntax: properties of\nthe synt ax (canonicity\, normalization\, etc.) are proven through\ninterpretation of the syntax into various models.\n\nThe proofs of many properties do not immediately follow from the\ninduction principle\, but require a suitable strengthening of the\ninduction hypotheses. This is typically achieved us ing methods such as\ncategorical gluing. However\, constructing the corres ponding model\nfully explicitly would be tedious\, due for instance to the need to\ncheck many naturality conditions.\n\nI will present "relative in duction principles"\, which are stronger\ninduction principles that can be used to more directly prove the\ndesired properties of the syntax.\n\nThi s is based on the paper "For the Metatheory of Type Theory\,\nInternal Sco ning is Enough" (joint work with Ambrus Kaposi and\nChristian Sattler)\, a nd on my upcoming PhD thesis "Relative Induction\nPrinciples for Second-Or der Generalized Algebraic Theories". URL:https://chocola.ens-lyon.fr/events/seminaire-2025-10-16/sessions/330/ END:VEVENT BEGIN:VEVENT SUMMARY:Étienne Miquey - Generic approaches to effectful realizability DTSTART:20251016T103000 DTEND:20251016T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-10-16/sessions/329/ CATEGORIES: DESCRIPTION:Constructive foundations have for decades been built upon real izability models\nfor higher-order logic and type theory. However\, tradit ional realizability\nmodels have a rather limited notion of computation\, which only supports\nnon-termination and avoids many other commonly used e ffects. Nonetheless\, many\nrecent works have shown how realizability mode ls could benefit from side\neffects to provide computational interpretatio n for logic principles. In\nearlier work with Cohen and Tate [1]\, we addr essed the challenge of finding a\nuniform and generic algebraic framework encompassing (effectful) realizability\nmodels\, introducing evidenced fra mes for this purpose. These structures not\nonly enable a factorization of the usual construction of a realizability topos\nfrom a tripos—evidence d frames are complete with respect to triposes—but are\nalso flexible en ough to accommodate a wide range of effectful models.\n\nWe pursued this a long two main directions:\n\n- first\, by extending the syntactic (typed) approach to realizability\,\nfollowing Kreisel’s tradition\, where propo sitions from a ground logic (e.g.\,\nHOL) are translated into specificatio ns and typed programs (realizers) that\nsatisfy them. We introduce EffHOL [2]\, a new framework that expands syntactic\nrealizability. It combines h igher-kinded polymorphism—enabling typing of\nrealizers for higher-order propositions—with a computational term language\nusing monads to repres ent and reason about effectful computations.\n\n- second\, by generalizing the traditional notion of Partial Combinatory\nAlgebras (PCAs)\, which un derpins classical realizability models. To better\ninternalize a broad spe ctrum of computational effects\, we propose the concept\nof Monadic Combin atory Algebras (MCAs) [3]\, in which the combinatory algebra\nis structure d over an underlying computational effect captured by a monad. As\nwe shal l see\, MCAs provide a smooth generalization of traditional PCA-based\nrea lizability semantics.\n\n[1] Evidenced Frames: A Unifying Framework Broade ning Realizability Models. \nCohen\, Miquey & Tate. LICS 2021\n\n[2] Synta ctic Effectful Realizability in Higher-Order Logic. Cohen\, Grünfeld\,\nK irst & Miquey.\, LICS 2025\n\n[3] From Partial to Monadic : Combinatory Al gebras with Effect. Cohen\,\nGrünfeld\, Kirst & Miquey. FSCD 2025 URL:https://chocola.ens-lyon.fr/events/seminaire-2025-10-16/sessions/329/ END:VEVENT BEGIN:VEVENT SUMMARY:Étienne Miquey [ Reporté ] - Generic approaches to effectful rea lizability DTSTART:20250918T151500 DTEND:20250918T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-09-18/sessions/327/ CATEGORIES: DESCRIPTION:Constructive foundations have for decades been built upon real izability models\nfor higher-order logic and type theory. However\, tradit ional realizability\nmodels have a rather limited notion of computation\, which only supports\nnon-termination and avoids many other commonly used e ffects. Nonetheless\, many\nrecent works have shown how realizability mode ls could benefit from side\neffects to provide computational interpretatio n for logic principles. In\nearlier work with Cohen and Tate [1]\, we addr essed the challenge of finding a\nuniform and generic algebraic framework encompassing (effectful) realizability\nmodels\, introducing evidenced fra mes for this purpose. These structures not\nonly enable a factorization of the usual construction of a realizability topos\nfrom a tripos—evidence d frames are complete with respect to triposes—but are\nalso flexible en ough to accommodate a wide range of effectful models.\n\nWe pursued this a long two main directions:\n\n* first\, by extending the syntactic (typed) approach to realizability\,\nfollowing Kreisel’s tradition\, where propo sitions from a ground logic (e.g.\,\nHOL) are translated into specificatio ns and typed programs (realizers) that\nsatisfy them. We introduce EffHOL [2]\, a new framework that expands syntactic\nrealizability. It combines h igher-kinded polymorphism—enabling typing of\nrealizers for higher-order propositions—with a computational term language\nusing monads to repres ent and reason about effectful computations.\n\n* second\, by generalizing the traditional notion of Partial Combinatory\nAlgebras (PCAs)\, which un derpins classical realizability models. To better\ninternalize a broad spe ctrum of computational effects\, we propose the concept\nof Monadic Combin atory Algebras (MCAs) [3]\, in which the combinatory algebra\nis structure d over an underlying computational effect captured by a monad. As\nwe shal l see\, MCAs provide a smooth generalization of traditional PCA-based\nrea lizability semantics.\n\n[1] Evidenced Frames: A Unifying Framework Broade ning Realizability Models. \nCohen\, Miquey & Tate. LICS 2021\n\n[2] Synta ctic Effectful Realizability in Higher-Order Logic. Cohen\, Grünfeld\,\nK irst & Miquey.\, LICS 2025\n\n[3] From Partial to Monadic : Combinatory Al gebras with Effect. Cohen\,\nGrünfeld\, Kirst & Miquey. FSCD 2025 URL:https://chocola.ens-lyon.fr/events/seminaire-2025-09-18/sessions/327/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafaël Bocquet [ Reporté ] - TBA DTSTART:20250918T134500 DTEND:20250918T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-09-18/sessions/328/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2025-09-18/sessions/328/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Blain Levy [ Annulé ] - TBA DTSTART:20250918T103000 DTEND:20250918T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2025-09-18/sessions/326/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2025-09-18/sessions/326/ END:VEVENT BEGIN:VEVENT SUMMARY:Elaine Pimentel - Alternative Semantic Views of Modality: From the Modal Cube to Linear Logic DTSTART:20250626T151500 DTEND:20250626T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-06-26/sessions/325/ CATEGORIES: DESCRIPTION:*PART I: A Proof-Theoretic Approach to the Semantics of Classi cal Linear Logic*\n\nLinear logic (LL) is a resource-aware\, abstract logi c programming language that refines both classical and intuitionistic logi c.\nThe semantics of linear logic is typically presented in one of two way s: by associating each formula with the set of all contexts that can be us ed to prove it (e.g. phase semantics) or by assigning meaning directly to proofs (e.g. coherence spaces).\n\nThis work proposes a different approach by adopting a proof-theoretic perspective.\nMore specifically\, we employ base-extension semantics (BeS) to characterise proofs through the notion of base support.\n\n*PART II: The Modal Cube Revisited: Semantics without Worlds*\n\nWe present a non-deterministic semantic framework for all modal logics in the modal cube\, extending prior works by Kearns and others. Ou r approach introduces modular and uniform multi-valued non-deterministic m atrices (Nmatrices) for each logic. The semantics is grounded in an eight- valued system and provides a sound and complete decision procedure for eac h modal logic\, extending and refining earlier semantics as particular cas es. Additionally\, we propose a novel model-theoretic perspective that lin ks our framework to relational (Kripke-style) semantics\, addressing longs tanding conjectures regarding the correspondence between modal axioms and semantic conditions within non-deterministic settings. The result is a phi losophically robust and technically modular alternative to standard possib le-world semantics. URL:https://chocola.ens-lyon.fr/events/meeting-2025-06-26/sessions/325/ END:VEVENT BEGIN:VEVENT SUMMARY:Danielle Marshall - Linearity\, Uniqueness\, Ownership: An Entente Cordiale DTSTART:20250626T134500 DTEND:20250626T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-06-26/sessions/324/ CATEGORIES: DESCRIPTION:Substructural type systems\, which restrict the use of weakeni ng and\ncontraction rules from intuitionistic logic\, are growing in popul arity because\nthey allow for a resourceful interpretation of data which c an be used to rule\nout software bugs. Substructurality is finally taking hold in practical\nprogramming: Haskell now has linear types based on Gira rd's linear logic but\nintegrated via graded function arrows\, Clean has u niqueness types ensuring\nthat values have at most a single reference\, an d Rust has an intricate\nownership system guaranteeing memory safety. But despite this broad range of\nresourceful type systems\, there has been com paratively little work on\nunderstanding their relative strengths and weak nesses. We demonstrate how\nlinear types and uniqueness types can be used within a single system in the\nsetting of the Granule language to offer bo th restrictions on local program\nbehaviour and guarantees about global me mory usage. We then extend this\nframework further\, by showing that just like graded type systems as in Granule\nor Idris build upon linearity\, Ru st's ownership model builds upon uniqueness.\nWe develop an extended type system incorporating ownership and borrowing based\non ideas from both fra ctional permissions and graded types\, and implement this\nin Granule. URL:https://chocola.ens-lyon.fr/events/meeting-2025-06-26/sessions/324/ END:VEVENT BEGIN:VEVENT SUMMARY:Vikraman Choudhury - The Duality of λ-Abstraction DTSTART:20250626T103000 DTEND:20250626T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-06-26/sessions/320/ CATEGORIES: DESCRIPTION:There are well-known dualities of computation in both function al and\nconcurrent programming: input/output\, expression/context\, strict /lazy\, sender/\nreceiver\, forward/backwards\, and several others. When v iewed through an\nalgebraic lens\, these can be understood as metaphysical interpretations of\nrigorous mathematical dualities. \n\nIn this talk\, I will explore the duality of values and continuations\n(Filinski'89) thro ugh the lens of cartesian closure/co-cartesian co-closure.\nThe main obser vation is that\, just as higher-order functions give\nexponentials\, highe r-order continuations give co-exponentials. Using this\nsemantic duality\, I will present a λλ~ (lambda-lambda-bar or tilde) calculus\,\nwhich is a call-by-value calculus extended with a classical disjunction type\,\ntha t exhibits a duality of abstraction/co-abstraction. I will develop the\nsy ntax and semantics of this language\, and give a computational interpretat ion\nin terms of speculative execution and backtracking. Using the langua ge\, I will\nshow how to recover classical control operators\, the computa tional\ninterpretation of classical logic\, and axiomatise control effects . Finally\, I\nwill show how this duality gives a nice programming idiom f or control effects\,\nthat can be used in existing functional programming languages. URL:https://chocola.ens-lyon.fr/events/meeting-2025-06-26/sessions/320/ END:VEVENT BEGIN:VEVENT SUMMARY:Hiroshi Unno - Refinement Types and Higher-Order Model Checking fo r Algebraic Effects and Handlers DTSTART:20250515T151500 DTEND:20250515T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-05-15/sessions/323/ CATEGORIES: DESCRIPTION:Algebraic effects and handlers provide a modular way to struct ure programs\nwith computational effects and are increasingly adopted in p ractical\nprogramming languages such as OCaml. Their expressivity and util ity stem from\nthe capability to manipulate delimited continuations. Howev er\, delimited\ncontinuations also introduce complex control flows\, makin g program\nverification more challenging.\n\nIn this talk\, we present two complementary approaches to verifying programs\nwith algebraic effects an d handlers. Both approaches are based on Answer Type\nModification (ATM)\, which enables type systems to precisely track what effects\noccur and in what order during program execution\, reflecting this information\nas modi fications to the answer types of delimited continuations. However\, they\n use ATM in different ways.\n\nThe first approach introduces a novel depend ent refinement type system for\nalgebraic effects and handlers. This syste m incorporates a mechanism called\nAnswer Refinement Modification (ARM)\, which can be seen as a specialization of\nATM that applies modifications t o the refinement predicates of answer\nrefinement types. We automate refin ement type checking and inference for the\nsystem by reducing them to solv ing Constrained Horn Clauses (CHCs) and\nintegrating with existing CHC sol vers\, and have implemented this approach in\nRCaml\, a refinement type-ba sed verifier for OCaml.\n\nThe second approach extends higher-order model checking (HOMC) to programs\nwith algebraic effects and handlers. While HO MC achieves decidability for pure\nhigher-order programs with finite data domains\, simply adding algebraic\neffects and handlers makes model checki ng undecidable due to the potential for\nan unbounded number of active han dlers. To address this\, we propose\nrestricting programs using ATM\, ther eby bounding the number of active\nhandlers. Under this restriction\, the model checking problem becomes decidable\nagain while still supporting a w ide range of practical effects. To enable\nreuse of existing HOMC tools fo r pure programs\, we present a CPS\ntransformation that reduces the model checking of programs with algebraic\neffects and handlers to that of pure programs. We have implemented this\napproach in EffCaml\, a transformation -based verifier for OCaml\, which\nincorporates a type inference algorithm for our type system with ATM\, the CPS\ntransformation\, and integration with HOMC tools. URL:https://chocola.ens-lyon.fr/events/meeting-2025-05-15/sessions/323/ END:VEVENT BEGIN:VEVENT SUMMARY:Elies Harington - ∞-categorical models of linear logic : higher polynomials\, higher species DTSTART:20250515T134500 DTEND:20250515T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-05-15/sessions/322/ CATEGORIES: DESCRIPTION:The notion of categorical model of linear logic is now well st udied and established around the notion of linear-non-linear adjunction\, which encompasses the previous notions of Seely categories\, Lafont catego ries and linear categories. These categorical structures have counterparts in the realm of ∞-categories\, which can thus be thought of as "weak"\, or "homotopical" models of linear logic. In this talk\, we give a tour of categorical semantics of linear logic\, and show examples of ∞-categori cal models generalizing polynomial functors\, generalized species\, and mo dels from linear algebra. URL:https://chocola.ens-lyon.fr/events/meeting-2025-05-15/sessions/322/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Gratzer - Modal dependent type theory and synthetic categor y theory DTSTART:20250515T103000 DTEND:20250515T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-05-15/sessions/321/ CATEGORIES: DESCRIPTION:In this talk\, we discuss the process of extending Martin-Löf dependent type\ntheory with one or more\nmodalities: special unary type c onstructors distinguished by their relatively\npoor behavior. We\nintroduc e a proposed class of modalities—weak dependent right adjoints—which\n proven flexible enough\nto accommodate many interesting examples (guarded recursion\, internalized\nparametricity\, cohesion\,\netc.) but still rigi d enough to admit a calculus with good syntactic\nproperties. We show then how\nthese weak dependent right adjoints may be assembled into a general framework\nfor modal type theory\n(MTT). Finally\, time permitting\, we hi ghlight a recent application of MTT to\nRiehl and Shulman's\ntheory of syn thetic ∞-categories.\n\nThis talk contains joint work with Alex Kavvos\, Andreas Nuyts\, Lars Birkedal\,\nJonathan Weinberger\,\nand Ulrik Buchhol tz. URL:https://chocola.ens-lyon.fr/events/meeting-2025-05-15/sessions/321/ END:VEVENT BEGIN:VEVENT SUMMARY:Chase Ford - Algebraic reasoning in locally presentable categories DTSTART:20250403T103000 DTEND:20250403T113000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-04-03/sessions/319/ CATEGORIES: DESCRIPTION:A seminal result in category theory is the Lawvere-Linton corr espondence\nbetween the equational theories of Birkhoff and (finitary) mon ads on the\ncategory of sets. Over the last decade\, several variants of t his result have\nbeen established in numerous settings including the categ ory of posets and the\ncategory of metric spaces. The aim of this talk is to discuss a generic\nframework of universal algebra in categories of rela tional structures given by\nmodels of the (infinitary) limit-theories of C oste and Rosický: these are\nperhaps better known as locally presentable categories. We will sketch the\nconstruction of an enriched and accessible monad from a given relational\nalgebraic theory.\n\nThe content of this t alk emerged from joint work with Lutz Schröder and Stefan\nMilius: [https ://arxiv.org/abs/2107.03880](https://arxiv.org/abs/2107.03880). URL:https://chocola.ens-lyon.fr/events/meeting-2025-04-03/sessions/319/ END:VEVENT BEGIN:VEVENT SUMMARY:Elena di Lavore - Kleene-cartesian bicategories for program logics . DTSTART:20250313T151500 DTEND:20250313T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-03-13/sessions/318/ CATEGORIES: DESCRIPTION:We introduce Kleene bicategories. In the same way that cartesi an bicategories\nof relations capture the structure of relations with cart esian product\, Kleene\nbicategories capture the structure of relations wi th disjoint union.\nKleene-cartesian bicategories combine these two struct ures by distributing the\ncartesian product over the disjoint union\, and are expressive enough to deal\nwith imperative programs. The derivation ru les of Hoare logic follow from the\naxioms of Kleene-cartesian bicategorie s.\n\nThis talk is based on recent joint work with Filippo Bonchi and Ales sandro Di\nGiorgio. URL:https://chocola.ens-lyon.fr/events/meeting-2025-03-13/sessions/318/ END:VEVENT BEGIN:VEVENT SUMMARY:Victoria Barrett - Subatomic logic and eversion in deep inference DTSTART:20250313T134500 DTEND:20250313T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-03-13/sessions/317/ CATEGORIES: DESCRIPTION:Deep inference is a methodology for the design of proof formal isms\,\nmotivated by the pursuit of linearity in the composition mechanism s. Proofs\ncan be composed not only by inference rules but also sequential ly and\nhorizontally by connective. This allows for proof systems in which all\nstructural rules are decomposed to their atomic forms\, supplemented by linear\nrule schemes which only move information around.\n \nSubatomic logic is a recent area of development in deep inference in which\neven th e atomic rules are given linearly\, by taking atoms not as base elements\n of a proof but as non-commutative binary connectives whose arguments are t heir\ntruth values.\n \nI will present some recent work in a subatomic sys tem for propositional\nclassical logic\, in particular the 'eversion lemma ' and two of its\napplications\, one of which has to do with proof compres sion and the other with\ncut elimination\, and I will discuss some future directions for research.\n \n[Link to CSL paper](https://drops.dagstuhl.de /entities/document/10.4230/LIPIcs.CSL.2025.39) URL:https://chocola.ens-lyon.fr/events/meeting-2025-03-13/sessions/317/ END:VEVENT BEGIN:VEVENT SUMMARY:Maribel Fernandez - Specifying Calculi with Binders in Rewriting L ogic DTSTART:20250313T103000 DTEND:20250313T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-03-13/sessions/316/ CATEGORIES: DESCRIPTION:Formalising languages with binders (such as programming langua ges and logics)\nwithin a logical framework with zero representational di stance (i.e.\, the\ncalculus and its representation look the same) poses n on-trivial challenges\,\nincluding: faithful representation of syntax and binding operators\; support\nfor calculus-specific equivalences\; faithful representation of the language\ndynamics (operational semantics)\; and ge neration of correct-by-construction\nimplementations. \n\nWe show how to u se rewriting logic to meet these challenges. More precisely\,\nwe show how a general notion of binder signature can be axiomatised in\nrewriting log ic following the nominal approach\, and we propose a general\nmethodology to specify languages with binders\, including their structural\ncongruence s and operational semantics. We also show how rewriting logic\nmethods pro vide executable specifications of languages with binders. We use\nthe pi-c alculus as a running example because it illustrates well the\nabove-mentio ned challenges.\n\n(Joint work with Jose Meseguer) URL:https://chocola.ens-lyon.fr/events/meeting-2025-03-13/sessions/316/ END:VEVENT BEGIN:VEVENT SUMMARY:Shin-Ya Katsumata - Codensity liftings and their applications to s emantics DTSTART:20250206T151500 DTEND:20250206T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-02-06/sessions/314/ CATEGORIES: DESCRIPTION:Codensity lifting is a method to construct liftings of\nendofu nctors/monads along fibrations. They subsume several\nconstructions in mat hematics\, such as the Kantorovich metric and the\nlower/upper preorders o n powersets. In this talk\, I will give an\noverview of codensity lifting and its applications to program\nsemantics and formalization of bisimulati ons over coalgebras. URL:https://chocola.ens-lyon.fr/events/meeting-2025-02-06/sessions/314/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Maestracci - The Lambda Calculus can be Quantified DTSTART:20250206T134500 DTEND:20250206T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-02-06/sessions/315/ CATEGORIES: DESCRIPTION:In this paper we introduce several quantitative methods for th e\nlambda-calculus based on partial metrics\, a well-studied variant of st andard\nmetric spaces that have been used to metrize non-Hausdorff topolog ies\, like\nthose arising from Scott domains. First\, we study quantitativ e variants\, based\non program distances\, of sensible equational theories for the λ-calculus\, like\nthose arising from Böhm trees and from the c ontextual preorder. Then\, we\nintroduce applicative distances capturing h igher-order Scott topologies\,\nincluding reflexive objects like the D∞ model. Finally\, we provide a\nquantitative insight on the well-known conn ection between the Böhm tree of a\nλ-term and its Taylor expansion\, by showing that the latter can be presented\nas an isometric transformation. URL:https://chocola.ens-lyon.fr/events/meeting-2025-02-06/sessions/315/ END:VEVENT BEGIN:VEVENT SUMMARY:Justin Hsu - Type Systems for Numerical Error Analysis DTSTART:20250206T103000 DTEND:20250206T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2025-02-06/sessions/313/ CATEGORIES: DESCRIPTION:Programs in numerical analysis and scientific computing make h eavy\nuse\nof floating-point numbers to approximate ideal real numbers. Op erations on\nfloating-point numbers incur roundoff error\, and an importan t practical\nproblem\nis to bound the overall magnitude of the error for c omplex computations.\nExisting work employs a variety of strategies such a s interval arithmetic\, SMT\nencodings\, and global optimization\; however \, current methods are not\ncompositional and are limited in scalability\, precision\, and expressivity.\n\nToday\, I'll talk about some of our rece nt work on NumFuzz\, a higher-order\nlanguage that can bound forward error using a linear\, coeffect type system for\nsensitivity analysis combined with a novel quantitative error type. Our type\ninference procedure can de rive precise relative error bounds for programs that\nare several orders o f magnitude larger than previously possible.\n\nIf time permits\, I'll bri efly discuss a second type system called Bean for\nbounding backward error . Like NumFuzz\, Bean is based on a linear coeffect type\nsystem\, but it features a semantics based on a novel category of lenses on\nmetric spaces . Bean is the first system to soundly reason about backward error\nin nume rical programs.\n\nJoint work with Ariel Kellison (Cornell). URL:https://chocola.ens-lyon.fr/events/meeting-2025-02-06/sessions/313/ END:VEVENT BEGIN:VEVENT SUMMARY:Théo Winterhalter - Dependent Ghosts Have a Reflection for Free DTSTART:20241121T151500 DTEND:20241121T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-11-21/sessions/312/ CATEGORIES: DESCRIPTION:We introduce ghost type theory (GTT) a dependent type theory e xtended with a new universe for ghost data that can safely be erased when running a program but which is not proof irrelevant like with a universe o f (strict) propositions. Instead\, ghost data carry information that can b e used in proofs or to discard impossible cases in relevant computations. Casts can be used to replace ghost values by others that are propositional ly equal\, but crucially these casts can safely be ignored for conversion. We provide a type-preserving erasure procedure which gets rid of all ghos t data and proofs\, a step which may be used as a first step to program ex traction. We give a syntactical model of GTT using a program translation a kin to the parametricity translation and thus show consistency of the theo ry. Because it is a parametricity model\, it can also be used to derive fr ee theorems about programs using ghost code. We further extend GTT to supp ort equality reflection and show that we can eliminate its use without the need for the usual extra axioms of function extensionality and uniqueness of identity proofs. In particular we validate the intuition that indices of inductive types—such as the length index of vectors—do not matter f or computation and can safely be considered modulo theory. The results of the paper have been formalised in Coq. URL:https://chocola.ens-lyon.fr/events/meeting-2024-11-21/sessions/312/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrienne Lancelot - Interaction Equivalence DTSTART:20241121T134500 DTEND:20241121T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-11-21/sessions/311/ CATEGORIES: DESCRIPTION:Contextual equivalence is the de facto standard notion of \npr ogram equivalence. A key theorem is that contextual equivalence is an \neq uational theory. Making contextual equivalence more intensional\, for \nex ample taking into account the time cost of the computation\, seems a \nnat ural refinement. Such a change\, however\, does not induce an \nequational theory\, for an apparently essential reason: cost is not \ninvariant unde r reduction.\n\nIn the paradigmatic case of the untyped λ-calculus\, we i ntroduce \ninteraction equivalence. Inspired by game semantics\, we observ e the \nnumber of interaction steps between terms and contexts but -- cruc ially \n-- ignore their own internal steps. We prove that interaction \neq uivalence is an equational theory and we characterize it as B\, the \nwell -known theory induced by Böhm tree equality. Ours is the first \nobservat ional characterization of B obtained without enriching the \ndiscriminatin g power of contexts with extra features such as \nnon-determinism. To prov e our results\, we develop interaction-based \nrefinements of the Böhm-ou t technique and of intersection types.\nJoint work with Beniamino Accattol i\, Giulio Manzonetto and Gabriele \nVanoni. URL:https://chocola.ens-lyon.fr/events/meeting-2024-11-21/sessions/311/ END:VEVENT BEGIN:VEVENT SUMMARY:Isabelle Collet - Femmes et numérique : pratiques égalitaires\, dispositifs inclusifs DTSTART:20241121T103000 DTEND:20241121T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-11-21/sessions/304/ CATEGORIES: DESCRIPTION:L’informatique joue un rôle croissant dans l’évolution d e nos sociétés\, mais les femmes sont largement sous-représentées dans ces métiers depuis plusieurs décennies. On retrouve\navec l’informati que la division sociosexuée des savoirs : il y a des savoirs considérés comme normaux ou adaptés pour un genre\, mais tabou\, inadaptés ou inac cessibles pour l’autre…\nLes composantes de cette division fluctuent\, historiquement et géographiquement : le peu de femmes en informatique es t un problème récent et local : il est apparu après les années\n80\, e n occident.\n\nLe but de cette conférence est tout d’abord de déconstr uire des idées reçues sur les femmes et l’informatique\, puis de passe r en revue quelques bonnes pratiques qui ont permis de\ns’approcher de l a parité dans plusieurs institutions. Ces bonnes pratiques\, mises en pla ce notamment aux États-Unis ou en Norvège\, peinent à s’installer en France à cause d’un\nsystème éducatif assez rigide aux réformes parf ois contre-productives. Les succès internationaux montrent qu’il n’y a pas de fatalité ou de prédétermination. Toutefois\, ils\nmontrent aus si qu’il faut des mesures fortes pour renverser la tendance.\n\n\n*The t alk will be in french.* URL:https://chocola.ens-lyon.fr/events/meeting-2024-11-21/sessions/304/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Marie Pédrot - Upon This Quote I Will Build My Church Thes is DTSTART:20241017T151500 DTEND:20241017T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-10-17/sessions/310/ CATEGORIES: DESCRIPTION:The internal Church thesis (CT) is a logical principle stating that any function\nf : N → N is computed by a concrete program in some Turing-complete language.\nCT has been widely used in constructive mathema tics\, most specifically in the Russian\ntradition. On the other side of t he iron curtain\, Martin-Loef Type Theory (MLTT) was\ndesigned as the mode rn embodiment of Bishop-style neutral mathematics. It should\ncome as a su rprise that the natural type-theoretic equivalent of CT was conjectured\nt o be inconsistent with MLTT. In this talk\, we will prove that this conjec ture is false\,\nby introducing “MLTT”\, a consistent extension of MLT T with quoting primitives that\nimplements CT in a computational way. URL:https://chocola.ens-lyon.fr/events/meeting-2024-10-17/sessions/310/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonas Frey - The shape of contexts DTSTART:20241017T134500 DTEND:20241017T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-10-17/sessions/309/ CATEGORIES: DESCRIPTION:Contexts x_1:A_1\,...\,x_n:A_n in simple type theory can be vi ewed as “flat”\, since the variable declarations don’t depend on eac h other and can be permuted.\n\nIn dependent type theory\, the general for m of contexts is (x_1:A_1\, x_2:A_2(x_1)\, ...\,x_n:A_n(x_1\,...\,x_{n-1}) ) with a linear dependency chain between the variable declarations:\nHowev er\, the specific contexts occuring in practice are not always totally ord ered. For example\, in the context (x y:O\, f:A(x\,y)) the first two varia bles are not interdependent.\n\nSo maybe we should allow finite posets as shapes of contexts? It turns out to be better to use an even more general class of structures: *finite direct categories*\, i.e. finite\ncategories which have no nontrivial isomorphisms and endomorphisms.\n\nFDCs were intr oduced by Makkai [1] as part of his notion of “First order logic with de pendent sorts”\, but the perspective on FDCs proposed in this talk is so mewhat different since\nFDCs are not used to represent dependency structur es of theories\, but of contexts.\n\nIn the talk I will explain why FDCs s eem to provide a good abstract notion of “shape” for contexts\, that t he category of FDCs and discrete fibrations forms a coclan\, and how to\nd erive a notion of dependent algebraic theory from these ideas which is ver y close to Chaitanya Leena Subramaniam’s “dependently typed theories ”.\n\n\n[1]\n[https://www.math.mcgill.ca/makkai/folds/foldsinpdf/FOLDS.p df]( https://www.math.mcgill.ca/makkai/folds/foldsinpdf/FOLDS.pdf) URL:https://chocola.ens-lyon.fr/events/meeting-2024-10-17/sessions/309/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominik Kirst - Separating Markov’s Principles in Constructive T ype Theories DTSTART:20241017T103000 DTEND:20241017T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-10-17/sessions/308/ CATEGORIES: DESCRIPTION:Markov's principle (MP) is an axiom in some varieties of const ructive mathematics\, stating that Σ1-propositions (i.e. existential quan tification over a decidable predicate on N) are stable under double negati on. However\, there are various non-equivalent definitions of decidable pr edicates and thus Σ1-propositions in constructive foundations\, leading t o non-equivalent Markov's principles. While this fact is well-reported in the literature\, it is often overlooked\, leading to wrong claims in stand ard references and published papers.\n\nIn this talk\, I will illustrate t he status of three natural variants of MP in Martin-Löf's constructive ty pe theory (MLTT)\, by first giving respective equivalence proofs to differ ent formulations of Post's theorem\, stability of termination of computati ons\, completeness of various proof systems w.r.t. some model-theoretic se mantics for Σ1-theories\, and finiteness principles for both extended nat ural numbers and trees. Afterwards\, I describe how these three variants o f MP can be separated using effectful models of MLTT\, adapting Kreisel’ s original proof strategy using free choice sequences to Cohen and Rahli ’s framework of stateful type theories. URL:https://chocola.ens-lyon.fr/events/meeting-2024-10-17/sessions/308/ END:VEVENT BEGIN:VEVENT SUMMARY:Zeinab Galal - Combining fixpoint and differentiation theory DTSTART:20240919T151500 DTEND:20240919T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-09-19/sessions/307/ CATEGORIES: DESCRIPTION:Interactions between derivatives and fixpoints have many impor tant applications in both computer science and mathematics. In this paper\ , we provide a categorical framework to combine fixpoints with derivatives by studying Cartesian differential categories with a fixpoint operator. W e introduce an additional axiom relating the derivative of a fixpoint with the fixpoint of the derivative. We show how the standard examples of Cart esian differential categories where we can compute fixpoints provide canon ical models of this notion. We also consider when the fixpoint operator is a Conway operator\, or when the underlying category is closed. As an appl ication\, we show how this framework is a suitable setting to formalize th e Newton-Raphson optimization for fast approximation of fixpoints and exte nd it to higher order languages. \n\nsee [https://arxiv.org/abs/2407.12691 ](https://arxiv.org/abs/2407.12691)\n\nThis is joint work with Jean-Simon Pacaud Lemay. URL:https://chocola.ens-lyon.fr/events/meeting-2024-09-19/sessions/307/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Moreau - Profinite trees\, through monads and the lambda-c alculus DTSTART:20240919T134500 DTEND:20240919T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-09-19/sessions/306/ CATEGORIES: DESCRIPTION:In its simplest form\, the theory of regular languages is the study of sets of finite words recognized by finite monoids. The finiteness condition on monoids gives rise to a topological space whose points\, cal led profinite words\, encode the limiting behavior of words with respect t o finite monoids. Yet\, some aspects of the theory of regular languages ar e not particular to monoids and can be described in a general setting. On the one hand\, Bojańczyk has shown how to use monads to generalize the th eory of regular languages and has given an abstract definition of the free profinite structure\, defined by codensity\, given a fixed monad and a no tion of finite structure. On the other hand\, Salvati has introduced the n otion of language of λ-terms\, using denotational semantics\, which gener alizes the case of words and trees through the Church encoding. In recent work\, the author and collaborators defined the notion of profinite λ-ter m using semantics in finite sets and functions\, which extend the Church e ncoding to profinite words.\n\nIn this work\, we prove that these two gene ralizations\, based on monads and denotational semantics\, coincide in the case of trees. To do so\, we consider the monad of abstract clones which\ , when applied to a ranked alphabet\, gives the associated clone of ranked trees. This induces a notion of free profinite clone\, and hence of profi nite trees. The main contribution is a categorical proof that the free pro finite clone on a ranked alphabet is isomorphic\, as a Stone-enriched clon e\, to the clone of profinite λ-terms of Church type. Moreover\, we also prove a parametricity theorem on families of semantic elements which provi des another equivalent formulation of profinite trees in terms of Reynolds parametricity. \n\nsee \n[https://arxiv.org/abs/2402.13086](https://arxiv .org/abs/2402.13086) URL:https://chocola.ens-lyon.fr/events/meeting-2024-09-19/sessions/306/ END:VEVENT BEGIN:VEVENT SUMMARY:Clovis Eberhart - A Compositional Approach to Verification Models DTSTART:20240919T103000 DTEND:20240919T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-09-19/sessions/305/ CATEGORIES: DESCRIPTION:We present a compositional approach to graph-like\nverificatio n models (e.g.\, parity games\, Markov decision processes\, or\nPetri nets ) based on "open" structures. Such open structures are\ngraphs with potent ially dangling edges called "open ends"\, and which\nform interfaces along which open structures can be composed. We thus\ndefine a syntactic catego ry of interfaces and open structures between\nthem.\nWe then define a sema ntic category representic relevant information\nabout the structure (e.g.\ , a category of probabilistic rewards).\nFinding an interpretation functor from the syntactic category to the\nsemantic one shows that these structu res' sematics can be computed\ncompositionally. URL:https://chocola.ens-lyon.fr/events/meeting-2024-09-19/sessions/305/ END:VEVENT BEGIN:VEVENT SUMMARY:Aloÿs Dufour - Böhm and Taylor for all DTSTART:20240627T151500 DTEND:20240627T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-06-27/sessions/303/ CATEGORIES: DESCRIPTION:Böhm approximations\, used in the definition of Böhm trees\, are a staple of the semantics of the\nlambda-calculus. Introduced more re cently by Ehrhard and Regnier\, Taylor approximations provide\na quantitat ive account of the behavior of programs and are well-known to be connected to intersection\ntypes. The key relation between these two notions of app roximations is a commutation theorem\,\nroughly stating that Taylor approx imations of Böhm trees are the same as Böhm trees of Taylor\napproximati ons. Böhm and Taylor approximations are available for several variants or extensions of\nthe lambda-calculus and\, in some cases\, commutation theo rems are known. In this paper\, we define\nBöhm and Taylor approximations and prove the commutation theorem in a very general setting.\nWe also int roduce (non-idempotent) intersection types at this level of generality. Fr om this\, we show\nhow the commutation theorem and intersection types may be applied to any calculus embedding in\na sufficiently nice way into our general calculus. All known Böhm-Taylor commutation theorems\, as\nwell a s new ones\, follow by this uniform construction.\n\nJoint work with Damia no Mazza. URL:https://chocola.ens-lyon.fr/events/meeting-2024-06-27/sessions/303/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthieu Piquerez - Machine-Checked Categorical Diagrammatic Reaso ning DTSTART:20240627T134500 DTEND:20240627T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-06-27/sessions/302/ CATEGORIES: DESCRIPTION:We describe a formal proof library\, developed using the Coq p roof assistant\, designed to assist users in writing correct diagrammatic proofs\, for 1-categories. This library proposes a deep-embedded\, domain- specific formal language\, which features dedicated proof commands to auto mate the synthesis\, and the verification\, of the technical parts often e luded in the literature. \n\nJoint work with Benoît Guillemet and Assia M ahboubi\, see\n[https://arxiv.org/abs/2402.14485](https://arxiv.org/abs/24 02.14485) URL:https://chocola.ens-lyon.fr/events/meeting-2024-06-27/sessions/302/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Clairambault - An Analysis of Symmetry in Quantitative Sema ntics DTSTART:20240627T103000 DTEND:20240627T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-06-27/sessions/301/ CATEGORIES: DESCRIPTION:Drawing inspiration from linear logic\, quantitative semantics aim at \nrepresenting quantitative information about programs and their \ nexecutions: they include the relational model and its numerous \nextensio ns\, game semantics\, and syntactic approaches such as \nnon-idempotent in tersection types and the Taylor expansion of \nlambda-terms. The crucial f eature of these models is that programs are \ninterpreted as witnesses whi ch consume *bags* of resources.\n\nBags are often taken to be finite multi sets\, i.e. quotiented structures. \nAnother approach typically seen in ca tegorifications of the relational \nmodel is to work with unquotiented str uctures (e.g. sequences) related \nwith explicit morphisms referred to her e as symmetries\, which express \nthe exchange of resources. Symmetries ar e obviously at the core of these \ncategorified models\, but we argue thei r interest reaches beyond those \n--- notably\, symmetry leaks in some non -categorified quantitative models \n(such as the weighted relational model \, or Taylor expansion) under the \nform of numbers whose combinatorial in terpretation is not always clear.\n\nIn this work\, we build on a recent b icategorical model called thin spans \nof groupoids. Notably\, thin spans feature a decomposition of symmetry \ninto two sub-groupoids of polarized --- *positive* and *negative* --- \nsymmetries. We first construct a varia tion of the original exponential \nof thin spans\, based on sequences rath er than families. Then we give a \nsyntactic characterisation of the inter pretation of simply-typed \nlambda-terms in thin spans\, in terms of rigid intersection types and \nrigid resource terms. Finally\, we formally rela te thin spans with the \nweighted relational model and generalized species of structure. This \nallows us to show how some quantities in those model s reflect polarized \nsymmetries: in particular we show that the weighted relational model \ncounts witnesses from generalized species of structure\ , divided by the \ncardinal of a group of positive symmetries.\n\nThis is joint work with Simon Forest. URL:https://chocola.ens-lyon.fr/events/meeting-2024-06-27/sessions/301/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Arrial - Genericity Through Stratification DTSTART:20240523T151500 DTEND:20240523T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2024-05-23/sessions/299/ CATEGORIES: DESCRIPTION:A fundamental issue in the λ-calculus is to find appropriate notions for meaningfulness. It is well-known that in the call-by-name λ-c alculus (CbN) the meaningful terms can be identified with the solvable one s\, and that this notion is not appropriate in the call-by-value λ-calcul us (CbV). This paper validates the challenging claim that yet another noti on\, previously introduced in the literature as potential valuability\, ap propriately represents meaningfulness in CbV. Akin to CbN\, this claim is corroborated by proving two essential properties. The first one is generic ity\, stating that meaningless subterms have no bearing on evaluating norm alizing terms. To prove this (which was an open problem)\, we use a novel approach based on stratified reduction\, indifferently applicable to CbN a nd CbV\, and in a quantitative way. The second property concerns consisten cy of the smallest congruence relation resulting from equating all meaning less terms. While the consistency result is not new\, we provide the first direct operational proof of it. We also show that such a congruence has a unique consistent and maximal extension\, which coincides with a well-kno wn notion of observational equivalence. Our results thus supply the formal concepts and tools that validate the informal notion of meaningfulness un derlying CbN and CbV.\n\nA preprint is available at [https://arxiv.org/abs /2401.12212](https://arxiv.org/abs/2401.12212). URL:https://chocola.ens-lyon.fr/events/seminaire-2024-05-23/sessions/299/ END:VEVENT BEGIN:VEVENT SUMMARY:Maaike Zwart - What Monads Can and Cannot Do With a Bit of Extra T ime DTSTART:20240523T134500 DTEND:20240523T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2024-05-23/sessions/300/ CATEGORIES: DESCRIPTION:The delay monad provides a simple way to introduce general rec ursion in type\ntheory. Combining this monad with other monads then allows us to write\nprograms in type theory that use a wide range of computation al effects. In\nthis talk I will look at two ways of combining the delay m onad with monads\nthat can be described by higher inductive types (HITs). The first way is via a\ndistributive law\, which describes the interaction between the two effects.\nBut… such distributive laws do not always exi st. In fact\, I will show that\nthere is no distributive law for combining the delay monad with the finite\npowerset monad (modelling non-determinis m) or the finite distribution monad\n(modelling probability). We therefore also look at a second way\, via a free\ncombination with no interaction b etween the two effects. This still gives a\nrich language allowing us to r eason about non-determinism and probabilistic\neffects in the presence of recursion. URL:https://chocola.ens-lyon.fr/events/seminaire-2024-05-23/sessions/300/ END:VEVENT BEGIN:VEVENT SUMMARY:Stelios Tsampas - Logical Relations in Higher-Order Mathematical O perational Semantics DTSTART:20240523T103000 DTEND:20240523T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2024-05-23/sessions/298/ CATEGORIES: DESCRIPTION:Logical relations constitute a key method for reasoning in hig her-order\nlanguages. They are usually developed on a per-case basis\, wit h a new theory\nrequired for each variation of the language or of the prob lem setting. In\nrecent work\, we have introduced general constructions of logical relations at\nthe level of Higher-Order Mathematical Operational Semantics (HO-MOS)\, a\nhighly parametric categorical framework for modeli ng the operational semantics\nof higher-order languages. Additionally\, we have developed efficient\nprinciples that simplify reasoning on logical r elations for languages\nspecified in the HO-MOS framework. In this present ation\, I will be dissecting\nlogical relations to expose their coalgebrai c core\, and explain how our theory\nuncovers the lightweight reasoning pr inciples hidden underneath the surface.\n For instance\, within this frame work\, if a given operational semantics\nis sufficiently well-behaved\, on e can automatically construct a logical\nrelation that is sound for contex tual equivalence. Examples I will be covering\ninclude unary\, binary and step-indexed logical relations\, for simple as well\nas recursive types. URL:https://chocola.ens-lyon.fr/events/seminaire-2024-05-23/sessions/298/ END:VEVENT BEGIN:VEVENT SUMMARY:Christine Tasson - Density-Based Semantics for Reactive Probabilis tic Programming DTSTART:20240404T151500 DTEND:20240404T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-04-04/sessions/297/ CATEGORIES: DESCRIPTION:Synchronous languages are now a standard industry tool for cri tical embedded systems. Designers write high-level specifications by compo sing streams of values using block diagrams. These languages have been ext ended with Bayesian reasoning to program state-space models which compute a stream of distributions given a stream of observations. However\, the se mantics of probabilistic models is only defined for scheduled equations -- a significant limitation compared to dataflow synchronous languages and b lock diagrams which do not require any ordering.\n\nIn this paper we propo se two schedule agnostic semantics for a probabilistic synchronous languag e. The key idea is to interpret probabilistic expressions as a stream of u n-normalized density functions which maps random variable values to a resu lt and positive score. The co-iterative semantics interprets programs as s tate machines and equations are computed using a fixpoint operator. The re lational semantics directly manipulates streams and is thus a better fit t o reason about program equivalence. We use the relational semantics to pro ve the correctness of a program transformation required to run an optimize d inference algorithm for state-space models with constant parameters. \n\ nThis is joint work with Guillaume Baudart and Louis Mandel. URL:https://chocola.ens-lyon.fr/events/meeting-2024-04-04/sessions/297/ END:VEVENT BEGIN:VEVENT SUMMARY:Peio Borthelle - Operational Game Semantics\, certified in Coq DTSTART:20240404T134500 DTEND:20240404T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-04-04/sessions/295/ CATEGORIES: DESCRIPTION:Operational game semantics (OGS) is a method for interpreting programs\nas strategies in suitable games\, or more precisely as labelled\ ntransition systems over suitable games\, in the sense of Levy and\nStaton . Such an interpretation is called sound when\, for any two\ngiven program s\, bisimilarity of associated strategies entails\ncontextual equivalence. OGS has been applied to a variety of\nlanguages\, with rather tedious sou ndness proofs. Concretely they \ntransform a reduction relation into a ful l blown model interpreting open \nterms as a strategy for interacting with all possible execution \nenvironments. We have developed a Coq formalizat ion of this \nconstruction\, abstracting away some syntactic details of th e considered \nlanguage and keeping the computational content intact.\n\nI will start this talk by motivating and presenting OGS intuitively\, and \ nwill then give an overview of our contributions. Finally I will detail a \ntechnical point of the soundness proof\, namely well-definedness of the \ncomposition of Proponent- and Opponent-strategies. Indeed this crucial \ npoint involves a variant of the so-called infinite chattering problem\, \ nwhich we solve by looking into uniqueness properties of fixpoint \nequati ons in iterative monads. URL:https://chocola.ens-lyon.fr/events/meeting-2024-04-04/sessions/295/ END:VEVENT BEGIN:VEVENT SUMMARY:Brigitte Pientka - A Framework for Certified Meta-programming DTSTART:20240404T103000 DTEND:20240404T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2024-04-04/sessions/296/ CATEGORIES: DESCRIPTION:Meta-programming is the art of writing programs that produce o r\nmanipulate other programs. This allows programmers to automate\nerror-p rone or repetitive tasks\, and exploit\ndomain-specific knowledge to custo mize the generated code. Hence\,\nmeta-programming is widely used in a ran ge of technologies: % from\n%generating optimized code for matrix computat ions in machine learning\nfrom cryptographic message authentication in sec ure network\nprotocols to supporting reflection in proof environments\nsuc h as Lean.\n\n Unfortunately\, writing safe meta-programs remains very cha llenging and sometimes frustrating\, as traditionally errors in the genera ted code are only detected when running it\, but not at the time when code is generated. To make it easier to write and\nmaintain meta-programs\, to ols that allow us to detect errors during code\ngeneration -- instead of w hen running the generated code -- are\nessential.\n\nThis talk presents a framework for certified meta-programming based on Cocon\,\n a Martin-Le of dependent type theory for defining\nlogics and proofs that allows us to represent domain-specific\nlanguages (DSL) within the logical framework L F. In addition\, Cocon allows us write\nrecursive programs and proofs abou t those DSLs. We show how to embed into LF STLC or System F\, etc. and th en write programs about those encodings using Cocon itself. More important ly\, we extend Cocon with the ability to reflect STLC terms defined in LF back into Cocon which allows us to execute and run those objects.\nThis es tablishes Cocon as a target for compiling meta-programming systems -- from compiling meta-programming with STLC or System F to compiling meta-progra mming in CoC. URL:https://chocola.ens-lyon.fr/events/meeting-2024-04-04/sessions/296/ END:VEVENT BEGIN:VEVENT SUMMARY:Rémi di Guardia - Retractions in Multiplicative Linear Logic DTSTART:20240314T151500 DTEND:20240314T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2024-03-14/sessions/293/ CATEGORIES: DESCRIPTION:Given formulas A and B\, A is a retraction of B if there exist proofs of A |- B\nand B |- A which compose to the axiom on A\, up to cut- elimination and\naxiom-expansion. This gives a natural notion of sub-tying \, and corresponds to\nretractions in the category of proofs: objects are formulas\, and morphisms\nproofs up to cut-elimination and axiom-expansion . While isomorphisms for\nmultiplicative linear logic have been characteri zed (Balat & Di Cosmo gave a\ncorresponding equational theory in 1999)\, a nd there is a well-known retraction\n(which is not an isomorphism)\, there is not even a conjecture on what the set\nof retractions could be.\n\nI w ill present a work in progress about this problem\, giving properties\nsho wing the problem should not be too hard\, then solving the case "an atom X \nis a retraction of a formula B" using proof nets. Meanwhile\, I will als o show\ndifficulties for solving the general case\, as well as what happen s in other\nfragments of linear logic. URL:https://chocola.ens-lyon.fr/events/seminaire-2024-03-14/sessions/293/ END:VEVENT BEGIN:VEVENT SUMMARY:Luc Pellissier - Droit expérimental des algorithmes publics DTSTART:20240314T134500 DTEND:20240314T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2024-03-14/sessions/294/ CATEGORIES: DESCRIPTION:Les programmes utilisés par les administrations publiques ont des\nobligations théoriques de transparence et de compréhension par la\ nsociété. Nous verrons ces droits\, comment ils sont appliqués\, et ce\ nqu'on peut dire des notions de spécification ou d'algorithme\nsous-jacen tes. Sur l'exemple du programme qui pseudonymise les décisions\nde justic e judiciaire avant mise en ligne\, je présenterai une stratégie\njuridic tionnelle pour faire vivre ces droits.\n\n*The talk will be in french.* URL:https://chocola.ens-lyon.fr/events/seminaire-2024-03-14/sessions/294/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Ehrhard - Intégration dans les cônes DTSTART:20240314T103000 DTEND:20240314T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2024-03-14/sessions/292/ CATEGORIES: DESCRIPTION:On a utilisé les cônes positifs de Selinger\, munis de tests de \nmesurabilité\, pour faire un modèle de la programmation fonctionne lle \nprobabiliste dans un papier de 2018\, avec Michele Pagani et Christi ne \nTasson. Dans ce modèle\, l'échantillonnage était interprété au m oyen \nd'une intégrale dont l'existence n'était pas toujours garantie (i l y en \navait assez pour interpréter une version de PCF\, mais on n'aura it pas pu \ninterpréter par exemple un langage call-by-value ou call-by-p ush-value). \nDans un travail récent avec Guillaume Geoffroy\, on montre comment \nl'existence systématique d'intégrales peut être axiomatisée très \nsimplement dans une version légèrement modifiée de ces cônes\, qui \ndonnent un modèle de la logique linéaire intuitionniste. Ces int égrales \nsont définies dans le style des intégrales faibles de Pettis. On montre \naussi comment la présence de ces intégrales permet de donne r au modèle \ndes propriétés très souhaitables qui n'étaient pas disp onibles avant.\n\n*The talk will be in english upon request* URL:https://chocola.ens-lyon.fr/events/seminaire-2024-03-14/sessions/292/ END:VEVENT BEGIN:VEVENT SUMMARY:Marie Kerjean - DiLL est dans Laplace DTSTART:20240125T151500 DTEND:20240125T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2024-01-25/sessions/290/ CATEGORIES: DESCRIPTION:What do exponential maps and exponential connectives have in c ommon? \nWell\, more than we thought! This talk will describe several way in which \nthey interact.\n\nFirst\, we will see how the exponential map h elps construct the \ndifferentiation monad\, a variant of the continuation monad where the \nunit is the differential. This monad has the nice prope rty of \ncharacterizing quantitative programs\, equal to their Taylor expa nsion.\n\nWe will also see how the exponential map gives a good interpreta tion of \nthe co-digging\, a fourth co-structural exponential rule missing to those \nadded by Differential Linear Logic to Linear Logic. If time pe rmits\, we \nwill look at its nice graded properties.\n\nFinally\, we will see how the exponential function defines the Laplace \ntransformation\, w hich transforms exponential connectives by turning \ndistributions of type "!" into functions of type "?". We will see how \nthis Laplace transforma tion turns co-structural rules into structural \nones and explore its beau tiful categorical properties.\n\nThis is joint work with Jean-Simon Pacaud Lemay. URL:https://chocola.ens-lyon.fr/events/seminaire-2024-01-25/sessions/290/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Scherer - Constructor unboxing DTSTART:20240125T134500 DTEND:20240125T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2024-01-25/sessions/291/ CATEGORIES: DESCRIPTION:In this work I will present a new feature proposed for the OCa ml programming\nlanguage\, “constructor unboxing”\, first suggested by Jeremy Yallop in March\n2020. It enables a more efficient representation of certain sum types\, but\nrequires a static analysis to forbid certain u nboxing requests that would be\nunsound.\n\nTo define this static analysis \, one has to solve a problem of normalization of\nfirst-order definitions in presence of recursion. In the talk I hope to\nexplain my current under standing of this halting problem\, and present an\nalgorithm to compute no rmal forms and reject (in finite time) non-normalizable\ndefinitions. URL:https://chocola.ens-lyon.fr/events/seminaire-2024-01-25/sessions/291/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmanuel Beffara - Concurrent Realizability on Conjunctive Structu res DTSTART:20240125T103000 DTEND:20240125T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2024-01-25/sessions/289/ CATEGORIES: DESCRIPTION:This work aims at exploring the algebraic structure of concurr ent processes and their behavior\nindependently of a particular formalism used to define them. We propose a new algebraic structure\ncalled conjunct ive involutive monoidal algebra (CIMA) as a basis for an algebraic present ation of\nconcurrent realizability\, following ideas of the algebrization program already developed in the realm\nof classical and intuitionistic re alizability. In particular\, we show how any CIMA provides a sound\ninterp retation of multiplicative linear logic. This new structure involves\, in addition to the tensor\nand the orthogonal map\, a parallel composition. W e define a reference model of this structure as\ninduced by a standard pro cess calculus and we use this model to prove that parallel composition\nca nnot be defined from the conjunctive structure alone.\n\nThis is joint wor k with Félix Castro\, Mauricio Guillermo and Étienne Miquey URL:https://chocola.ens-lyon.fr/events/seminaire-2024-01-25/sessions/289/ END:VEVENT BEGIN:VEVENT SUMMARY:Lionel Vaux Auclair - Extensional Taylor Expansion DTSTART:20231214T151500 DTEND:20231214T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-12-14/sessions/288/ CATEGORIES: DESCRIPTION:We introduce a calculus of extensional resource terms. These a re resource terms à la Ehrhard-Regnier\, but in infinite η-long form\, w hile retaining a finite syntax and dynamics: in particular\, we prove stro ng confluence and normalization.\n\nThen we define an extensional version of Taylor expansion\, mapping ordinary λ-terms to sets (or infinite linea r combinations) of extensional resource terms: just like for ordinary Tayl or expansion\, the dynamics of our resource calculus allows to simulate th e β-reduction of λ-terms\; the extensional nature of expansion shows in that we are also able to simulate η-reduction.\nIn a sense\, extensional resource terms form a language of (non-necessarily normal) finite approxim ants of Nakajima trees\, much like ordinary resource terms are approximant s of Böhm-trees. Indeed\, we show that the equivalence induced on λ-term s by the normalization of extensional Taylor-expansion is nothing but H∗ \, the greatest consistent sensible λ-theory.\n\nTaylor expansion has pro foundly renewed the approximation theory of the λ-calculus by providing a quantitative alternative to order-based approximation techniques\, such a s Scott continuity and Böhm trees. Extensional Taylor expansion enjoys si milar advantages: e.g.\, to exhibit models of H∗\, it is now sufficient to provide a model of the extensional resource calculus. We apply this str ategy to give a new\, elementary proof of a result by Manzonetto: H∗ is the λ-theory induced by a well-chosen reflexive object in the relational model of the λ-calculus. \n\nThis is joint work with Lison Blondeau-Patis sier and Pierre Clairambault.\n\n[https://arxiv.org/abs/2305.08489](https: //arxiv.org/abs/2305.08489) URL:https://chocola.ens-lyon.fr/events/meeting-2023-12-14/sessions/288/ END:VEVENT BEGIN:VEVENT SUMMARY:Paige Randall North - Coinductive control of inductive data types DTSTART:20231214T134500 DTEND:20231214T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-12-14/sessions/287/ CATEGORIES: DESCRIPTION:In classical programming language theory\, characterizing data types as initial\nalgebras of an endofunctor that represents a specificat ion of the data types\nis an important tool. In this work\, we observe tha t the category of algebras\nof such an endofunctor is often enriched in it s category of coalgebras. This\nenrichment carries strictly more informati on than the traditional\, unenriched\ncategory. For example\, when conside ring the endofunctor whose initial algebra\nis the natural numbers\, we fi nd that the enrichment encodes a notion of\n'partial' homomorphism\, while the unenriched category encodes only `total'\nhomomorphisms. We can also leverage this extra information to generalize the\nnotion of initial algeb ras\, following the theory of weighted limits.\n\nJoint work with Maximili en Péroux: [arXiv:2303.16793](https://arxiv.org/abs/2303.16793) URL:https://chocola.ens-lyon.fr/events/meeting-2023-12-14/sessions/287/ END:VEVENT BEGIN:VEVENT SUMMARY:Marianna Girlando & Sonia Marin - Decidability of intuitionistic S 4: a proof theoretic algorithm DTSTART:20231214T103000 DTEND:20231214T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-12-14/sessions/286/ CATEGORIES: DESCRIPTION:Intuitionistic S4 (IS4) is one of the intuitionistic variants of modal logic\nS4. Its semantics was defined by Fisher Servi in terms of birelational models\,\nand it comprises two reflexive and transitive acces sibility relations: one\ncorresponding to the accessibility relation of mo dal logic S4 and the other\ncorresponding to the order relation of intuiti onistic Kripke frames. The\nquestion of whether IS4 is decidable has been open for almost 30 years\, since\nSimpson posed it in his PhD thesis. We s how that IS4 is decidable by\nperforming proof search in a fully labelled sequent calculus for IS4\, closely\nmatching the birelational semantics. O ur search algorithm outputs either a\nproof or a finite counter-model\, th us additionally establishing the finite\nmodel property for intuitionistic S4.\n\nIn this talk\, I will first introduce IS4 and discuss the strategi es to\nestablish decidability through proof search in the modal and intuit ionistic\ncase. Then\, I will sketch the main ingredients of our proof sea rch algorithm.\n\nThis talk is based on joint work with Roman Kuznets\, Ma rianela\nMorales and Lutz Straßburger\n\nA preprint is available here: [ https://arxiv.org/abs/2304.12094](https://arxiv.org/abs/2304.12094) URL:https://chocola.ens-lyon.fr/events/meeting-2023-12-14/sessions/286/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Forest - Thin spans and their modelling of rigid intersectio n types DTSTART:20231116T151500 DTEND:20231116T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-11-16/sessions/284/ CATEGORIES: DESCRIPTION:Thin spans were recently introduced as a quantitative\, or \np roof-relevant\, model\nof programming languages based on spans of groupoid s. As a model of linear\nlogic\, they can be seen as an extension of the r elational model Rel \nwhere\, in\nthe interpretation of a program\, not on ly some inputs are related to some\noutputs\, but the different ways or co mputations a program can make to \ntransform\nthe given inputs to the give n outputs are recorded.\n\nIn an ongoing work\, we show that thin spans pr ovide a useful model of\nso-called rigid intersection types\, that are non -idempotent and \nnon-commutative\nintersection types. It is already known that the relational model Rel can be\nsyntactically described using a non -idempotent but commutative \nintersection type\nsystem. The commutativity is essential for the property of subject \nreduction\,\nstating that the interpretation of a program is not changed by reduction.\nNevertheless\, t he interpretation of programs in thin spans can be \ndescribed by a\nrigid intersection type system\, while still enjoying a relaxed subject \nreduc tion\nproperty.\n\nIn this talk\, a rather light-weight presentation of th in spans will be \ngiven\,\nfollowed by a presentation of the rigid inters ection type system \nassociated to\nthem.\n\nThis is joint work with Pierr e Clairambault. URL:https://chocola.ens-lyon.fr/events/meeting-2023-11-16/sessions/284/ END:VEVENT BEGIN:VEVENT SUMMARY:Cyril Cohen - Trocq: Proof Transfer for Free\, With or Without Uni valence DTSTART:20231116T134500 DTEND:20231116T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-11-16/sessions/283/ CATEGORIES: DESCRIPTION:Libraries of formalized mathematics use a possibly broad range of different representations for a same mathematical concept. Yet light t o major manual input from users remains most often required for obtaining the corresponding variants of theorems\, when such obvious replacements ar e typically left implicit on paper. This talk presents Trocq\, a new proof transfer framework for dependent type theory. Trocq is based on a novel f ormulation of type equivalence\, used to generalize the univalent parametr icity translation. This framework takes care of avoiding dependency on the axiom of univalence when possible\, and may be used with more relations t han just equivalences. We have implemented a corresponding plugin for the Coq proof assistant\, in the CoqElpi meta-language. We use this plugin on a gallery of representative examples of proof transfer issues in interacti ve theorem proving\, and illustrate how Trocq covers the spectrum of sever al existing tools\, used in program verification as well as in formalized mathematics in the broad sense. \n\nJoint work with Enzo Crance and Assia Mahboubi. URL:https://chocola.ens-lyon.fr/events/meeting-2023-11-16/sessions/283/ END:VEVENT BEGIN:VEVENT SUMMARY:Morgan Rogers - A topos theory travel guide DTSTART:20231116T103000 DTEND:20231116T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-11-16/sessions/285/ CATEGORIES: DESCRIPTION:Topos theory can be a little intimidating: it's a vast subject with\na lot of baggage attached\, and like many areas of category theory you need to\nbe prepared to go quite deep to be rewarded. Unfortunately\, that entry barrier\nmakes the subject almost inaccessible to a casual read er! In this talk\, I will\nhelp you get your head around the jargon. What is a subobject classifier? What\nis the difference between an elementary t opos and a Grothendieck topos? Where\ndo sheaves come in and what are they \, anyway? How are these generalized\nspaces? What is a classifying topos? What's the internal language? Nominal\nsets form some kind of topos\, rig ht? What about infinity-toposes? Armed with\nthis knowledge and a bunch of examples\, you'll stand a better chance of\nfiguring out how to make topo ses work for you.\n\nFor the uninitiated\, I will spend the first 15 minut es or so introducing\ncategory theory through some examples (which may mir aculously turn out to be\ntoposes). I don't expect to have a lot of time f or non-examples\, but I am\nhappy to field questions. I also don't know in advance whether I will be able\nto cover everything I wrote above\, but I will try my best.\n\n\n*(note for people following at a distance: the tal k will be given on a blackboard)* URL:https://chocola.ens-lyon.fr/events/meeting-2023-11-16/sessions/285/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Paquet - Element-free probability distributions and Bayesian clustering DTSTART:20231019T151500 DTEND:20231019T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-10-19/sessions/282/ CATEGORIES: DESCRIPTION:An "element-free" probability distribution is what remains of a probability\ndistribution after we forget the elements to which the prob abilities were\nassigned. These objects naturally arise in Bayesian statis tics\, in situations\nwhere the specific identity of elements is not impor tant.\n\nThis talk is about the theory of element-free distributions in th e category of\nmeasurable spaces. I will give the basic theory\, and then discuss two results\nwhich demonstrate that element-free distributions are a canonical notion. The\nfirst result is a new categorical version of a r epresentation theorem for\nrandom partitions\, originally due to Kingman\, which characterises the space of\nelement-free distributions as a limit i n the Kleisli category for the Giry\nmonad G. The second result establishe s a correspondence between random\nelement-free distributions and natural transformations of type G → GG. I will\nsketch the relevance of this the ory to nonparametric models for clustering.\n\nJoint work with Victor Blan chi. URL:https://chocola.ens-lyon.fr/events/meeting-2023-10-19/sessions/282/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandre Moine - Diamonds Are Forever: Reasoning about Heap Space in a Concurrent and Garbage Collected Language DTSTART:20231019T134500 DTEND:20231019T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-10-19/sessions/281/ CATEGORIES: DESCRIPTION:Memory management is notoriously difficult in a concurrent\nse tting. The presence of garbage collection greatly simplifies the\nlife of the programmer\, eradicating many memory-related bugs. However\,\nthe heap space usage of garbage-collected programs can be tricky to\nunderstand an d reason about\, as there is no explicit program point\nwhere space is rec laimed.\n\nWe recently presented a Separation Logic with Space Credits to reason\nabout heap space under garbage collection in a high-level\, yet\ns equential\, language.\n\nIn this talk\, we scale up to a concurrent langua ge. For this purpose\,\nwe introduce new "pointed-by-thread" assertions\, which keep track of\nthe existence of stack-to-heap pointers in a reasonab ly lightweight\nmanner. We illustrate our logic on several lock-free data structures\,\nunveiling their subtle heap space usage. URL:https://chocola.ens-lyon.fr/events/meeting-2023-10-19/sessions/281/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Hirschowitz - A categorical framework for congruence of applic ative bisimilarity DTSTART:20231019T103000 DTEND:20231019T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-10-19/sessions/279/ CATEGORIES: DESCRIPTION:Research in programming languages mostly proceeds language by\ nlanguage. This in particular means that key ideas are often introduced\nf or one typical language\, and must then be adapted to other languages.\n\n A prominent example of this is Howe's method for proving that\napplicative bisimilarity\, a notion of program equivalence in\ncall-by-name λ-calcul us\, is a congruence. This method has been adapted\nto call-by-value λ-ca lculus\, PCF\, λ-calculus with delimited\ncontinuations\, higher-order π -calculus\,…\n\nIn this work\, using category theory\, we establish an a bstract congruence\ntheorem for applicative bisimilarity\, of which most e xisting adaptations\nof Howe's method are instances. The framework is both simpler and more\ngeneral than our previous attempts.\n\nThis is joint wo rk with Ambroise Lafont. URL:https://chocola.ens-lyon.fr/events/meeting-2023-10-19/sessions/279/ END:VEVENT BEGIN:VEVENT SUMMARY:Lison Blondeau-Patissier - Strategies as Resource Terms\, and thei r Categorical Semantics DTSTART:20230928T151500 DTEND:20230928T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-09-28/sessions/278/ CATEGORIES: DESCRIPTION:As shown by Tsukada and Ong\, normal (extensional) simply-type d resource terms correspond to plays in Hyland-Ong games\, quotiented by M elliès’ homotopy equivalence. Though inspiring\, their proof is indirec t\, relying on the injectivity of the relational model w.r.t. both sides o f the correspondence — in particular\, the dynamics of the resource calc ulus is taken into account only via the compatibility of the relational mo del with the composition of normal terms defined by normalization.\n\nIn t he present paper\, we revisit and extend these results. Our first contribu tion is to restate the correspondence by considering causal structures we call augmentations\, which are canonical representatives of Hyland-Ong pla ys up to homotopy. This allows us to give a direct and explicit account of the connection with normal resource terms. As a second contribution\, we extend this account to the reduction of resource terms: building on a noti on of strategies as weighted sums of augmentations\, we provide a denotati onal model of the resource calculus\, invariant under reduction. A key ste p — and our third contribution — is a categorical model we call a reso urce category\, which is to the resource calculus what differential catego ries are to the differential λ-calculus.\n\nJoint work with P. Clairambau lt and I. Vaux-Auclair. URL:https://chocola.ens-lyon.fr/events/meeting-2023-09-28/sessions/278/ END:VEVENT BEGIN:VEVENT SUMMARY:Antoine Allioux - Higher Structures in Homotopy Type Theory DTSTART:20230928T134500 DTEND:20230928T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-09-28/sessions/277/ CATEGORIES: DESCRIPTION:The definition of algebraic structures on arbitrary types in h omotopy type\ntheory (HoTT) has proven elusive so far. This is due to type s behaving like\nspaces instead of plain sets in general with equalities b etween elements of a\ntype behaving like homotopies. Equational laws of al gebraic structures must\ntherefore be stated coherently. However\, in set- based mathematics\, the\npresentation of this coherence data relies on set -level algebraic structures\nsuch as operads or presheaves which are thus not subject to additional\ncoherence conditions. Replicating this approach in HoTT leads to a situation\nof circular dependency as these structures must be defined coherently from the\nbeginning.\n\nWe break this situation of circular dependency by extending type theory with a\nuniverse of carte sian polynomial monads which\, crucially\, satisfy their laws\ndefinitiona lly. This extension permits the presentation of types and their\nhigher st ructures as opetopic types which are infinite collections of cells\nwhose geometry is described by opetopes. Opetopes are geometric shapes\noriginal ly introduced by Baez and Dolan in order to give a definition of\nn-catego ries. The constructors under which our universe of cartesian\npolynomial m onads is closed allow us to define\, in particular\, the Baez-Dolan\nslice construction on which is based our definition of opetopic type.\n\nOpetop ic types then enable us to define coherent higher algebraic structures\,\n among which infinity-groupoids and (infinity\, 1)-categories. Crucially\, their\nhigher structure coincides with the one induced by their identity t ypes. We\nthen establish some expected results in order to motivate our de finitions. URL:https://chocola.ens-lyon.fr/events/meeting-2023-09-28/sessions/277/ END:VEVENT BEGIN:VEVENT SUMMARY:William Simmons - An exact logic for compatibility of higher-order causal structures DTSTART:20230928T103000 DTEND:20230928T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-09-28/sessions/276/ CATEGORIES: DESCRIPTION:The Caus[C] construction takes a base category of unnormalised processes (e.g.\nstochastic\, quantum\, or affine maps) and applies doubl e-glueing with an\northogonality to restrict to deterministic/normalisatio n-preserving processes\,\nlifting the monoidal product of C to many produc ts representing different\ncausal structures. Previous work by the authors has shown such categories are\nmodels of MLL and\, later\, BV. In this fo llow-on work\, we devise a sound and\ncomplete logic for compatibility of causal structures with respect to\ncomposition and show it is independent of both the base category and the local\nsystem types (beyond the identifi cation of first-order systems). This logic is\na conservative extension of pomset logic with additional directed axioms\,\nwhich themselves can be f aithfully encoded back into pomset. Using this\, we\ncan relate a known se parating statement between pomset and BV to a standard\nresult of process matrices in quantum causality. \n\nJoint work with Aleks\nKissinger. URL:https://chocola.ens-lyon.fr/events/meeting-2023-09-28/sessions/276/ END:VEVENT BEGIN:VEVENT SUMMARY:Bryce Clarke - Reflections on delta lenses DTSTART:20230615T151500 DTEND:20230615T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-06-15/sessions/273/ CATEGORIES: DESCRIPTION:What is a lens? As with many questions in mathematics\, the an swer\ndepends on who you ask! Delta lenses are a particular kind of lens i ntroduced\nin 2011 to model bidirectional transformations between systems. In elementary\nterms\, a delta lens is a functor equipped with a suitable choice of lifts\,\ngeneralising the notion of split opfibration. However\ , despite admitting a\nsimple definition\, many of the interesting and nat ural category-theoretic\nproperties of delta lenses remain hidden from vie w without alternative\ncharacterisations. In this talk\, I will reflect up on several perspectives of\ndelta lenses developed in my PhD thesis\, The double category of lenses\, and\ndemonstrate their richness as a mathemati cal structure. The talk will explore\nthe connections between these differ ent approaches\, while emphasising the\nrelationship between lenses and do uble categories\, and conclude with several\navenues for future work. URL:https://chocola.ens-lyon.fr/events/meeting-2023-06-15/sessions/273/ END:VEVENT BEGIN:VEVENT SUMMARY:Aymeric Walch - Cartesian Coherent Differential Categories DTSTART:20230615T134500 DTEND:20230615T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-06-15/sessions/275/ CATEGORIES: DESCRIPTION:We extend to general Cartesian categories the idea of Coherent Differentiation recently introduced by Ehrhard in the setting of categori cal models of Linear Logic. The first ingredient is a summability structur e which induces a partial left-additive structure on the category. Additio nal functoriality and naturality assumptions on this summability structure implement a differential calculus which can also be presented in a formal ism close to Blute\, Cockett and Seely's Cartesian differential categories . URL:https://chocola.ens-lyon.fr/events/meeting-2023-06-15/sessions/275/ END:VEVENT BEGIN:VEVENT SUMMARY:Noam Zeilberger - Parsing as a lifting problem and the Chomsky-Sch ützenberger representation theorem DTSTART:20230615T103000 DTEND:20230615T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-06-15/sessions/274/ CATEGORIES: DESCRIPTION:The classical statement of the Chomsky-Schützenberger represe ntation\ntheorem says that any context-free language may be represented as the\nhomomorphic image of the intersection of a Dyck language of balanced \nparentheses with a regular language.  In the talk I will discuss a\nfib rational perspective on context-free grammars and finite-state\nautomata t hat grew out of a long-running project with Paul-André\nMelliès on type refinement systems\, but with a surprising twist that\nonly emerged when w e considered the C-S theorem.  It turns out that\nunderlying that theorem is a basic adjunction between categories\nand colored operads (= multicat egories)\, where the right adjoint\n$W : Cat \\to Oper$ builds a "spliced arrow operad" out of any category\,\nand the left adjoint $C : Oper \\to \ \Cat$ sends any operad to a\n"contour category" whose arrows have a geomet ric interpretation as\noriented contours of operations.\n\nBased on joint work with Paul-André Melliès that appeared at MFPS 2022\n[https://hal.sc ience/hal-03702762](https://hal.science/hal-03702762)\, as well as a long version of that\narticle in preparation. URL:https://chocola.ens-lyon.fr/events/meeting-2023-06-15/sessions/274/ END:VEVENT BEGIN:VEVENT SUMMARY:Axel Kerinec - Why Are Proofs Relevant in Proof-Relevant Models? DTSTART:20230511T151500 DTEND:20230511T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-05-11/sessions/270/ CATEGORIES: DESCRIPTION:Relational models of lambda-calculus can be presented as type systems\, the \nrelational interpretation of a lambda-term\nbeing given by the set of its typings. Within a distributors-induced \nbicategorical sem antics generalizing the\nrelational one\, we identify the class of ‘cate gorified’ graph models and \nshow that they can be presented as type\nsy stems as well. We prove that all the models living in this class \nsatisfy an Approximation Theorem stating\nthat the interpretation of a program co rresponds to the filtered colimit \nof the denotations of its approximants .\n\nAs in the relational case\, the quantitative nature of our models all ows \nto prove this property via a simple\ninduction\, rather than using i mpredicative techniques. Unlike relational \nmodels\, our 2-dimensional gr aph\nmodels are also proof-relevant in the sense that the interpretation o f a \nlambda-term does not contain only its typings\,\nbut the whole type derivations. The additional information carried by a \ntype derivation per mits to reconstruct\nan approximant having the same type in the same envir onment. From this\, \nwe obtain the characterization of\nthe theory induce d by the categorified graph models as a simple \ncorollary of the Approxim ation Theorem:\ntwo lambda-terms have isomorphic interpretations exactly w hen their Böhm \ntrees coincide. URL:https://chocola.ens-lyon.fr/events/meeting-2023-05-11/sessions/270/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrienne Lancelot - Normal Form Bisimulations by Value DTSTART:20230511T134500 DTEND:20230511T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-05-11/sessions/272/ CATEGORIES: DESCRIPTION:Sangiorgi's normal form bisimilarity is call-by-name\, identif ies all the call-by-name meaningless terms\, and rests on open terms in it s definition. The literature contains a normal form bisimilarity for the c all-by-value λ-calculus\, Lassen's enf bisimilarity\, which validates all of Moggi's monadic laws. The starting point of this work is the observati on that enf bisimilarity is not the call-by-value equivalent of Sangiorgi' s\, because it does not identify the call-by-value meaningless terms. The issue has to do with open terms. We then develop a new call-by-value norma l form bisimilarity\, deemed net bisimilarity\, by exploiting an existing formalism for dealing with open terms in call-by-value. It turns out that enf and net bisimilarities are incomparable\, as net bisimilarity identifi es meaningless terms but it does not validate Moggi's laws. Moreover\, the re is no easy way to merge them. To better understand the situation\, we p rovide a detailed analysis of the rich range of possible call-by-value nor mal form bisimilarities\, relating them to Ehrhard's call-by-value relatio nal semantics. URL:https://chocola.ens-lyon.fr/events/meeting-2023-05-11/sessions/272/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriele Vanoni - Monadic Intersection Types DTSTART:20230511T103000 DTEND:20230511T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-05-11/sessions/271/ CATEGORIES: DESCRIPTION:We extend intersection types to a computational\nlambda-calcul us with algebraic operations à la Plotkin and Power. We\nachieve this by considering monadic intersections\, whereby\ncomputational effects appear not only in the operational semantics\,\nbut also in the type system. Sinc e in the effectful setting\ntermination is not anymore the only property o f interest\, we want to\nanalyze the interactive behavior of typed program s with the\nenvironment. Indeed\, our type system is able to characterize the\nnatural notion of observation\, both in the finite and in the\ninfini tary setting\, and for a wide class of effects\, such as output\,\ncost\, pure and probabilistic nondeterminism\, and combinations thereof.\nThe mai n technical tool is a novel combination of syntactic techniques\nwith abst ract relational reasoning\, which allows us to lift all the\nrequired noti ons\, e.g. of typability and logical relation\, to the\nmonadic setting.\n \n\nJoint work with Francesco Gavazzo and Riccardo Treglia URL:https://chocola.ens-lyon.fr/events/meeting-2023-05-11/sessions/271/ END:VEVENT BEGIN:VEVENT SUMMARY:Will Troiani - Computation in logic as the splitting of idempotent s in algebraic geometry\; two models of multiplicative linear logic DTSTART:20230330T151500 DTEND:20230330T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2023-03-30/sessions/269/ CATEGORIES: DESCRIPTION:A hypersurface f = 0 in complex affine space is singular if an d only\nif there exists a non-contractible matrix factorization (to be def ined in the\ntalk). Matrix factorisations are organised into a bicategory where composition\nis defined via a two-step process\, first an infinite  model of the composite is\ndescribed\, and then a terminating procedure is followed to extract a *finite*\n presentation. Is this terminating proce dure a semantics of cut-elimination?\nBy considering simple cases\, Daniel Murfet and myself have uncovered two\nmodels of multiplicative linear log ic\, one in the space of coordinate rings\nwhere cut-elimination correspon ds to the celebrated Buchberger Algorithm\, and\nthe other in the space of Quantum Error Correction Codes\, where\ncut-elimination corresponds to qu antum error correction. The general picture\nhas led Murfet and myself to postulate that the splitting of idempotents has \n*fundamental relevance*  to the theory of computation. This talk defends this\nproposition. URL:https://chocola.ens-lyon.fr/events/seminaire-2023-03-30/sessions/269/ END:VEVENT BEGIN:VEVENT SUMMARY:Jules Jacobs - Fast Coalgebraic Bisimilarity Minimization DTSTART:20230330T134500 DTEND:20230330T144500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2023-03-30/sessions/268/ CATEGORIES: DESCRIPTION:Coalgebraic bisimilarity minimization generalizes classical au tomaton minimization to a large class of automata whose transition structu re is specified by a functor\, subsuming strong\, weighted\, and probabili stic bisimilarity. This offers the enticing possibility of turning bisimil arity minimization into an off-the-shelf technology\, without having to de velop a new algorithm for each new type of automaton. Unfortunately\, ther e is no existing algorithm that is fully general\, efficient\, and able to handle large systems.\n\nWe present a generic algorithm that minimizes co algebras over an arbitrary functor in the category of sets as long as the action on morphisms is sufficiently computable. The functor makes at most O(m logn) calls to the functor-specific action\, where n is the number of states and m is the number of transitions in the coalgebra.\n\nWhile more specialized algorithms can be asymptotically faster than our algorithm (us ually by a factor of (m/n))\, our algorithm is especially well suited to e fficient implementation\, and our tool often uses much less time and memor y on existing benchmarks\, and can handle larger automata\, despite being more generic. URL:https://chocola.ens-lyon.fr/events/seminaire-2023-03-30/sessions/268/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Clairambault - The Geometry of Causality : Multi-token Geom etry of Interaction and Its Causal Unfolding DTSTART:20230330T103000 DTEND:20230330T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2023-03-30/sessions/267/ CATEGORIES: DESCRIPTION:Concurrent Games is a framework developed in the past decade \ nfor semantics of programming languages. In Concurrent Games\, a program \ nis interpreted as an event structure\, representing its interactive \nbeh aviour with its execution environment. The representation is \nextremely f ine-grained: it is causal as in so-called truly concurrent \nmodels of con currency\, showing explicitely the dependence and \nindependence of comput ational events\, and the non-deterministic \nbranching points.\n\nThis int erpretation is computed in a modular way by induction on \nprograms\, foll owing the methodology of denotational semantics. This is \ngood\, because it means that the semantics can be used to reason \ncompositionally on pro grams. But it is also bad\, because the many layers \nof the interpretatio n of the source code in a denotational model and the \ncomplexity of the o perations involved (notably\, the composition of \nstrategies) blurs the r elationship between the source code and the \nsemantics.\n\nIn this work\, we make concurrent games operational. More precisely\, we \nshow that pro grams can be translated compositionally intro certain \ncoloured Petri net s\, combining intuitions from game semantics\, Girard's \nGeometry of Inte raction\, and folklore ideas on the representation of \nfirst-order impera tive concurrent programs as Petri nets. We regard \nthese coloured Petri n ets as a kind of intermediate representation\, \nstill close to the source code. But as finite graphs *unfold* to \ninfinite trees\, Petri nets *unf old* to event structures\; and here we \nshow that this unfolding yields t he same event structure obtained \ndenotationally from the interpretation in concurrent games.\n\nWe deploy this for Idealized Parallel Algol\, a ca ll-by-name higher-order \nconcurrent programming language that is well-stu died in the game \nsemantics literature. The translation is implemented\, and available at:\n\n[https://ipatopetrinets.github.io/](https://ipatopetr inets.github.io/)\n\nThis is joint work with Simon Castellan. URL:https://chocola.ens-lyon.fr/events/seminaire-2023-03-30/sessions/267/ END:VEVENT BEGIN:VEVENT SUMMARY:Meven Lennon-Bertrand - Bidirectional typing is not just an implem entation technique DTSTART:20230126T151500 DTEND:20230126T161500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-01-26/sessions/266/ CATEGORIES: DESCRIPTION:In 2000\, Pierce and Turner introduced a new technique to perf orm type inference for ML-like languages\, whose main idea was to carefull y understand the local flow of information in typing rules. This technique \, which came to be referred to as bidirectional typing\, did not come out of a void: similar ideas had appeared independently in other contexts. In particular\, bidirectional typing has been a part of\n the folklore of de pendently typed languages implementers since the dawn of time.\n\nBut even in that context where it has a long history\, bidirectional typing was mi ssing an understanding that would detach from implementations to focus on the type-theoretic structure. Fortunately\, such \na type-theoretic bidire ctional structure turns out to be a very interesting tool when studying (d ependent) type systems.\n\nIn my talk\, I will try and give some of my und erstanding of bidirectional typing\, how it is both rooted in type-checker implementations but is more than just this\, and how it can be used to ma ke the infamously painful meta-theory of dependent type systems a bit less painful. URL:https://chocola.ens-lyon.fr/events/meeting-2023-01-26/sessions/266/ END:VEVENT BEGIN:VEVENT SUMMARY:Zeinab Galal - Bidimensional fixpoint operators DTSTART:20230126T135000 DTEND:20230126T145000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-01-26/sessions/265/ CATEGORIES: DESCRIPTION:Fixpoint operators are tools to reason on recursive programs a nd \ninfinite data types obtained by induction (e.g. lists\, trees) or \nc oinduction (e.g. streams). They were given a categorical treatment with \n the notion of categories with fixpoints. An important result by Plotkin \n and Simpson in this area states that provided some conditions on bifree \n algebras are satisfied\, we obtain the existence of a unique uniform \nfix point operator. This theorem allows to recover the well-known \nexamples o f the category Cppo (complete pointed partial orders and \ncontinuous func tions) in domain theory and the relational model in \nlinear logic. In thi s talk\, I will present a categorification of this \nresult where the 2-di mensional framework allows to study the coherences \nassociated to the red uctions of λ-calculi with fixpoints i.e. the \nequations satisfied by the program computations steps. URL:https://chocola.ens-lyon.fr/events/meeting-2023-01-26/sessions/265/ END:VEVENT BEGIN:VEVENT SUMMARY:Yannick Zakowski - Monadic Definitional Interpreters as Formal Sem antic Models of Computations DTSTART:20230126T103000 DTEND:20230126T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2023-01-26/sessions/264/ CATEGORIES: DESCRIPTION:Monadic interpreters have been used for a long time as a\n mean to embed arbitrary computations in purely functional contexts. At \n its core\,\n the idea is elementary: the object language of interest is implemented\n as an\n executable interpreter in the host language\, and monads are simply the\n abstraction used to embed features such as side effects\, failure\,\n non-determini sm. By building these interpreters on top of the free\n monad\, the \n approach has offered a comfortable design point notably enabling an\n extensible\n syntax\, reusable modular components\, st ructural compositional\n definitions\, as\n well as algebrai c reasoning.\n \nThe approach has percolated beyond its programming roots: it is also\n used as a way to\n formalize the semanti cs of computational systems\, programming\n languages notably\, in\ n proof assistants based on dependently typed theories. In such\n assistants\, the host\n language is even more restricted: pro grams are all pure\, but also\n provably terminating.\n Dive rgent programs can nonetheless be embedded using for instance the\n Capretta monad:\n intuitively\, a lazy\, infinite (coinductive) tr ee models the dynamic of\n the computation. \n \nInteraction trees are a specific implementation\, in the Coq proof\n assistant\ , of a set of tools\n realizing this tradition. They provide a coin ductive implementation of\n the iterative free monad\,\n equ ipped with a set of combinators\, allowing notably for general\n re cursion. Each iterator comes\n with its equational theory establish ed with respect to a notion of\n weak bisimulation --- i.e.\n termination sensitive\, but ignoring the amount of fuel consumed ---\n and practical support for\n equational reasoning.\n Fu rther effects are implemented into richer monads via a general\n no tion of interpretation\,\n allowing one to introduce the missing al gebras required for proper\n semantic reasoning.\n Beyond pr ogram equivalence\, support for arbitrary heterogeneous\n relationa l reasoning is provided\,\n typically allowing one to prove a compi lation pass correct.\n \nIntroduced in 2020\, the project has spawne d realistic applications ---\n they are used to model LLVM IR's\n semantics notably ---\, as well as extensions to reduce the necessar y\n boilerplate\, or to offer\n proper support for non-deter minism. In this talk\, I will attempt to\n paint an illustrative ov erview of\n the core ideas and contributions constitutive of this l ine of work. URL:https://chocola.ens-lyon.fr/events/meeting-2023-01-26/sessions/264/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Herbelin - Computing with Gödel’s completeness theorem: We ak Fan Theorem\, Markov’s Principle and Double Negation Shift in action DTSTART:20221124T150000 DTEND:20221124T163000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-11-24/sessions/259/ CATEGORIES: DESCRIPTION:Completeness of first-order logic against Tarski semantics\, t hat is\nGödel's completeness theorem\, has been abundantly studied in the \ncontext of classical and intuitionistic reverse mathematics in either\ns econd-order arithmetic or set theory\, sometimes with inconsistent\nresult s (e.g. Krivine asserting it is fully constructive\, Kreisel\nderiving Mar kov's principle\, McCarty asserting it requires\nexcluded-middle\, Simpson asserting it is classically Weak Kőnig Lemma\,\nHenkin that it is classi cally the Ultrafilter Theorem\, etc.).\n\nWe will survey these results\, s orting out the reasons for these\napparently inconsistent results\, eventu ally clarifying that\ncompleteness with respect to Tarski semantics over r ecursively\nenumerable theories intuitionistically requires:\n\n* a purely intuitionistic (unexpected) predicative form of the Weak\n Fan Theorem f or dealing with the underlying logical structure and\n the negative conne ctives\,\n* Markov's Principle for dealing with positive/additive falsity\ ,\n* a form of Double Negation Shift for dealing with positive disjunction .\n\nInterestingly\, Markov's Principle and Double Negation Shift are weak ly\nclassical principles which preserve the witness and disjunction\nprope rties\, and thus\, are in this sense "valid" intuitionistic\nprinciples. URL:https://chocola.ens-lyon.fr/events/meeting-2022-11-24/sessions/259/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulio Guerrieri - The theory of call-by-value solvability DTSTART:20221124T133000 DTEND:20221124T143000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-11-24/sessions/260/ CATEGORIES: DESCRIPTION:The semantics of the untyped (call-by-name) lambda-calculus is a\nwell developed field built around the concept of solvable terms\, whic h are\nelegantly characterized in many different ways. In particular\, uns olvable\nterms provide a consistent notion of meaningless term. The semant ics of the\nuntyped call-by-value lambda-calculus (CbV) is instead still i n its infancy\,\nbecause of some inherent difficulties but also because Cb V solvable terms are\nless studied and understood than in call-by-name. On the one hand\, we show\nthat a carefully crafted presentation of CbV allo ws us to recover many of the\nproperties that solvability has in call-by-n ame\, in particular qualitative and\nquantitative characterizations via mu lti types. On the other hand\, we stress\nthat\, in CbV\, solvability play s a different role: identifying unsolvable terms\nas meaningless induces a n inconsistent theory.\n\nThis is joint work with Beniamino Accattoli\, pu blished at ICFP 2022 \n[https://dl.acm.org/doi/10.1145/3547652](https://dl .acm.org/doi/10.1145/3547652) URL:https://chocola.ens-lyon.fr/events/meeting-2022-11-24/sessions/260/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniela Petrisan - Semialgebras and Weak Distributive Laws DTSTART:20221124T103000 DTEND:20221124T113000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-11-24/sessions/261/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/meeting-2022-11-24/sessions/261/ END:VEVENT BEGIN:VEVENT SUMMARY:accueil DTSTART:20221124T100000 DTEND:20221124T103000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-11-24/sessions/263/ CATEGORIES: URL:https://chocola.ens-lyon.fr/events/meeting-2022-11-24/sessions/263/ END:VEVENT BEGIN:VEVENT SUMMARY:Tito Nguyễn - A transducer model for simply typed λ-definable f unctions DTSTART:20221020T153000 DTEND:20221020T163000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-10-20/sessions/258/ CATEGORIES: DESCRIPTION:Among the natural ways to define functions ℕ^k → ℕ in th e simply typed λ-calculus\, one of them allows hyperexponential growth (a ny tower of exponentials) but excludes many basic functions such as subtra ction and equality\, as was discovered by Statman in the 1980s. Until now\ , this function class did not have any characterization not mentioning the λ-calculus. We provide the first one\, which more generally encompasses λ-definable tree-to-tree functions\, using an automata model: "collapsibl e pushdown transducers". As the name of our machines suggests\, we draw on the known connections between collapsible pushdown automata and simply ty ped λ-calculus with fixpoints\; in fact\, one might think of our results as being about recursion schemes parameterized by finite input trees. Othe r significant inspirations include: \n\n* Engelfriet et al.'s work on high er-order pushdown tree transducers\, which are included in our model while already being to our knowledge the most expressive transducer model in th e literature (polyregular functions\, macro tree transducers\, etc. define strict subclasses)\; \n\n* an old result of Plotkin\, recently made avail able thanks to Urzyczyn \n\n([https://arxiv.org/abs/2206.08413](https://ar xiv.org/abs/2206.08413))\, showing that the presence of fixpoints does not affect what total functions can be expressed.\n\nThis (unpublished) work is a sequel to my collaboration with Pierre Pradic (Swansea University) on "implicit automata".\n\n*NDLR: the talk will be given on the blackboard\, so it might be not so easy to follow at a distance\, given the available technology* URL:https://chocola.ens-lyon.fr/events/meeting-2022-10-20/sessions/258/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Baillon - Gardening with the Pythia\, A model of continuity in a dependent setting DTSTART:20221020T140000 DTEND:20221020T150000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-10-20/sessions/256/ CATEGORIES: DESCRIPTION:We generalize to a rich dependent type theory a proof original ly developed by Escardó that all System T functionals are continuous. It relies on the definition of a syntactic model of Baclofen Type Theory\, a type theory where dependent elimination must be strict\, into the Calculus of Inductive Constructions. \n\nThe model is given by three translations: the axiom translation\, that adds an oracle to the context\; the branchin g translation\, based on the dialogue monad\, turning every type into a tr ee\; and finally\, a layer of algebraic binary parametricity\, binding tog ether the two translations. In the resulting type theory\, every function f : (N → N) → N is externally continuous. URL:https://chocola.ens-lyon.fr/events/meeting-2022-10-20/sessions/256/ END:VEVENT BEGIN:VEVENT SUMMARY:Marie Fortin - FO = FO^3 for Linear Orders with Monotone Binary Re lations DTSTART:20221020T103000 DTEND:20221020T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-10-20/sessions/257/ CATEGORIES: DESCRIPTION:It is well-known that linear orders have the 3-variable proper ty\, meaning that over linear orders\, every monadic first-order formula w ith up to 3 free variables is equivalent to one that uses at most 3 variab les in total. This is usually shown through Ehrenfeucht–Fraïssé games\ , or as a corollary of the expressive completeness of linear temporal logi c (with Stavi connectives). Over the years\, this has been extended to ric her classes of structures\, such as the real line with the +1 relation\, M azurkiewicz traces\, or message sequence charts. In this talk\, I will pre sent a unifying proof that generalizes those facts. It is based on star-fr ee PDL\, a variant of propositional dynamic logic that is closely related to Tarski’s calculus of relations and captures precisely the 3-variable fragment of first-order logic. More precisely\, I will show that over stru ctures consisting of one linear order and arbitrarily many binary relation s satisfying some monotonicity conditions\, star-free PDL has the same exp ressive power as full first-order logic. This implies that any class of su ch structures has the 3-variable property. URL:https://chocola.ens-lyon.fr/events/meeting-2022-10-20/sessions/257/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudia Faggian - Bayesian Networks and Proof Nets: Curry-Howard m eets Bayes DTSTART:20220922T150000 DTEND:20220922T160000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-09-22/sessions/254/ CATEGORIES: DESCRIPTION:(joint work with Thomas Ehrhard and Michele Pagani )\n\nThis talk proposes a proof-theoretical account of Bayesian Inference\,\n by u ncovering a close correspondence between two graphical languages\,\n nam ely Bayesian Networks and Proof Nets. The former is a prominent\n graphi cal model for probabilistic reasoning. The latter is a graph\n formali sm for Linear Logic proofs and (via the Curry-Howard\n correspondence of proofs as programs) a powerful tool to analyze the\n dynamics of proof/ the execution of programs. Their natural\n interpretation into Probabili stic Coherence Spaces makes Proof Nets\n into probabilistic models.\n\nT he correspondence which we develop involves both the\n *representation* and the *computation* of a probabilistic model. In\n particular\, we rel ate the most widely used algorithm for exact\n inference (message passin g over clique trees) with the inductive\n interpretation of a proof\, op portunely factorized into a composition of\n smaller proofs. The corresp ondence turns out to be so tight\, that even\n the computational cost of inference is similar. We will also discuss\n some of the perspectives which proof theory could bring\, such as\n compositionality (via types) and structure (hierarchical models). URL:https://chocola.ens-lyon.fr/events/meeting-2022-09-22/sessions/254/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Geoffroy - A first-order completeness result about chara cteristic Boolean algebras in classical realizability DTSTART:20220922T140000 DTEND:20220922T150000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-09-22/sessions/255/ CATEGORIES: DESCRIPTION:We prove the following completeness result about classical\nre alizability: given any Boolean algebra with at least two\nelements\, there exists a Krivine-style classical realizability\nmodel whose characteristi c Boolean algebra is elementarily\nequivalent to it. This is done by contr olling precisely which\ncombinations of so-called “angelic” (or “may ”) and “demonic”\n(or “must”) nondeterminism exist in the underl ying model\nof computation. URL:https://chocola.ens-lyon.fr/events/meeting-2022-09-22/sessions/255/ END:VEVENT BEGIN:VEVENT SUMMARY:Romain Couillet - Pourquoi et comment démanteler l'IA et le numé rique? DTSTART:20220922T103000 DTEND:20220922T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-09-22/sessions/253/ CATEGORIES: DESCRIPTION:*(the talk will be given in french)*\n\nLa civilisation occide ntale est engagée depuis 10\,000 ans dans \nun processus technicien\, auj ourd'hui verrouillé par une ontologie \nnaturaliste (cette vision du mond e qui fait de la "nature" le grand \nsupermarché de l'humanité) qui entr aîne dans son sillon les dynamiques \nexponentielles des consumérisme\, extractivisme et colonialisme. La \nconséquence immédiate en est la dest ruction des écosystèmes (6e \nextinction de masse\, 30x plus rapide que l'extinction du Crétacé et \ns'accélérant) et le dérèglement des dyn amiques géophysiques planétaires \n(réchauffement\, déplétions minér ales). De gré ou de force (pic \npétrolier\, pénuries de ressources\, c hocs environnementaux et \nalimentaires)\, la société occidentale telle que nous la connaissons \ns'effondrera\, vraisemblablement au cours de not re génération. Les \ntechnologies numériques\, dont le point d'orgue es t l'intelligence \nartificielle (IA)\, contribuent tout à la fois à la d estruction \nsocio-environnementale mais surtout à la perte massive d'out ils de \nrésilience (interpénétration de tous les domaines techniques\, dépendance \nau pétrole\, dépendance aux machines\, dépendance aux d écisions \nautomatiques) en vue de la transition post-industrielle (retou r à la \nterre et à l'artisanat)\, comme l'illustre parfaitement le cas de Cuba en \n1990. \n\nDans cette présentation\, je ferai un état des li eux de la \nsituation du numérique et de l'IA\, vus par Alexandre Monnin comme des \ntechnologies "zombie" (vivantes aujourd'hui mais de fait déj à mortes)\, \net questionnerai les pistes de leur démantèlement nécess aire\, *de mon \npoint de vue un axe prioritaire de la recherche numériqu e aujourd'hui*. \nJ'évoquerai ensuite la question anthropologique de l'on tologie \nnaturaliste occidentale\, absolument unique dans l'histoire de \ nl'humanité\, et en conflit avec les connaissances ethnographiques\, de \ npsychologie sociale et cognitive modernes: en deux mots\, nous n'avons \n pas besoin d'un *nouveau* récit pour le monde\, mais de retisser les \nli ens animistes avec le vivant qui sont une partie intégrante de notre \nAD N\, aujourd'hui masquée par notre culture et nos tabous \nauto-destructeu rs. Ce travail *écopsychologique* est\, selon moi\, *la \nclé de voûte de l'engagement de tou·tes les chercheur·ses-ingénieur·es* vers la tra nsition nécessaire\, enthousiaste\, collective et \ninterspécifique que nous devons mener. URL:https://chocola.ens-lyon.fr/events/meeting-2022-09-22/sessions/253/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Blot - A direct computational interpretation of seco nd-order arithmetic via update recursion DTSTART:20220602T150000 DTEND:20220602T160000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-06-02/sessions/251/ CATEGORIES: DESCRIPTION:Second-order arithmetic has two kinds of computational interpr etations: \nvia Spector's bar recursion of via Girard's polymorphic lambda -calculus. \nBar recursion interprets the negative translation of the axio m of choice \nwhich\, combined with an interpretation of the negative tran slation of \nthe excluded middle\, gives a computational interpretation of the \nnegative translation of the axiom scheme of comprehension. It is th en \npossible to instantiate universally quantified sets with arbitrary \n formulas (second-order elimination). On the other hand\, polymorphic \nlam bda-calculus interprets directly second-order elimination by means of \npo lymorphic types. The present work aims at bridging the gap between \nthese two interpretations by interpreting directly second-order \nelimination t hrough update recursion\, which is a variant of bar recursion. URL:https://chocola.ens-lyon.fr/events/meeting-2022-06-02/sessions/251/ END:VEVENT BEGIN:VEVENT SUMMARY:Louise Dubois de Prisque - Sniper\, a general proof automation tac tic in Coq DTSTART:20220602T133000 DTEND:20220602T143000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-06-02/sessions/252/ CATEGORIES: DESCRIPTION:Sniper is a Coq plugin which provides a two steps general auto mation tactic\ncalled snipe. The first step consists of a modular combinat ion of small\ncertifying pre-processing transformations.\nEach of them tra nsforms a Coq goal in order to generate first-order statements.\nThen\, th e new generated goal is solved automatically by the second step\, which\nc alls external SMT solvers. In the current implementation of snipe\, we dea l with\nalgebraic datatypes\, uninterpreted functions\, prenex polymorphis m and different\nrepresentations of logic and integers. In this talk\, we will present the general\nmethodology of snipe and we will detail the tran sformation it uses. URL:https://chocola.ens-lyon.fr/events/meeting-2022-06-02/sessions/252/ END:VEVENT BEGIN:VEVENT SUMMARY:Yannick Forster - Synthetic Computability in Constructive Type The ory DTSTART:20220602T103000 DTEND:20220602T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-06-02/sessions/250/ CATEGORIES: DESCRIPTION:Mathematical practice in most areas of mathematics is based on the\n assumption that proofs could be made fully formal in a chosen\n foundation in principle. This assumption is backed by decades of\n form alising various areas of mathematics in various proof assistants\n and v arious foundations. An area that has been largely neglected for\n comput er-assisted and machine-checked proofs is computability theory.\n This i s due to the fact that making computability theory (and its\n sibling co mplexity theory) formal is several orders of magnitude more\n involved t han formalising other areas of mathematics\, due to the --\n citing Emil Post -- ``forbidding\, diverse and alien formalisms in which\n this [.. .] work of Gödel\, Church\, Turing\, Kleene\, Rosser [...] is\n embodie d.''. For instance\, there have been various approaches of\n formalising Turing machines\, all to the ultimate dissatisfaction of the\n respecti ve authors\, and none going further than constructing a\n universal mach ine and proving the halting problem undecidable.\n Professional computab ility theorist and teachers of computability\n theory thus rely on the i nformal Church Turing thesis to carry out\n their work and only argue th e computability of described algorithms\n informally.\n\nA way out was p roposed in the 1980s by Richman and developed during\n the last decade b y Bauer: Synthetic computability theory\, where one\n assumes axioms in a constructive foundation which essentially identify\n all (constructive ly definable) functions with computable functions. A\n drawback of the a pproach is that assuming such an axiom on top of the\n axiom of countabl e choice - which is routinely assumed in this branch\n of constructive m athematics and computable analysis - is that the law\n of excluded middl e\, i.e. classical logic\, becomes invalid.\n Computability theory is ho wever dedicatedly classical: Almost all basic\n results are presented by appeal to classical axioms and even the full\n axiom of choice.\n\n W e observe that a slight foundational shift rectifies the situation: By\n basing synthetic computability theory in the Calculus of Inductive\n Co nstructions\, the type theory underlying amongst others the Coq proof\n assistant\, where countable choice is independent and thus not provable\,\ n axioms for synthetic computability are compatible with the law of\n excluded middle.\n\n I will give an overview over a line of research inv estigating a\n synthetic approach to computability theory in constructiv e type theory\,\n discussing suitable axioms\, a Coq library of undecida bility proofs\,\n results in the theory of reducibility degrees\, a synt hetic definition\n of Kolmogorov complexity\, constructive reverse analy sis of theorems\,\n and work-in-progress on synthetic oracle computabili ty.\n\n Parts of results are in collaboration with Dominik Kirst\, Gert Smolka\,\n Felix Jahn\, Fabian Kunze\, Nils Lauermann\, Niklas Mück\, a nd the\n contributors of the Coq Library of Undecidability Proofs. URL:https://chocola.ens-lyon.fr/events/meeting-2022-06-02/sessions/250/ END:VEVENT BEGIN:VEVENT SUMMARY:Farzad Jafarrahmani - Linear logic with fixpoints from a Curry-How ard perspective. DTSTART:20220505T153000 DTEND:20220505T163000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-05-05/sessions/249/ CATEGORIES: DESCRIPTION:I first\, briefly\, present the syntax of MuLL which is an\n extension of David Baelde’s MuMALL (multiplicative and additive linear\ n logic with least and greatest fixpoints) with exponentials. Then we\n will study the categorical model of Mu LL and provide two concrete\n m odels of MuLL based and REL (sets and and relation) and NUTS (non\n unif orm totality spaces) which are sets equipped with a notion of\n totality and a relation preserving it. Then we will study a polarized\n version of muLL\, and will try to develop a calculus based on this\n polarized v ersion\, called mu LLP. We equip this language with a\n deterministic re duction semantics as well as a denotational semantics\n based on NUTS. F inally\, We prove an adequacy result between these\n operational and den otational semantics\, from which we derive a\n normalization property fo r mu LLP thanks to the properties of the\n totality interpretation.\n\n This presentation is based on joint work with Thomas Ehrhard and Alexis\ n Saurin. URL:https://chocola.ens-lyon.fr/events/meeting-2022-05-05/sessions/249/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathanaëlle Courant - Testing convertibility in parallel DTSTART:20220505T140000 DTEND:20220505T150000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-05-05/sessions/247/ CATEGORIES: DESCRIPTION:In this talk\, I will present a machine for testing the conver tibility of \nlambda-terms. This machine is based on implementations of st rong \ncall-by-need evaluation\, and is able to exploit that convertibilit y is \nclosed by context: to prove that `f x` is convertible with `f y` wh en \n`f` is a constant\, it it enough to prove that `x` and `y` are \nconv ertible. However\, it is sometimes more efficient to unfold `f` to \nprove convertibility\, for instance if it does not use its argument. Our \nmach ine solves both convertibility problems in parallel while sharing \ncomput ations\, and stops as soon as it is able to conclude about the \ninitial p roblem. URL:https://chocola.ens-lyon.fr/events/meeting-2022-05-05/sessions/247/ END:VEVENT BEGIN:VEVENT SUMMARY:Gianluca Curzi - Cyclic implicit complexity DTSTART:20220505T103000 DTEND:20220505T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-05-05/sessions/248/ CATEGORIES: DESCRIPTION:Circular (or cyclic) proofs have received increasing\n atten tion in recent years\, and have been proposed as an alternative\n settin g for studying (co)inductive reasoning. In particular\,\n now several ty pe systems based on circular reasoning have\n been proposed. However\, l ittle is known about the complexity theoretic\n aspects of circular proo fs\, which exhibit sophisticated loop structures\n atypical of more comm on ‘recursion schemes’. This talk attempts to\n bridge the gap betwe en circular proofs and implicit computational\n complexity (ICC). Namely we introduce a circular proof system based on\n Bellantoni and Cook’s famous safe-normal function algebra\, and we\n identify proof theoretic al constraints\, inspired by ICC\, to\n characterise the polynomial-time and elementary computable\n functions. Along the way we introduce new r ecursion theoretic\n implicit characterisations of these classes that ma y be of interest\n in their own right. Finally\, we study non-wellfounde d proof systems to\n capture non-uniform complexity classes such as P/po ly. URL:https://chocola.ens-lyon.fr/events/meeting-2022-05-05/sessions/248/ END:VEVENT BEGIN:VEVENT SUMMARY:Federico Olimpieri - Categorifying graph models of lambda calculus DTSTART:20220331T153000 DTEND:20220331T163000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-03-31/sessions/246/ CATEGORIES: DESCRIPTION:We study a family of distributor-induced bicategorical\n mod els of lambda-calculus\, proving that they can be syntactically\n presen ted via intersection type systems. In this framework we define a\n proo f-relevant semantics: the interpretation of a term associates to it\n th e set of its typing derivations in appropriate systems. We then\n restr ict to a particular case of our construction and show that the\n interpr etation of a program corresponds to the interpretation of its\n Böhm tr ee. We prove this result exploiting the proof-relevance of our\n model\, which allows a fine-grained analysis of programs evaluation. We\n then obtain the characterization of the theory induced by the\n bicategorical model: two lambda-terms share the same interpretation\n exactly when th eir Bohm trees coincide. URL:https://chocola.ens-lyon.fr/events/meeting-2022-03-31/sessions/246/ END:VEVENT BEGIN:VEVENT SUMMARY:Abhishek De - Provability of linear logic with fixed points DTSTART:20220331T140000 DTEND:20220331T150000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-03-31/sessions/245/ CATEGORIES: DESCRIPTION:Fixed point logics are logics enriched with one or more fixed point\noperators. There are several motivations for investigating fixed po int logics\nfrom the study of algebraic structures\n(like Kleene lattices) to the study of (co)inductive type systems. In this talk\,\nI will give a brief overview of fixed point logics and concentrate specifically\non lin ear logic with fixed points\ndiscussing various proof systems\, their expr essivity\, and truth semantics. URL:https://chocola.ens-lyon.fr/events/meeting-2022-03-31/sessions/245/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristina Matache - A unified treatment of concrete sheaf models fo r higher-order recursion DTSTART:20220331T103000 DTEND:20220331T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-03-31/sessions/244/ CATEGORIES: DESCRIPTION:In this talk I will discuss how to build models of\n program ming languages using monads on categories of sheaves.\n The goal of the talk is to explain how several well-known models from\n different applic ation domains\,\n such as probability\, differentiability and full abstr action\, are\n instances of the same general framework.\n\n I will exp lain what sheaves are and how in all these models partiality\n and recur sion are treated uniformly\n using ideas from synthetic domain theory.\n \n The talk is based on joint work with Sean Moss and Sam Staton. URL:https://chocola.ens-lyon.fr/events/meeting-2022-03-31/sessions/244/ END:VEVENT BEGIN:VEVENT SUMMARY:Marie Kerjean - ∂ is for Dialectica DTSTART:20220310T153000 DTEND:20220310T163000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-03-10/sessions/243/ CATEGORIES: DESCRIPTION:*[The talk will take place in amphi A\, 3rd & 4th floors\, at the other end of the corridor w.r.t. amphi B\, if you know where this is.] *\n\nDialectica is a proof transformation acting of intuitionnistic logic \nwhich factors through Girard's translation\, allowing the realization of \nseveral semi-classical axioms such as Markov's principle. By taking the \nviewpoint of differential lambda-calculus and recent developments in \n differentiable programming\, we will show how Dialectica computes \nhigher -order backward differentiation. We will illustrate this through \nthe len s of categories\, types and lambda-terms.\n\n This is joint work with \nPi erre-Marie Pédrot. URL:https://chocola.ens-lyon.fr/events/meeting-2022-03-10/sessions/243/ END:VEVENT BEGIN:VEVENT SUMMARY:Loïc Pujet - Extensionality in intensional type theory DTSTART:20220310T140000 DTEND:20220310T150000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-03-10/sessions/242/ CATEGORIES: DESCRIPTION:*[The talk will take place in amphi A\, 3rd & 4th floors\, at the other end of the corridor w.r.t. amphi B\, if you know where this is.] *\n\nMartin-Löf Type Theory is a sweet spot in the correspondence between \nproofs and programs: dependent types and inductive types allow for \nre markably expressive program specifications\, and adding a universe \nhiera rchy results in a theory with enough logical power to encode most \nday-to -day mathematical constructions -- an all-around foundational tool \nfor p roof assistants.\n\nHowever the inductive equality supplied by MLTT is not quite suitable \nfor mathematical reasoning\, because it encodes program equality \n("intensionality") instead of behavioral equality ("extensional ity"). \nThis has unfortunate consequences: one cannot prove that the func tions n \n-> n+2 and n -> 2+n are equal\, there is no way to quotient a ty pe by an \nequivalence relation\, etc.\n\nObservational Type Theory was de signed to remediate to this very state \nof affairs. A complete implementa tion of OTT would feature these desired \nextensionality principles\, whil e preserving the philosophy of the \ncorrespondence between proofs and pro grams and the nice properties that \ncome with it (normalization\, canonic ity\, decidability of typing...).\n\nIn my talk\, after some preliminary e xposition about dependent types\, I \nwill introduce TT^obs\, a conceptual ly simple extension of Martin-Löf \nType Theory that turns it into a full y observational type theory. I will \nillustrate with some use cases\, and if time allows I will go over its \nmeta-theory. URL:https://chocola.ens-lyon.fr/events/meeting-2022-03-10/sessions/242/ END:VEVENT BEGIN:VEVENT SUMMARY:Denis Kuperberg - Positive First-order Logic on Words and Graphs DTSTART:20220310T103000 DTEND:20220310T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-03-10/sessions/241/ CATEGORIES: DESCRIPTION:*[The talk will take place in room M7 411\, 4th floor\, turn l eft when you exit the elevator.]*\n\nWe will investigate the gap between s yntactically and semantically\n positive first-order logic formulas.\n\n A formula is syntactically positive if it does not contain negated\n predicates\, while it is semantically positive when the class of\n struc tures it defines is monotone\, i.e. closed under making the\n predicates true on more tuples.\n\n Starting with finite words\, I will present th e logic FO+\, where letter\n predicates are required to appear positivel y. The words considered here\n are on a "powerset alphabet": predicates a(x) and b(x) can be true\n simultaneously on the same position x of the word. We will ask a syntax\n versus semantics question: FO+-definable l anguages are monotone in the\n letters\, but can every FO-definable mono tone language be expressed in\n FO+ ? On general structures\, Lyndon's t heorem gives a positive answer\n to this question\, but it is known to f ail on finite structures. We will\n see that it already fails on finite words\, by giving a simple\n counter-example language. This gives a new proof for the failure of\n Lyndon's theorem on finite structures\, that is much more elementary\n than previous proofs.\n\n We will also study the problem on finite graphs: if a class of finite\n graphs is FO-defin able and closed under edge addition\, can it be\n defined with a negatio n-free formula ? To our knowledge this was an\n open question\, which we can answer negatively via a suitable encoding\n of our counter-example language.\n\n Finally\, if time permits\, we will go back to regular lan guages of\n finite words and see that FO+-definability is surprisingly u ndecidable\n in this framework.\n\n This talk is based on work publish ed in LICS 2021\, with a full version\n currently submitted to a special issue of LMCS\, available [on Arxiv](https://arxiv.org/abs/2201.11619). URL:https://chocola.ens-lyon.fr/events/meeting-2022-03-10/sessions/241/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Dinis - Functional interpretations and applications DTSTART:20220120T101500 DTEND:20220120T113000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/meeting-2022-01-20/sessions/240/ CATEGORIES: DESCRIPTION:Functional interpretations are maps of formulas from the langu age of\n one theory into the language of another theory\, in such a way that\n provability is preserved. These interpretations typically replace \n logical relations by functional relations. Functional interpretations \n have many uses\, such as relative consistency results\, conservation\ n results\, and extraction of computational content from proofs as is th e\n case in the so-called proof mining program.\n\n I will present sev eral recent functional interpretations and some\n results that come from these interpretations. I will also give examples\n of application of fu nctional interpretations\, in the spirit of the\n proof mining program. URL:https://chocola.ens-lyon.fr/events/meeting-2022-01-20/sessions/240/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Gavazzo - A Relational Theory of Effects and Coeffects DTSTART:20211202T153000 DTEND:20211202T163000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2021-12-02/sessions/239/ CATEGORIES: DESCRIPTION:Graded modal types systems and coeffects are becoming a standa rd\n formalism to deal with context-dependent\, usage-sensitive computat ions\,\n especially when combined with computational effects. From a sem antic\n perspective\, effectful and coeffectful languages have been stud ied\n mostly by means of denotational semantics and almost nothing has b een\n done from the point of view of relational reasoning. This is quite \n surprising since many cornerstone results — such as non-interferenc e\n and metric preservation — on concrete coeffects are inherently\n relational. In this talk\, I will present a general theory and calculus\n of program relations for higher-order languages with combined effects\n and coeffects. The calculus builds upon classic relational notions to\n deal with effectful and higher-order features\, and upon the novel\n notion of a corelator (or comonadic lax extension) to handle coeffects\,\n relationally. I will show how the aforementioned relational theory\n provides a unifying framework for defining and studying the metatheory\n of the main notions of program equivalence and refinement\, such as\n c ontextual and logical equivalence and approximation\, and applicative\n (bi)similarity. As a main result\, I will present a general congruence\n theorem showing how simple relational properties ensure congruence\n pr operties of a large family of effectful and coffectful program\n equival ences. URL:https://chocola.ens-lyon.fr/events/seminaire-2021-12-02/sessions/239/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Silva - Concurrent NetKAT: Modeling and analyzing statef ul\, concurrent networks DTSTART:20211202T140000 DTEND:20211202T150000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2021-12-02/sessions/237/ CATEGORIES: DESCRIPTION:We introduce Concurrent NetKAT (CNetKAT)\, an extension of the network programming language NetKAT with multiple packets and with operat ors to specify and reason about concurrency and state in a network. We pro vide a model of the language based on partially ordered multisets\, well-e stablished mathematical structures in the denotational semantics of concur rent languages. We prove that CNetKAT is a sound and complete axiomatizat ion of this model\, and we illustrate the use of CNetKAT through various e xamples. More generally\, CNetKAT is an algebraic framework to reason abou t programs with both local and global state. In our model these are\, resp ectively\, the packets and the global variable store\, but the scope of ap plications is much more general\, including reasoning about hardware pipel ines inside an SDN switch.\n\nThis is joint work with Jana Wagemaker\, Nat e Foster\, Tobias Kappe\, Dexter Kozen\, and Jurriaan Rot. URL:https://chocola.ens-lyon.fr/events/seminaire-2021-12-02/sessions/237/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Reggio - Game comonads: towards an axiomatic theory of resour ces DTSTART:20211202T103000 DTEND:20211202T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2021-12-02/sessions/238/ CATEGORIES: DESCRIPTION:Game comonads\, introduced by Abramsky\, Dawar et al. in 2017\ , provide a categorical approach to finite model theory. A basic instance of this fremework allows to recover\, in a purely syntax-free way\, the fo llowing ingredients: the Ehrenfeucht-Fraïssé game\, fragments of first-o rder logic with bounded quantifier rank (and variations thereof)\, and the combinatorial parameter of tree-depth. Other instances cover\, e.g.\, k-p ebble games and bisimulation games\, and the corresponding logic fragments and combinatorial parameters.\n\nAfter an introduction to game comonads\, I shall present an axiomatic framework which captures the essential commo n features of these constructions. This is based on the notion of arboreal cover\, a resource-indexed family of adjunctions with some `process categ ory' - which unfolds relational structures into treelike forms\, allowing resource parameters to be assigned to these unfoldings. Beyond this basic level\, a landscape is beginning to emerge\, in which structural features of the resource categories and comonads are reflected in degrees of tracta bility of the corresponding logic fragments.\n\nI will then discuss an app lication of game comonads to homomorphism counting results in finite model theory. The prototypical homomorphism counting result is Lovasz' theorem (1967)\, stating that graphs A and B are isomorphic if and only if\, for e very graph C\, the number of homomorphisms from C to A is the same as the number of homomorphisms from C to B. Game comonads yield uniform proofs of Lovasz' theorem and more recent results of Dvorak (2010) and Grohe (2020) \, as well as a novel homomorphism counting result in modal logic. URL:https://chocola.ens-lyon.fr/events/seminaire-2021-12-02/sessions/238/ END:VEVENT BEGIN:VEVENT SUMMARY:Armaël Guéneau - Program verification on a capability machine in the presence of untrusted code DTSTART:20211022T101500 DTEND:20211022T114500 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-10-22/sessions/236/ CATEGORIES: DESCRIPTION:A capability machine is a kind of CPU with hardware support fo r\n fine-grained\n privilege separation. Practical designs and prototy pes for such\n machines are\n seeing recent development as part of the CHERI project (University of\n Cambridge\,\n SRI\, ARM) (cheri-cpu.or g\, morello-project.org)\, making capability\n machines a\n promising target for designing and building new software with security\n in mind.\ n In this talk\, I will present some of the work done at Aarhus Universi ty\n and KU\n Leuven on developing formal principles for reasoning abo ut security\n properties\n of code running on capability machines.\n I will show how one can prove functional correctness of programs that\n interact\n with untrusted (and possibly malicious) code while leveragin g\n capabilities to\n protect their private state. The key aspects of this methodology are a\n program\n logic for reasoning about known cod e\, and a logical relation providing\n a\n /universal contract/ of unk nown code.\n\n The whole work has been mechanized in Coq using the Iris framework. URL:https://chocola.ens-lyon.fr/events/online-2021-10-22/sessions/236/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Varacca - Milner and Alur walk into a bar DTSTART:20210701T100000 DTEND:20210701T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-07-01/sessions/234/ CATEGORIES: DESCRIPTION:The chef kicks them out: "I'm sorry\, in my kitchen we only us e\ninduction"\n\nThis talk will start from Morris' PhD thesis in 1968 and present 50\nyears of theoretical computer science\, through PCF\, CCS\, Al ternating\ntransition systems\, contexts and strategies\, ending up at the footsteps\nof the monumental Palace of Justice in Créteil. URL:https://chocola.ens-lyon.fr/events/online-2021-07-01/sessions/234/ END:VEVENT BEGIN:VEVENT SUMMARY:Sonia Marin - Focused nested calculi applied to the logic of bunch ed implications DTSTART:20210617T100000 DTEND:20210617T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-06-17/sessions/235/ CATEGORIES: DESCRIPTION:Focusing is a general technique for syntactically compartmenta lising the non-deterministic choices in a proof system\, which not only im proves proof search but also has the representational benefit of distillin g sequent proofs into synthetic normal forms. However\, since focusing was traditionally specified as a restriction of the sequent calculus\, the te chnique had not been transferred to logics that lack a (shallow) sequent p resentation\, as is the case for some modal or substructural logics.\n\nWi th K. Chaudhuri and L. Straßburger\, we extended the focusing technique t o nested sequents\, a generalisation of ordinary sequents which allows us to capture all the logics of the classical and intuitionistic S5 cube in a modular fashion. This relied\, following the method introduced by O. Laur ent\, on an adequate polarisation of the syntax and an internal cut-elimin ation procedure for the focused system which in turn is used to show its c ompleteness.\n\nRecently\, with A. Gheorghiu\, we applied a similar method to the logic of Bunched Implications (BI)\, a logic that freely combines intuitionistic logic and multiplicative linear logic. For this we had firs t to reformulate the traditional bunched calculus for BI using nested sequ ents\, followed by a polarised and focused variant that (again) we show is sound and complete via a cut-elimination argument. URL:https://chocola.ens-lyon.fr/events/online-2021-06-17/sessions/235/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlo Angiuli - Internalizing Representation Independence with Uni valence DTSTART:20210603T150000 DTEND:20210603T170000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-06-03/sessions/233/ CATEGORIES: DESCRIPTION:In their usual form\, representation independence metatheorems provide an external guarantee that two implementations of an abstract int erface are interchangeable when they are related by an operation-preservin g correspondence. In the dependently-typed setting\, however\, we would li ke to appeal to such invariance results within a language itself\, in orde r to transfer theorems from simple to complex implementations. Homotopy ty pe theorists have noted that Voevodsky's univalence principle equates isom orphic structures\, but unfortunately many instances of representation ind ependence are not isomorphisms.\n\nIn this talk\, we describe a technique for establishing internal relational representation independence results i n Cubical Agda by using higher inductive types to simultaneously quotient two related implementation types by a heterogeneous correspondence between them. The correspondence becomes an isomorphism between the quotiented ty pes\, thereby allowing us to obtain an equality of implementations by univ alence. Joint work with Evan Cavallo\, Anders Mörtberg\, and Max Zeuner. Available at https://dl.acm.org/doi/10.1145/3434293. URL:https://chocola.ens-lyon.fr/events/online-2021-06-03/sessions/233/ END:VEVENT BEGIN:VEVENT SUMMARY:Valeria Vignudelli - Monads\, equational theories\, and metrics fo r nondeterministic and probabilistic systems DTSTART:20210520T100000 DTEND:20210520T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-05-20/sessions/232/ CATEGORIES: DESCRIPTION:Monads and their presentations via equational theories provide a tool for reasoning about programs with computational effects. In recent works\, we have studied monads resulting from the combination of nondeter minism\, probabilities\, and termination\, as well as their extensions to the category of metric spaces.\nIn this talk\, we'll introduce this framew ork and show applications to proving equivalences and distances of nondete rministic and probabilistic systems.\n\nBibliography:\n\nBonchi\, Sokolova \, Vignudelli. The theory of traces for systems with nondeterminism and pr obabilities. LICS 2019. Available at: https://arxiv.org/abs/1808.00923\n\n Mio\, Vignudelli. Monads and quantitative equational theories for nondeter minism and probabilities. CONCUR 2020. Available at: https://arxiv.org/abs /2005.07509\n\nMio\, Sarkis\, Vignudelli. Combining nondeterminism\, proba bility\, and termination: equational and metric reasoning. LICS 2021. Avai lable at: https://arxiv.org/abs/2012.00382 URL:https://chocola.ens-lyon.fr/events/online-2021-05-20/sessions/232/ END:VEVENT BEGIN:VEVENT SUMMARY:Barbara König - Fixpoint Theory -- Upside Down DTSTART:20210506T100000 DTEND:20210506T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-05-06/sessions/231/ CATEGORIES: DESCRIPTION:Knaster-Tarski's theorem\, characterising the greatest fixpoin t of a\nmonotone function over a complete lattice as the largest post-fixp oint\,\nnaturally leads to the so-called coinduction proof principle for s howing\nthat some element is below the greatest fixpoint (e.g.\, for provi ding\nbisimilarity witnesses). The dual principle\, used for showing that an\nelement is above the least fixpoint\, is related to inductive invarian ts.\nThis talks considers proof rules which are similar in spirit but for\ nshowing that an element is above the greatest fixpoint or\, dually\, belo w\nthe least fixpoint.\n\nThe theory is developed for non-expansive monoto ne functions on suitable\nlattices of the form M^Y\, where Y is a finite s et and M an MV-algebra\,\nand it is based on the construction of (finitary ) approximations of the\noriginal functions. We show that our theory appl ies to a wide range of\nexamples\, including termination probabilities\, b ehavioural distances for\nprobabilistic automata and bisimilarity. Moreove r it allows us to\ndetermine original algorithms for solving simple stocha stic games. URL:https://chocola.ens-lyon.fr/events/online-2021-05-06/sessions/231/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriele Vanoni - The Time and Space of Interaction DTSTART:20210422T100000 DTEND:20210422T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-04-22/sessions/230/ CATEGORIES: DESCRIPTION:Girard's Geometry of Interaction (GOI) can be made concrete by \nconsidering it as an implementation technique for functional programs\,\ nin particular the lambda calculus. Our work is about the complexity\nanal ysis of the abstract machine based on the GOI\, the interaction\nabstract machine (IAM). We have adapted in a non trivial way de\nCarvalho's non ide mpotent intersection types so that type derivations\ncompletely characteri ze the time and space complexity of the IAM\, thus\nproviding a logical ac count of the IAM resource usage. Moreover\, by\nthe way of the type system s we have introduced\, we are able to state\nsome negative results about t ime and space cost models for the lambda\ncalculus based on the IAM.\nThis is joint work with Beniamino Accattoli and Ugo Dal Lago. URL:https://chocola.ens-lyon.fr/events/online-2021-04-22/sessions/230/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Gratzer - Sketching type theories DTSTART:20210408T100000 DTEND:20210408T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-03-25/sessions/229/ CATEGORIES: DESCRIPTION:Recent developments in type theory have attempted to systemati cally recast properties of the syntax of a type theories (canonicity\, nor malization\, etc.) into equivalent questions about the category of models. This dictionary relies on a formal link between the syntax of a theory an d its category of models: the syntax of the theory must organize into an i nitial model. To expedite this process\, several logical frameworks have b een proposed which provide schemata for defining a type theory so that it automatically determines a category of models in which syntax is initial.\ n\nIn this talk\, rather than giving a new logical framework per se\, we p ropose a new discipline for creating logical frameworks based around finit ary 2-monads and sketches. As a case study of this approach\, we show how locally Cartesian closed categories provide a suitable doctrine for type t heories. We illustrate how a general theory of sketches [KPT99] can be use d to define syntactic categories for type theories in a style that resembl es the use of Martin-Löf's Logical Framework [NPS90]\, following the "jud gments as types" principle [HHP93\, ML87].\n\nWe prove a semantic adequacy result for locally Cartesian closed categories relative to Uemura's repre sentable map categories [Uem19]: if a theory is definable in the framework of Uemura\, the locally Cartesian closed category that it generates is a conservative (fully faithful) extension of its syntactic representable map category. On this basis\, we argue for the use of locally Cartesian close d categories as a simpler alternative to Uemura's representable map catego ries.\n\nThis is joint work with Jonathan Sterling\, and a preprint is ava ilable on arxiv: https://arxiv.org/abs/2012.10783 URL:https://chocola.ens-lyon.fr/events/online-2021-03-25/sessions/229/ END:VEVENT BEGIN:VEVENT SUMMARY:Assia Mahboubi - Machine-Checked Computer-Aided Mathematics DTSTART:20210311T100000 DTEND:20210311T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2021-03-11/sessions/228/ CATEGORIES: DESCRIPTION:This talk presents an overview of three contributions to the f ormal\nverification of mathematics in dependent type theory. The first of these contributions deals with the realization of a library of digitized m athematics\, covering the standard undergraduate background in algebra as well as some more advanced chapters in finite group theory. The two other contributions are related to the issues\npertaining to the formal verifica tion of computational mathematical\nproofs\, by the means of symbolic algo rithms and of rigorous numerical methods\nrespectively. We conclude with a few perspectives on the formal\nverification of computer-aided mathematic s. URL:https://chocola.ens-lyon.fr/events/seminaire-2021-03-11/sessions/228/ END:VEVENT BEGIN:VEVENT SUMMARY:Zeinab Galal - Stable Species of Structures DTSTART:20210225T100000 DTEND:20210225T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-02-25/sessions/227/ CATEGORIES: DESCRIPTION:In this talk\, I will present a new stable model of classical linear\nlogic based on groupoids and profunctors between them. It can be s een as\na refinement of the model of generalized species of structures\nin troduced by Fiore et al.\nThis refinement is based on an orthogonality on subgroups of\nendomorphisms for each object in a groupoid and it can also be\ntranslated to an orthogonality on the category of presheaves associate d\nwith a groupoid. The resulting bicategory is a model of differential\nl inear logic where the functors in the cartesian closed Kleisli\nbicategory are precisely those satisfying a stability condition as\nstudied by Berry \, Girard\, Taylor and many others. This is joint work\nwith Marcelo Fiore and Hugo Paquet. URL:https://chocola.ens-lyon.fr/events/online-2021-02-25/sessions/227/ END:VEVENT BEGIN:VEVENT SUMMARY:Enguerrand Prebet - Sequentiality\, References and Well-bracketing in the pi-calculus DTSTART:20210211T100000 DTEND:20210211T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-02-11/sessions/226/ CATEGORIES: DESCRIPTION:The pi-calculus is used as a model for programming languages.\ nIts contexts exhibit arbitrary concurrency\, making them very\ndiscrimina ting. This may prevent validating desirable behavioural\nequivalences in c ases when more disciplined contexts are expected.\nWe formalise using type s three different disciplines: sequentiality or\nthe idea of having a sing le thread of computation \; reference types for\nwhich channels behave lik e bits of store or atomic register \; and\nwell-bracketing which strengthe ns the sequentiality constraints to also\nobey a stack-like discipline. Fo r each\, we present the type system along\nwith its consequences on behavi oural equivalence and the corresponding\nbisimulation techniques. URL:https://chocola.ens-lyon.fr/events/online-2021-02-11/sessions/226/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoît Montagu - Stable Relations and Abstract Interpretation of Higher-Order Programs DTSTART:20210128T100000 DTEND:20210128T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2021-01-28/sessions/225/ CATEGORIES: DESCRIPTION:We present a novel denotational semantics for the untyped call -by-value\nλ-calculus\, where terms are interpreted as stable relations\, i.e. as\nbinary relations between substitutions and values\, enjoying a\n monotonicity property. The denotation captures the input-output\nbehaviour of higher-order programs\, and is proved sound and complete\nwith respect to the operational semantics. Following the principles of\nabstract inter pretation\, we use our denotational semantics as a\ncollecting semantics t o derive a modular relational analysis for\nhigher-order programs. The ana lysis infers equalities between the\narguments of a program and its result s---a form of frame condition for\nfunctional programs. URL:https://chocola.ens-lyon.fr/events/online-2021-01-28/sessions/225/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulio Manzonetto - About the power of Taylor expansion DTSTART:20210114T100000 DTEND:20210114T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/seminaire-2021-01-14/sessions/224/ CATEGORIES: DESCRIPTION:The speculative ambition of replacing the old theory of progra m\napproximation based on syntactic continuity with the theory of\nresourc e consumption based on Taylor expansion and originating from\nthe differen tial lambda-calculus is nowadays at hand. Using this\nresource sensitive t heory\, we provide simple proofs of important\nresults in lambda-calculus that are usually demonstrated by exploiting\nScott's continuity\, Berry's stability or Kahn and Plotkin's\nsequentiality theory.\n\nA paradigmatic e xample is given by the Perpendicular Lines Lemma for\nthe Böhm tree seman tics\, which is proved here simply by induction\, but\nrelying on the main properties of resource approximants: strong\nnormalization\, confluence a nd linearity. URL:https://chocola.ens-lyon.fr/events/seminaire-2021-01-14/sessions/224/ END:VEVENT BEGIN:VEVENT SUMMARY:Jérémie Koenig - Refinement-Based Game Semantics for Certified C omponents DTSTART:20201217T150000 DTEND:20201217T170000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2020-12-17/sessions/223/ CATEGORIES: DESCRIPTION:Current practices ensure software reliability through careful testing\, but while testing can reveal the presence of bugs\, it cannot en tirely guarantee their absence. By contrast\, certified systems come with a formal specification and a computer-checked proof of correctness\, provi ding strong evidence that the system behaves as expected in all possible s cenarios. Over the past decade\, researchers have been able to build certi fied systems of significant size and complexity\, including compilers\, pr ocessor designs\, operating system kernels and more.\nBuilding on these su ccesses\, the DeepSpec project seeks to assemble them as certified compone nts to build large-scale heterogeneous certified systems. However\, by nec essity\, these certified components use a broad variety of semantic models and verification techniques. To connect them\, we must first embed them i nto a common\, general-purpose model.\nThe work I will present proposes to combine game semantics\, algebraic effects and the refinement calculus to build models suitable for this task. In particular\, certified abstractio n layers and the certified compiler CompCert can be embedded into a single framework supporting heterogeneous components\, stepwise refinement\, and data abstraction. URL:https://chocola.ens-lyon.fr/events/online-2020-12-17/sessions/223/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Blanco - Bifibrations of polycategories and classical line ar logic DTSTART:20201203T100000 DTEND:20201203T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2020-12-03/sessions/221/ CATEGORIES: DESCRIPTION:In this talk we will explore four different ways of interpreti ng classical multiplicative linear logic categorically: as a *-autonomous category where the connectives are given by structures\, as a *-representa ble polycategory where the connectives are expressed through universal pro perties\, as a bifibred polycategory where the connectives are recovered b y fibrational properties and as a Frobenius pseudomonoid internal to a pol ycategory where the connectives are defined by internal operations. We wil l relate these approaches through different correspondences.\nFirst we wil l see that *-representable polycategories are unbiased alternatives to the two-tensor polycategories with duals that have been introduced by Cockett and Seely and that has been proven to be equivalent to *-autonomous categ ories. Then we will see that bifibred polycategories generalise those in t he sense that a polycategory is *-representable iff it is bifibred over th e terminal polycategory. Finally\, we will present a polycategorical Groth endieck correspondence between bifibrations of polycategories and pseudofu nctors into MAdj\, the 2-polycategory of multivariable adjunctions. When r estricted to bifibrations over the terminal polycategory we get back the c orrespondence between *-autonomous categories and Frobenius pseudomonoids in MAdj that was recently observed by Mike Shulman.\nIf time permits we wi ll also look at some refinements of *-autonomous categories by considering bifibred polycategories over a representable polycategory other than the terminal one. URL:https://chocola.ens-lyon.fr/events/online-2020-12-03/sessions/221/ END:VEVENT BEGIN:VEVENT SUMMARY:Paolo Pistone - The Yoneda Reduction of Polymorphic Types DTSTART:20201119T100000 DTEND:20201119T120000 DTSTAMP:20260612T104320Z UID:https://chocola.ens-lyon.fr/events/online-2020-11-09/sessions/222/ CATEGORIES: DESCRIPTION:We explore a family of type isomorphisms in System F whose val idity corresponds\, semantically\, to some form of the Yoneda isomorphism from category theory. These isomorphisms hold under theories of equivalenc e stronger than βη-equivalence\, like those induced by parametricity and dinaturality. Based on such isomorphisms\, we investigate a rewriting ove r types\, that we call Yoneda reduction\, which can be used to eliminate q uantifiers from a polymorphic type\, replacing them with a combination of monomorphic type constructors. We then demonstrate some applications of th is rewriting to problems like counting the inhabitants of a type or charac terizing program equivalence in some fragments of System F. URL:https://chocola.ens-lyon.fr/events/online-2020-11-09/sessions/222/ END:VEVENT BEGIN:VEVENT SUMMARY:Delia Kesner - The bang calculus\, revisited DTSTART:20200625T101500 DTEND:20200625T111500 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2020-06-25/sessions/220/ CATEGORIES: DESCRIPTION:Call-by-Push-Value (CBPV) is a programming paradigm subsuming both\nCall-by-Name (CBN) and Call-by-Value (CBV) semantics. The paradigm w as\nrecently modelled by means of the Bang Calculus\, a term language\ncon necting CBPV and Linear Logic.\n\nThis talk presents a revisited version o f the Bang Calculus\, called\nlambda!\, enjoying some important properties missing in the original\nsystem. Indeed\, the new calculus integrates co mmutative conversions\nto unblock value redexes while being confluent at t he same time. A\nsecond contribution is related to non-idempotent types. W e provide a\nquantitative type system for the lambda!-calculus\, and we sh ow that\nthe length of the (weak) reduction of a typed term to its normal\ nform plus} the size of this normal form is bounded by the size\nof its ty pe derivation. We also explore the properties of this type\nsystem with r espect to CBN/CBV translations. We keep the original CBN\ntranslation from lambda-calculus to the Bang Calculus\, which\npreserves normal forms and is sound and complete with respect to the\n(quantitative) type system for CBN. However\, in the case of CBV\, we\nreformulate both the translation and the type system to restore two\nmain properties: preservation of norma l forms and completeness. Last\nbut not least\, the quantitative system is refined to a tight\none\, which transforms the previous upper bound on th e length of\nreduction to normal form plus its size into two\nindependent exact measures for them. \n \n \n(joint work with A. Bucciarelli\, A. Rios and A. Viso) URL:https://chocola.ens-lyon.fr/events/meeting-2020-06-25/sessions/220/ END:VEVENT BEGIN:VEVENT SUMMARY:Cyrille Chenavier - Topological rewriting systems applied to stand ard bases and syntactic algebras DTSTART:20200611T101500 DTEND:20200611T111500 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2020-06-11/sessions/217/ CATEGORIES: DESCRIPTION:We introduce topological rewriting systems as a generalisation of abstract rewriting systems\, where we replace the set of terms by a to pological space. Abstract rewriting systems correspond to topological rewr iting systems for the discrete topology. We introduce the topological conf luence property as an approximation of the confluence property\, and use i t to characterise standard bases in terms of rewriting theory. Using a rep resentation of linear topological rewriting systems with continuous reduct ion operators\, we also interpret the topological confluence property in t erms of lattice operations. Finally\, we investigate duality for reduction operators that we relate to series representations and syntactic algebras \, from which we deduce a duality for proving that an algebra is syntactic or not. URL:https://chocola.ens-lyon.fr/events/meeting-2020-06-11/sessions/217/ END:VEVENT BEGIN:VEVENT SUMMARY:Neel Krishnaswami - TBA DTSTART:20200514T103000 DTEND:20200514T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2020-05-14/sessions/214/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/meeting-2020-05-14/sessions/214/ END:VEVENT BEGIN:VEVENT SUMMARY:Amina Doumane - Completeness for Identity-free Kleene Lattices DTSTART:20200312T153000 DTEND:20200312T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2020-03-12/sessions/216/ CATEGORIES: DESCRIPTION:We provide a finite set of axioms for identity-free Kleene lat tices\, which we prove sound and complete for the equational theory of the ir relational models. Our proof builds on the completeteness theorem for K leene algebra\, and on a novel automata construction that makes it possibl e to extract axiomatic proofs using a Kleene-like algorithm.\n\nWe provide a finite set of axioms for identity-free Kleene lattices\, which we prove sound and complete for the equational theory of their relational models. Our proof builds on the completeteness theorem for Kleene algebra\, and on a novel automata construction that makes it possible to extract axiomatic proofs using a Kleene-like algorithm. URL:https://chocola.ens-lyon.fr/events/meeting-2020-03-12/sessions/216/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulio Guerrieri - Factorization\, Normalization and all that. DTSTART:20200312T140000 DTEND:20200312T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2020-03-12/sessions/218/ CATEGORIES: DESCRIPTION:Lambda-calculi come with no fixed evaluation strategy. Differe nt \nstrategies may then be considered\, and it is important that they sat isfy \nsome abstract rewriting property\, such as factorization or nomaliz ation \ntheorems. We provide simple proof techniques for these theorems. O ur \nstarting point is a revisitation of Takahashi's technique to prove \n factorization for head reduction. Our appraoch is both simpler and more \n powerful\, as it works in cases where Takahishi's does not. We then pair \ nfactorization with two other abstract properties\, defining essential \ns ystems\, and show that normalization follows. Concretely\, we apply the \n technique to four case studies\, two classic ones\, head and the \nleftmos t-outermost reductions\, and two less classic ones\, \nnon-deterministic w eak call-by-value and least-level reductions.\n\nMoreover\, we present a n ew technique for proving factorization theorems \nfor compound rewriting s ystems in a modular way\, which is inspired by \nHindley-Rosen result for confluence. Our technique is first developed \nabstractly. In particular\, we isolate a simple sufficient condition \n(called linear swap) for lifti ng factorization from components to the \ncompound system. We then closely analyze some common factorization \nschemas for the lambda-calculus\, and show that the technique simplifies \neven more\, reducing to the test of elementary local commutations. \nConcretely\, we apply our modular techniq ue to various extensions of the \nlambda-calculus\, among which de' Liguor o and Piperno's non-deterministic \nlambda-calculus and --for call-by-valu e-- Carraro and Guerrieri's \nshuffling calculus. For both calculi the lit erature contains \nfactorization theorems. For each\, we provide a novel\, neat\, and \nstrikingly short modular proof.\n\nThis is joint work with B eniamino Accattoli and Claudia Faggian. URL:https://chocola.ens-lyon.fr/events/meeting-2020-03-12/sessions/218/ END:VEVENT BEGIN:VEVENT SUMMARY:Damiano Mazza - Automatic Differentiation in PCF DTSTART:20200312T103000 DTEND:20200312T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2020-03-12/sessions/219/ CATEGORIES: DESCRIPTION:Automatic differentiation (AD) is the science of efficiently c omputing \nthe derivative (or gradient\, or Jacobian) of functions specifi ed by \ncomputer programs. It is a fundamental tool in several fields\, m ost \nnotably machine learning\, where it is the key for training deep neu ral \nnetworks. Albeit AD techniques natively focus on a restricted class of \nprograms\, namely first-order straight-line programs\, the rise of \ nso-called differentiable programming in recent years has urged for the \n need of applying AD to complex programs\, endowed with control flow \noper ators and higher-order combinators\, such as map and fold. In this \ntalk \, I will discuss the extension of AD algorithms to PCF\, a(n \nidealized) purely functional programming language. We will first \nconsider the sim ply-typed lambda-calculus\, showing in particular how \nlinear negation is related to reverse mode AD (aka backpropagation)\, and \nthen see how the extra features of PCF\, namely full recursion and \nconditionals\, may be dealt with\, stressing the difficulties posed by the \nlatter.\n\n[Joint work with Aloïs Brunel (Deepomatic) and Michele Pagani (IRIF\, \nUniversi té de Paris)] URL:https://chocola.ens-lyon.fr/events/meeting-2020-03-12/sessions/219/ END:VEVENT BEGIN:VEVENT SUMMARY:Luc Pellissier - Glueability of resource proof-structures: inverti ng the Taylor expansion DTSTART:20200206T153000 DTEND:20200206T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2020-02-06/sessions/215/ CATEGORIES: DESCRIPTION:A Multiplicative-Exponential Linear Logic (MELL) proof-structu re can be expanded into a set of resource proof-structures: its Taylor exp ansion. We introduce a new criterion characterizing those sets of resource proof-structures that are part of the Taylor expansion of some MELL proof -structure\, through a rewriting system acting both on resource and MELL p roof-structures. URL:https://chocola.ens-lyon.fr/events/meeting-2020-02-06/sessions/215/ END:VEVENT BEGIN:VEVENT SUMMARY:Cyrille Chenavier - Topological rewriting systems applied to stand ard bases and syntactic algebras DTSTART:20200206T140000 DTEND:20200206T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2020-02-06/sessions/213/ CATEGORIES: DESCRIPTION:We introduce topological rewriting systems as a\n generalisa tion of\n abstract rewriting systems\, where we replace the set of ter ms by a\n topological space. Abstract rewriting systems correspond to\ n topological\n rewriting systems for the discrete topology. We intr oduce the\n topological confluence property as an approximation of the confluence\n property\, and use it to characterise standard bases in terms of\n rewriting\n theory. Using a representation of linear topo logical rewriting\n systems with\n continuous reduction operators\, we also interpret the topological\n confluence\n property in terms o f lattice operations. Finally\, we investigate\n duality for\n redu ction operators that we relate to series representations and\n syntactic \n algebras\, from which we deduce a duality for proving that an algeb ra\n is\n syntactic or not. URL:https://chocola.ens-lyon.fr/events/meeting-2020-02-06/sessions/213/ END:VEVENT BEGIN:VEVENT SUMMARY:Damiano Mazza - Backpropagation in the Simply Typed Lambda-calculu s with Linear Negation DTSTART:20200206T103000 DTEND:20200206T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2020-02-06/sessions/212/ CATEGORIES: DESCRIPTION:Backpropagation is a classic automatic differentiation algorit hm computing the gradient of functions specified by a certain class of sim ple\, first-order programs\, called computational graphs. It is a fundamen tal tool in several fields\, most notably machine learning\, where it is t he key for efficiently training (deep) neural networks. Recent years have witnessed the quick growth of a research field called differentiable progr amming\, the aim of which is to express computational graphs more syntheti cally and modularly by resorting to actual programming languages endowed w ith control flow operators and higher-order combinators\, such as map and fold. In this paper\, we extend the backpropagation algorithm to a paradig matic example of such a programming language: we define a compositional pr ogram transformation from the simply-typed lambda-calculus to itself augme nted with a notion of linear negation\, and prove that this computes the g radient of the source program with the same efficiency as first-order back propagation. The transformation is completely effect-free and thus provide s a purely logical understanding of the dynamics of backpropagation. URL:https://chocola.ens-lyon.fr/events/meeting-2020-02-06/sessions/212/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Gavazzo - Differential Logical Relations DTSTART:20191114T153000 DTEND:20191114T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-11-14/sessions/207/ CATEGORIES: DESCRIPTION:In this talk\, we introduce differential logical relations\, a new\n form of logical relation which\, in the spirit of metric relati ons\,\n assign each pair of programs a quantity measuring their distan ce\,\n rather than a boolean value standing for their being equivalent . The\n novelty of differential logical relations consists in measurin g the\n distance between programs not (necessarily) by a numerical val ue\,\n but by a mathematical object which somehow reflects the interac tive\n complexity of the compared programs.\n \nAfter having intro duced the notion of a program distance\, we will\n review some of the main notions of program distance offered by the\n literature and highl ight their strengths and weaknesses. We will\n then introduce differen tial logical relations\, their main\n properties\, and their relations hip with the aforementioned notions\n of program distance. Finally\, w e will discuss extensions and\n improvements of the current theory of differential logical\n relations. URL:https://chocola.ens-lyon.fr/events/seminaire-2019-11-14/sessions/207/ END:VEVENT BEGIN:VEVENT SUMMARY:Marie Kerjean - Higher-Order Distributions for Differential Linear Logic DTSTART:20191114T140000 DTEND:20191114T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-11-14/sessions/209/ CATEGORIES: DESCRIPTION:Is differentiation as it appears in computer science the same as the one \nfrom standard mathematics ? In particular\, can differentiati on in linear \nlogic compute on traditional objects of mathematics ?\n\nSu cceeding in finding such a smooth interpretation of differential \nlinear logic requires to overcome several issues: finding a good \ncategory of re flexive spaces and understanding how to handle \nhigher-order objects in f unctional analysis.\n\nThe first problem can be solved by exploiting the f act that polarities \nnaturally appear in the theory of topological vector spaces\; in \nparticular the categories of spaces of distributions and th eir dual will \nprovide an adequate example. For the second\, I will revie w several \nsolutions providing definitions for higher-order distributions . \n\nThis talk is based mainly on works in collaboration with Jean-Simon Lemay. URL:https://chocola.ens-lyon.fr/events/seminaire-2019-11-14/sessions/209/ END:VEVENT BEGIN:VEVENT SUMMARY:Yann Régis-Gianas - Towards certified incremental functional prog ramming DTSTART:20191114T103000 DTEND:20191114T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-11-14/sessions/208/ CATEGORIES: DESCRIPTION:Data constantly change. Google engineers make one commit every 2\nseconds on the same git repository. On average\, Twitter receives\napp roximatively 6000 tweets per second. A self-driving car typically\nupdates 100MB of its state each second.\n\nHow do we program software systems to handle these changes? When data\nis made of tiny flat records like tweets\ , and when data processing is\nmade of only purely local algorithms like s tatistical operators\,\nstream-based programming is most of the time the r ight approach.\n\nWhat if the data is more structured\, typically like a s ource code\nrepository? Can we follow a similar dataflow approach? That is not\nclear. We believe that incremental functional programming could\npro vide better tools for that kind of situations.\n\nIncremental functional p rogramming is about implementing\nchange-centric software systems using fi rst-class changes. From a\nbase input and a change to this input\, an incr emental program computes\na change of the base output. More formally\, if f is a function of type\nA → B and if there is a type ∆A for changes o ver values of type A\, and\na type ∆B for changes over values of type B\ , an incrementalization\nD(f) of f is such that f x ⊕ D(f) x dx = f (x ⊕ dx) where ⊕ is the\napplication of a change to a value and D(f ) has type A → ∆A → ∆B.\n\nIn this talk\, we will explain why increment al functional programming\nis important but error-prone. We will describe our ongoing work to\ndevelop ∆Caml and ∆Coq\, two tools that assist th e incremental\nprogrammer in certifying incremental functional programs. URL:https://chocola.ens-lyon.fr/events/seminaire-2019-11-14/sessions/208/ END:VEVENT BEGIN:VEVENT SUMMARY:Valeria Vignudelli - The Theory of Traces for Systems with Nondete rminism and Probability DTSTART:20191017T153000 DTEND:20191017T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-10-17-1/sessions/203 / CATEGORIES: DESCRIPTION:We study trace-based equivalences for labelled transition syst ems\n combining nondeterministic and probabilistic choices. We do so via a\n coalgebraic construction known as the generalized powerset\n cons truction\, which consists in first determinizing a system and then\n rec overing trace equivalence as bisimilarity on the determinized\n system. The generalized powerset construction allows us to apply these\n two ste ps\, inspired by the standard powerset construction for\n nondeterminist ic automata\, to a variety of systems\, such as labelled\n transition sy stems with different computational effects captured by\n monads (e.g.\, systems with probabilistic choices).\n We show how trace semantics for l abelled transition systems combining\n nondeterministic and probabilisti c choices can be recovered by\n instantiating the generalized powerset c onstruction\, and we\n characterise and compare the resulting semantics to known definitions\n of trace equivalences appearing in the literature s. Most of our results\n are based on the exciting interplay between mon ads and their\n presentations via algebraic theories.\n\n This talk is based on joint work with Filippo Bonchi and Ana Sokolova\,\n available at [https://arxiv.org/abs/1808.00923](https://arxiv.org/abs/1808.00923) URL:https://chocola.ens-lyon.fr/events/seminaire-2019-10-17-1/sessions/203 / END:VEVENT BEGIN:VEVENT SUMMARY:Dan Ghica - The next 700 abstract machines DTSTART:20191017T140000 DTEND:20191017T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-10-17-1/sessions/202 / CATEGORIES: DESCRIPTION:We propose a new core calculus for programming languages with effects\, \ninterpreted using a hypergraph-rewriting abstract machine insp ired by \nthe Geometry of Interaction. The intrinsic calculus syntax and s emantics \nonly deals with the basic structural aspects of programming lan guages: \nvariable binding\, name binding\, and thunking. Everything else\ , including \nfunction abstraction and application\, must be provided as e xtrinsic \noperations with associated rewrite rules. The graph representat ion \nyields natural concepts of locality and robustness for equational \n properties and reduction rules\, which enable a novel flexible and \npower ful reasoning methodology about (type-free) languages with effects. \nWe i llustrate and motivate the technique with challenging examples from \nthe literature.\n\nPaper: [https://arxiv.org/abs/1907.01257](https://arxiv.org /abs/1907.01257)\n\n(Joint work with Koko Muroya and Todd Waugh Ambridge.) URL:https://chocola.ens-lyon.fr/events/seminaire-2019-10-17-1/sessions/202 / END:VEVENT BEGIN:VEVENT SUMMARY:Eric Finster - An opetopic syntax for higher monoidal closed categ ories DTSTART:20191017T113000 DTEND:20191017T123000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-10-17-1/sessions/205 / CATEGORIES: DESCRIPTION:At the core of the modern understanding of the Curry-Howard\n correspondence between proofs and programs is the connection\n between \, on the one hand\, the syntax of logic and type theory\, and\n on the other\, certain mathematical structures\, often taking the form\n of str uctured categories and related objects. In one of its most\n well-known incarnations\, for example\, we can see the simply typed\n lambda calcul us as a syntactic notation for morphisms in a cartesian\n closed categor y. Equivalently\, free cartesian closed categories can\n be constructed directly from syntax in a way which gives them a\n well-understood comp utational interpretation.\n\n With the recent advances in understanding the homotopical nature of\n dependent type theory\, as well as the paral lel development of\n tractable models of higher categories\, it is natur al to wonder if\n this classical correspondence between syntax\, semanti cs and\n computation can be extended in a direct way to higher structure s.\n That is\, can we find some kind of natural syntactic description of \n higher structured categories? In this talk I will explain one\n po ssibility for such a description of monoidal closed higher\n categories using a graphical syntax based on opetopes. URL:https://chocola.ens-lyon.fr/events/seminaire-2019-10-17-1/sessions/205 / END:VEVENT BEGIN:VEVENT SUMMARY:Danel Ahman - Interacting with the external world using comodels ( aka runners) DTSTART:20191017T100000 DTEND:20191017T110000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-10-17-1/sessions/204 / CATEGORIES: DESCRIPTION:In languages with algebraic effects (resp. monads)\, the usual way of\nmodelling interactions with the external world is to define a ded icated\neffect (resp. monad) and then treat it specially in the compiler\, such\nas the RandomInt effect in the Eff language and the IO monad in Has kell.\nThis however has various drawbacks. For instance\, such languages o ften\nlack enforcement mechanisms to ensure that a program does not write\ nto an already closed file. And what is even worse\, in languages with\nal gebraic effects\, where all effects can be handled\, it is very easy\nto a ccidentally cause one's program not to even reach file closing\,\nby disca rding a continuation somewhere in the handler.\n\nIn this talk\, I will pr esent our ongoing work on using comodels of\nalgebraic effects as a progra mming abstraction for (i) modelling the\nexternal world and interactions w ith it\, (ii) ensuring the linearity\nof these interactions\, and (iii) co ntrolling which capabilities of the\nexternal world different parts of pro grams have access to. Regarding\n(ii)\, the novel aspect of our work is th at we do not ensure linearity\nof these interactions by the means of a lin ear type system\, but\ninstead we leave the external world implicit and in teract with it\nthrough a combination of algebraic operations and (under t he hood) a\nlinear state-passing translation analogous to that of Møgelbe rg and\nStaton. Regarding (i) and (ii)\, we do not limit the programmer to a\nsingle external world\, but instead allow them to modularly build thei r\nown intermediate external worlds. In addition\, in the talk I will also \ndiscuss two natural ways how a comodel (i.e.\, the external world) can\n communicate information back to the program being run using this comodel.\ n\n(This is joint work with Andrej Bauer) URL:https://chocola.ens-lyon.fr/events/seminaire-2019-10-17-1/sessions/204 / END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Férée - Contributing to Higher Order Complexity: Outcomes a nd Likely Applications DTSTART:20190926T153000 DTEND:20190926T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-09-26/sessions/198/ CATEGORIES: DESCRIPTION:Complexity theory has been mainly focused on computations over intrinsically\nfinite objects like finite words\, integers\, trees and gr aphs\, etc. In a broad\nsense\, higher-order complexity deals with computa tions over more general domains\nand codomains\, including real numbers\, co-inductive datatypes or higher-order\nfunctions.\n\nI will start by pres enting a few results related to second-order complexity\nwhich motivated t he main course of this talk: a proposition of definition for\nthe complexi ty of higher-order functions based on game semantics. Finally\, I\nwill en umerate some potential applications and extensions of this work that I\nin tend to pursue in the near future. URL:https://chocola.ens-lyon.fr/events/seminaire-2019-09-26/sessions/198/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Condoluci - Sharing Equality is Linear DTSTART:20190926T140000 DTEND:20190926T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-09-26/sessions/197/ CATEGORIES: DESCRIPTION:In this talk I will present joint work with Beniamino Accattol i and\n Claudio Sacerdoti Coen\, accepted at PPDP 19. The topic is how t o check\n efficiently whether given -terms are equal\, or more precisely -equal:\n as simple as it may sound\, the problem is non-trivial when - terms are\n represented succintly with sharing\, i.e. the reuse of subte rms. This\n problem is relevant in implementations of the -calculus\, fo r instance\n in proof assistants: type-checking algorithms for dependent type\n theories rely on a conversion subprocedure to check whether two -terms\n are convertible\, i.e. they reduce to the same term. A lot of r esearch\n has been carried on how to evaluate -terms in an efficient way \, which\n boils down to use sharing in one way or another\; the missing part is\n how to compare the shared results for equality.\n\n In pres ence of sharing\, one is actually interested in sharing equality\,\n i.e . the equality of the underlying unshared -terms. The naive\n algorithm for sharing equality is exponential in the size of the shared\n terms\, but in this talk I will present our linear-time algorithm (the\n first w ith such low complexity). As others before us\, we were inspired\n by Pa terson and Wegman's algorithm for first-order unification\, itself\n bas ed on representing terms with sharing as DAGs\, and sharing equality\n a s bisimulation of DAGs. URL:https://chocola.ens-lyon.fr/events/seminaire-2019-09-26/sessions/197/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Clairambault - Fix Your Semantic Cube Using This Simple Tri ck DTSTART:20190926T103000 DTEND:20190926T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2019-09-26/sessions/201/ CATEGORIES: DESCRIPTION:Game semantics usually present execution as a total chronologi cal\nordering of observable computational events. They proved to be a\npow erful tool in semantics\, yielding a great deal of full abstraction\nresul ts. Its first few achievements were striking\, capturing in a single\nfram ework combinations of state and control. This lead to Abramsky's\nfamous " semantic cube" programme: to capture in a single canvas a wide\nvariety of effects. However\, past the original "semantic square"\nresulting from th e combinations of control and state\, developments in\ngame semantics have since then been rather disconnected.\n\nThe family of game semantics usua lly known as "concurrent games"\,\noriginally introduced by Abramsky and M elliès in 1999\, has been actively\ndeveloped in the past decade or so. I n contrast with the total\nchronological ordering of traditional games\, c oncurrent games present\n(implicitly or explicitly) the causal constraints between computational\nevents. To that end they borrow tools from concurr ency theory\, and in\nparticular rely on structures coming from "true conc urrency". They are\ntherefore well suited to the denotational semantics of concurrent\nprogramming languages.\n\nIn this talk\, I will give an intro duction to concurrent games and\npresent some developments that highlight a different property: they are\ngood at linking distinct models with each other\, in and outside of game\nsemantics. Concretely\, I will present the first steps to fixing the cube\n{state\, parallelism\, probabilities} -- all its faces are currently\nbroken. First\, I will fix the face {state\, parallelism}. For that I\nwill introduce a notion of parallel innocence\, exploiting the causal\naspect of concurrent games. Time permitting\, I wi ll also fix\n{parallelism\, probabilities}\, via probabilistic concurrent games and\ntheir link with relational semantics. I will close on some pers pectives\non the full cube.\n\nThis talk builds on joint work with several people\, among whom Simon\nCastellan\, Hugo Paquet and Glynn Winskel. URL:https://chocola.ens-lyon.fr/events/seminaire-2019-09-26/sessions/201/ END:VEVENT BEGIN:VEVENT SUMMARY:Lutz Strassburger - Introduction to Combinatorial Proofs DTSTART:20190606T153000 DTEND:20190606T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-06-06/sessions/195/ CATEGORIES: DESCRIPTION:In this talk I will give an introduction to combinatorial proo fs\, explain the\nmotivation behind\, and discuss what it means for a proo f to be "without\nsyntax". The main emphasis will be on combinatorial proo fs for classical and\nintuitionistic propositional logic. URL:https://chocola.ens-lyon.fr/events/meeting-2019-06-06/sessions/195/ END:VEVENT BEGIN:VEVENT SUMMARY:Jérémy Ledent - Geometric semantics for asynchronous computabili ty DTSTART:20190606T140000 DTEND:20190606T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-06-06/sessions/196/ CATEGORIES: DESCRIPTION:Geometric methods have been used for 20 years to prove impossi bility\nresults for fault-tolerant concurrent computing. We study these me thods\nfrom a semantical perspective: in what sense do they constitute a\n semantics for concurrent programs?\n\nIn this talk\, I will explain how to derive these geometric models from\na concrete operational semantics base d on interleavings of execution\ntraces. To do so\, I will review and comp are different trace-based methods\nfor specifying behaviors of concurrent objects. URL:https://chocola.ens-lyon.fr/events/meeting-2019-06-06/sessions/196/ END:VEVENT BEGIN:VEVENT SUMMARY:Ohad Kammar - A tutorial on quasi-Borel spaces DTSTART:20190606T103000 DTEND:20190606T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-06-06/sessions/194/ CATEGORIES: DESCRIPTION:We have used Quasi-Borel spaces\, a new mathematical structure \, as\n a foundations of probabilistic programming and higher-order\n statistics. In this talk\, I will introduce this alternative\n to tradit ional measure theory. We will cover the basic definition\,\n and the con structions relevant to modelling and verification. URL:https://chocola.ens-lyon.fr/events/meeting-2019-06-06/sessions/194/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniela Petrisan - Up-To Techniques for Behavioural Metrics via Fi brations DTSTART:20190509T153000 DTEND:20190509T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-05-09/sessions/193/ CATEGORIES: DESCRIPTION:Up-to techniques are a well-known method for enhancing coinduc tive proofs of behavioural equivalences. We introduce up-to techniques for behavioural metrics between systems modelled as coalgebras and we provide abstract results to prove their soundness in a compositional way.\n\nIn o rder to obtain a general framework\, we need a systematic way to lift func tors: we show that the Wasserstein lifting of a functor\, introduced in a previous work\, corresponds to a change of base in a fibrational sense. Th is observation enables us to reuse existing results about soundness of up- to techniques in a fibrational setting. We focus on the fibrations of pred icates and relations valued in a quantale\, for which pseudo-metric spaces are an example. To illustrate our approach we provide an example on dista nces between regular languages. URL:https://chocola.ens-lyon.fr/events/meeting-2019-05-09/sessions/193/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathys Rennela - Operator algebras in categorical quantum foundati ons DTSTART:20190509T140000 DTEND:20190509T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-05-09/sessions/191/ CATEGORIES: DESCRIPTION:In this talk\, we will present an overview of our work on the\ n use of operator algebras as categorical models for quantum programming \n languages. Starting from a mathematical connection between operator\n theory and domain theory\, we will detail some of the categorical\n p roperties of operator algebras\, which can be represented as categories\n of presheaves. We present a general categorical framework for the\n se mantics of embedded quantum programming languages as instances of\n enri ched category theory\, and establish some connection with\n probabilisti c models\, and Benton-style linear-non-linear models.\n\n We explain how W\\*-algebras fit within this framework. In detail\, the\n denotational semantics is described as follows: every program type is\n interpreted as a W*-algebra and every program is interpreted as a\n normal completel y positive subunital map. These operator algebras were\n introduced by v on Neumann himself\, and motivated by his study of\n quantum mechanics. The theory of operator algebras has found direct\n application in variou s fields such as quantum information theory and\n quantum field theory.\ n\n We identify some relevant categorical properties of W\\*-algebras an d\n show they form a suitable setting for the mathematical interpretatio n\n of a first-order quantum programming language with inductive datatyp es.\n Since qubits are easily representable in a W\\*-algebra\, the deno tational\n semantics supports many features relevant to quantum programm ing\n languages. We finally consider applications to verification and\n categorical axiomatics for quantum computing. URL:https://chocola.ens-lyon.fr/events/meeting-2019-05-09/sessions/191/ END:VEVENT BEGIN:VEVENT SUMMARY:Radu Mardare - Non-standard semantics for stochastic computational phenomena DTSTART:20190509T103000 DTEND:20190509T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-05-09/sessions/186/ CATEGORIES: DESCRIPTION:Complex probabilistic/stochastic processes are of central\n importance in modern computing\, representing new challenges in\n Engine ering and Technology\, both from theoretical and practical\n perspective s. They involve real-valued parameters (probabilities of\n transitions\, distributions characterizing the residence-time in a\n state\, etc.) to abstract missing information\, model ignorance\,\n uncertainty or inher ent randomness. Advances in verification of\n probabilistic and real-tim e systems as well as the tremendous growth of\n applications in cyber-ph ysical systems\, machine learning\, and planning\n under uncertainty tes tify to their importance. To develop dedicated\n probabilistic/stochasti c programming languages or theories of systems\,\n one needs to reconsid er the foundations of computational theory\, since\n the classic logical principles supporting it must be replaced with\n non-classical (e.g.\, measure-theoretic) probabilistic principles. More\n concretely\, identif ying probabilistic processes with identical\n probabilistic behaviours\, as the classic computability theory does\, is\n too `exact' for most pu rposes. In applications\, one instead needs\n to know whether two proces ses that may differ by a small amount in\n their real-valued parameters have sufficiently similar behaviours\, or\n to study the behavioural div ergence-convergence of inequivalent\n probabilistic programs.\n\n In t his talk I will discuss two such non-standard semantics: the metric\n se mantics and the Boolean-valued semantics\, with their advantages and\n l imitations. And I will present some technical details and challenges\n e merging form the metric semantics.\n\n Bibliography:\n\n [1] R. Mardar e\, P. Panangaden\, G. Plotkin. Quantitative Algebraic\n Reasoning\, LIC S 2016.\n\n [2] R. Mardare\, P. Panangaden\, G. Plotkin. On the Axiomati zability of\n Quantitative Algebras\, LICS 2017.\n\n [3] G. Bacci\, R. Mardare\, P. Panangaden\, G. Plotkin. An Algebraic\n Theory of Markov P rocesses\, LICS 2018.\n\n [4] G. Bacci\, R. Furber\, D. Kozen\, R. Marda re\, P. Panangaden\, Dana\n Scott. Boolean-Valued Semantics for Stochast ic Lambda-Calculus\, LICS\n 2018. URL:https://chocola.ens-lyon.fr/events/meeting-2019-05-09/sessions/186/ END:VEVENT BEGIN:VEVENT SUMMARY:Ludovic Patey - Introduction to reverse mathematics DTSTART:20190404T153000 DTEND:20190404T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-04-04/sessions/189/ CATEGORIES: DESCRIPTION:Reverse mathematics is a fundational program whose goal is to find op-\ntimal axioms to prove ordinary theorems. They use the framework of second-\norder arithmetics\, with a base theory\, RCA 0 \, capturing co mputable mathematics.\nStarted in the 70s by Harvey Friedman\, they reveal ed five big systems of axioms\nsuch that most of the theorems coming from the heart of mathematics are either\nprovable within RCA 0 \, or provably equivalent to one of these systems.\n\nIn this talk\, we will introduce re verse mathematics with its motivations\, and\nwill give a glimpse of this computational structural phenomenon. Last\, we will\npresent the new probl ematics of modern reverse mathematics together with its\nmain remaining op en questions.\n\nReferences\n\n1. Hirschfeldt\, D.R.: Slicing the truth\, Lecture Notes Series. Institute for Mathematical\nSciences. National Unive rsity of Singapore\, vol. 28. World Scientific Publishing Co.\nPte. Ltd.\, Hackensack\, NJ (2015)\, on the computable and reverse mathematics of\nco mbinatorial principles\, Edited and with a foreword by Chitat Chong\, Qi F eng\,\nTheodore A. Slaman\, W. Hugh Woodin and Yue Yang\n\n2. Simpson\, S. G.: Subsystems of Second Order Arithmetic. Cambridge University Press\n(20 09) URL:https://chocola.ens-lyon.fr/events/meeting-2019-04-04/sessions/189/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphaëlle Crubillé - Probabilistic Stable Functions on Discrete Cones are Power Series. DTSTART:20190404T140000 DTEND:20190404T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-04-04/sessions/192/ CATEGORIES: DESCRIPTION:The category of probabilistic coherence spaces (PCoh_!)\, intr oduced by\n Danos and Ehrhard\, is a fully abstract model for PCF with * discrete*\n probabilities\, where morphisms can be seen as power series. The\n category Cstab_m\, of measurable cones and measurable stable func tions\,\n has been introduced by Ehrhard\, Pagani and Tasson as a model for PCF\n with *continuous* probabilities.\n\n In this talk\, we will study the shape of stable functions when they are\n between *discrete* c ones: we will show that they can actually be seen\n as generalized power series. The proof is based on a generalization of\n a theorem from real analysis due to Bernstein\, that states that all\n absolutely monotonou s functions on reals are power series. From there\,\n we will build a f ull and faithful functor from PCoh_! into Cstab_m that\n moreover preser ves the cartesian closed structure. URL:https://chocola.ens-lyon.fr/events/meeting-2019-04-04/sessions/192/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Leroy - Formal verification of a static analyzer: abst ract interpretation in type theory DTSTART:20190404T103000 DTEND:20190404T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-04-04/sessions/187/ CATEGORIES: DESCRIPTION:(Joint work with Jacques-Henri Jourdan\, Vincent Laporte\, San drine\n Blazy\, and David Pichardie)\n\n Static analysis is the automa tic inference and checking of simple\n properties of all executions of a program. Initially developed in the\n context of compilers to support c ode optimization\, static analysis is\n successful today for the formal verification of safety properties of\n critical software.\n\n Abstract interpretation provides an elegant\, powerful mathematical\n framework to define and reason about static analyses. However\, the\n classic pre sentation for abstract interpretation\, based on Galois\n connections\, is set-theoretic and not constructive. This is an issue\n when one want s to verify a static analyzer using Coq\, Agda\, or other\n provers base d on type theory.\n\n In this talk\, I will present a type-theoretic acc ount of abstract\n interpretation\, originally developed by David Pichar die\, and show how\n it scales up to the verification of Verasco\, a rea listic static\n analyzer for the C language that has been developed and proved correct\n using Coq as a programming language and as a proof assi stant.\n\n For more information: [http://compcert.inria.fr/verasco/](htt p://compcert.inria.fr/verasco/) URL:https://chocola.ens-lyon.fr/events/meeting-2019-04-04/sessions/187/ END:VEVENT BEGIN:VEVENT SUMMARY:Étienne Miquey - A constructive proof of dependent choice in clas sical arithmetic via memoization DTSTART:20190314T153000 DTEND:20190314T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-03-14/sessions/190/ CATEGORIES: DESCRIPTION:In 2012\, Herbelin developed a calculus (dPA^ω) in which cons tructive\n proofs for the axioms of countable and dependent choices can be derived\n via the memoization of choice functions However\, the prope rty of\n normalization (and therefore the one of soundness) was only\n conjectured. The difficulty for the proof of normalization is due to\n the simultaneous presence of dependent dependent types (for the\n constr uctive part of the choice)\, of control operators (for classical\n logic )\, of coinductive objects (to encode functions of type ℕ→A into\n s treams (a₀\,a₁\,…)) and of lazy evaluation with sharing (for these\n coinductive objects). Building on previous works\, we introduce a\n v ariant of dPA^ω presented as a sequent calculus. On the one hand\, we\n take advantage of a variant of Krivine classical realizability we\n dev eloped to prove the normalization of classical call-by-need. On the\n ot her hand\, we benefit of dL[tp]\, a classical sequent calculus with\n de pendent types in which type safety is ensured using delimited\n continua tions together with a syntactic restriction. By combining the\n techniqu es developed in these papers\, we manage to define a\n realizability int erpretation à la Krivine of our calculus that allows\n us to prove norm alization and soundness. This talk will go over the\n whole process\, st arting from Herbelin’s calculus dPA^ω until our\n introduction of its sequent calculus counterpart dLPA^ω. URL:https://chocola.ens-lyon.fr/events/meeting-2019-03-14/sessions/190/ END:VEVENT BEGIN:VEVENT SUMMARY:Ambroise Lafont - Higher-order Arities\, Signatures and Equations via Modules DTSTART:20190314T140000 DTEND:20190314T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-03-14/sessions/188/ CATEGORIES: DESCRIPTION:In their work on second-order equational logic\, Fiore and Hur have\nstudied presentations of simply typed languages by generating bindi ng\nconstructions and equations among them.\nTo each pair consisting of a binding signature and a set of equations\,\nthey associate a category of ` models'\,\nand they give a monadicity result which implies that this categ ory has\nan initial object\, which is the language presented by the pair.\ n\nIn the present work\, we propose\, for the untyped setting\, a variant of\ntheir approach where monads and modules over them are the central\nnot ions.\nMore precisely\, we study\, for monads over sets\, presentations by \ngenerating (`higher-order') operations and equations among them.\nWe con sider a notion of 2-signature which allows to specify a monad\nwith a fami ly of binding operations subject to a family of equations\,\nas is the cas e for the paradigmatic example of the lambda calculus\,\nspecified by its two standard constructions (application and\nabstraction) subject to $\\be ta$- and $\\eta$-equalities.\nSuch a 2-signature is hence a pair (Σ\,E) o f a binding signature Σ and\na family E of equations for Σ.\nThis notion of 2-signature has been introduced earlier by Ahrens in a\nslightly diffe rent context.\n\nWe associate\, to each 2-signature (Σ\,E)\, a category o f 'models of\n(Σ\,E)\; and we say that a 2-signature is 'effective' if th is category\nhas an initial object\;\nthe monad underlying this (essential ly unique) object is the 'monad\nspecified by the 2-signature'.\nNot every 2-signature is effective\; we identify a class of\n2-signatures\, which w e call 'algebraic'\, that are effective.\n\nImportantly\, our 2-signatures together with their models enjoy 'modularity':\nwhen we glue (algebraic) 2-signatures together\, their initial models\nare glued accordingly.\n\nWe provide a computer formalization for our main results. URL:https://chocola.ens-lyon.fr/events/meeting-2019-03-14/sessions/188/ END:VEVENT BEGIN:VEVENT SUMMARY:Filip Sieczkowski - Abstraction and equational reasoning for algeb raic effects and handlers DTSTART:20190314T103000 DTEND:20190314T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-03-14/sessions/184/ CATEGORIES: DESCRIPTION:Programming with algebraic effects and handlers is a fairly no vel\n technique of representing computational effects. Rooted in the\n theoretical work of Plotkin and Power\, from which the key notion of\n algebraicity of the effects stems\, this framework offers a more modular\n way of effectful programming — in particular\, a modular way of\n c omposing effectful programs.\n\n The distinction between algebraic effec ts and other models of effectful\n computation is its separation between "interface" and "implementation":\n algebraic operations\, such as rais ing an exception or reading/writing a\n cell of mutable state are treate d as mere syntax or pieces of a\n specification\, on their own devoid of interpretation. What Plotkin and\n Pretnar's insight adds to this view is the notion of a handler — a\n construct which provides an interpret ation for the operation\, within\n its scope. In connection with express ive type-and-effect systems\, these\n constructs allow programmers almos t unprecedented freedom to define and\n manage their own computational e ffects.\n\n In this talk I would like to discuss some of the choices tha t one faces\n while designing a calculus that allows programming with al gebraic\n effects\, and show how one of the most important aspects that one needs\n to pay attention to is parametricity. To this end we develop a model\n calculus of algebraic effects and handlers with a polymorphic \n type-and-effect system that allows for both universal and existential \n quantification over effects (thus providing a somewhat limited model\ n for modules in a setting with algebraic effects and handlers)\, and a\ n step-indexed relational interpretation of this calculus. We can then\n use the relational interpretation to show some interesting properties\n of the calculus\, in particular to show contextual equivalence and\n refinement results. URL:https://chocola.ens-lyon.fr/events/meeting-2019-03-14/sessions/184/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Nuyts - Degrees of Relatedness DTSTART:20190124T153000 DTEND:20190124T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-01-24/sessions/185/ CATEGORIES: DESCRIPTION:Dependent type theory allows us to write programs and to prove \n properties about those programs in the same language. However\, some\ n properties do not require much proof\, as they are evident from a\n program's implementation\, e.g. if a polymorphic program is not ad hoc\n but relationally parametric\, then we get parametricity theorems for\n free. If we want to safely shortcut proofs by relying on the evident\n g ood behaviour of a program\, then we need a type-level guarantee that\n the program is indeed well-behaved. This can be achieved by annotating\n function types with a modality describing the behaviour of functions.\n We consider a dependent type system with modalities for relational\n pa rametricity\, irrelevance (i.e. type-checking time erasability of an\n a rgument) and ad hoc polymorphism. The interplay of three modalities\n an d dependent types raises a number of questions. For example: If a\n term depends on a variable with a given modality\, then how should its\n typ e depend on it? Are all modalities always applicable\, e.g. should we\n consider parametric functions from the booleans to the naturals? Do we\n need any further modalities in order to properly reason about these\n t hree?\n\n We develop a type system\, based on a denotational presheaf mo del\, that\n answers these questions. The core idea is to equip every ty pe with a\n number of relations --- just equality for small types\, but more for\n larger types --- and to describe function behaviour by saying how\n functions act on those relations. The system has modality-aware\n equality judgements (ignoring irrelevant parts) and modality-aware\n proving operators (for proving free theorems) which are even\n self-appl icable. It also supports sized types\, some form of\n intersection and u nion types\, and parametric quantification over\n algebraic structures. We prove soundness in a denotational presheaf\n model.\n\n In this pre sentation I will give a relatively technical overview of how\n relationa l parametricity works in System F\, Fω and dependent type\n theory. I w ill explain how and why a parametric modality is needed in\n dependent t ype theory to assert free theorems for all types. Next\, I\n will explai n how the framework in which we formulate this modality\, is\n already p owerful enough to accommodate the other modalities mentioned\n above. Fi nally\, I will briefly discuss the novel structural modality\n which is of interest when working with algebraic structures\, as well as\n union and intersection types and the presheaf model.\n\n While prior knowledge about dependent type theory and relational\n parametricity is useful\, the presentation is intended to be accessible\n without. URL:https://chocola.ens-lyon.fr/events/meeting-2019-01-24/sessions/185/ END:VEVENT BEGIN:VEVENT SUMMARY:Aurore Alcolei - Resource-tracking concurrent games DTSTART:20190124T140000 DTEND:20190124T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-01-24/sessions/180/ CATEGORIES: DESCRIPTION:In the study of programming languages\, denotational semantics is used to\nabstract away from (some) intermediate steps of computation b y providing \ninvariants of reduction. Although these abstractions are ver y useful to help\nreasoning about qualitative program behaviours such as p rogram termination\, \nthey usually do not reflect quantitative informatio ns such as permissions or \ntime consumption.\n\nIn this talk\, I will pre sent a framework of annotated concurrent games\nand strategies on event st ructures that generally allows for keeping\ntrack of side-information\, t hat is\, data whose value may vary with the\nexecution flow but cannot mod ify it. In particular\, I will use this new\nframework to give a sound den otational semantics to R-IPA\, an affine\nconcurrent higher-order programm ing language with shared state and a\nprimitive for resource consumption\, parametrized by an algebraic\nstructure R expressing resources. Although this model is not adequate\nin general – its analysis being finer than t hat offered by the general\noperational semantics on resource R – I will show that adequacy holds \nfor an operational semantics specialized to ti me consumption. URL:https://chocola.ens-lyon.fr/events/meeting-2019-01-24/sessions/180/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul-André Melliès - Template games: a homotopy model of differe ntial linear logic DTSTART:20190124T103000 DTEND:20190124T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2019-01-24/sessions/181/ CATEGORIES: DESCRIPTION:In this introductory tutorial talk\, I will explain how the no tion of template game slowly emerged from the desire to develop a simple a nd purely combinatorial description of game semantics\, living in harmony with the relational semantics of linear logic. My talk will be in three pa rts. First\, I will recall the traditional game semantics of intuitionisti c linear logic (ILL) based on sequential alternating games and strategies. Then\, I will explain how to reformulate that model (or a slight variant of it) in the functorial language of template games. Finally\, I will show that template games provide the first game semantics of differential line ar logic (DiLL). The construction of the model will be driven by a healthy comparison with the model of generalised species formulated ten years ago by Marcelo Fiore\, Nicola Gambino\, Martin Hyland and Glynn Winskel. I wi ll in particular indicate why homotopy theory plays a fundamental role in the construction of the template game model\, while it remains hidden in t he model based on generalised species. In that way\, besides the resolutio n of an old open problem of game semantics\, the template game model revea ls an unexpected and promising convergence between linear logic and homoto py theory. If time permits\, I will also describe the concurrent template game model of differential linear logic\, and its connection to the semant ics of the pi-calculus through the translation by Thomas Ehrhard and Olivi er Laurent.\n\nSee also [this page](https://www.irif.fr/~mellies/template- games.html) about template games! URL:https://chocola.ens-lyon.fr/events/meeting-2019-01-24/sessions/181/ END:VEVENT BEGIN:VEVENT SUMMARY:Paolo Pistone - Coends and proof equivalence in second order multi plicative linear logic DTSTART:20181213T153000 DTEND:20181213T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-12-13/sessions/183/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/meeting-2018-12-13/sessions/183/ END:VEVENT BEGIN:VEVENT SUMMARY:Lê Thành Dũng Nguyễn - Around finite semantics for second-ord er multiplicative linear logic DTSTART:20181213T140000 DTEND:20181213T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-12-13/sessions/175/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/meeting-2018-12-13/sessions/175/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Hirschowitz - Familial monads and structural operational seman tics DTSTART:20181213T103000 DTEND:20181213T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-12-13/sessions/182/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/meeting-2018-12-13/sessions/182/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Leroy - Leçon inaugurale au Collège de France DTSTART:20181115T180000 DTEND:20181115T190000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-11-15/sessions/179/ CATEGORIES: DESCRIPTION:This is not part of the CHoCoLa day\, but you might be interes ted in attending!\nSee [this page](https://www.college-de-france.fr/site/x avier-leroy/inaugural-lecture-2018-11-15-18h00.htm). URL:https://chocola.ens-lyon.fr/events/meeting-2018-11-15/sessions/179/ END:VEVENT BEGIN:VEVENT SUMMARY:Shane Mansfield - An overview of empirical models DTSTART:20181115T153000 DTEND:20181115T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-11-15/sessions/178/ CATEGORIES: DESCRIPTION:Empirical models are a way of formalising data that arises in physical \nexperiments. They were first proposed by Abramsky and Brandenbu rger as \npart of a framework to analyse fundamentally non-classical pheno mena in \nquantum systems. Conveniently from a computer science perspectiv e\, they \nabstract away from the mathematical baggage of quantum theory a nd \ninstead allow the key phenomena to be characterised purely as feature s \nof empirical data. After introducing the basic framework I will discus s \nsome more recent results and developments\, drawing on joint work with a \nnumber of collaborators. In particular: quantum computations can simp ly \nbe modelled as classical computations with the additional ability to \ninteract with a resource empirical model\; quantitative measures of \nno n-classicality can be shown to relate directly to some basic \nquantum-ove r-classical computational advantages\; and the beginnings of a \ncategory- theoretic approach to reasoning about empirical models have \nemerged. URL:https://chocola.ens-lyon.fr/events/meeting-2018-11-15/sessions/178/ END:VEVENT BEGIN:VEVENT SUMMARY:Flavien Breuvart - Graded Types Parametricity : Principles and App lication to Abstract Interpretation DTSTART:20181115T140000 DTEND:20181115T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-11-15/sessions/177/ CATEGORIES: DESCRIPTION:In this talk\, we will briefly present the yet-to-start projec t CoGITARe\, \nwhich aims at developing further graded types expressivity and inference \nin order to use them to perform abstract interpretations.\ n\nIn a second time\, we give an historic on graded type systems and their \nexpressivity. Then\, we will see that this expressivity is limited by a \nlack of dependency/parametricity. We will thus explore two ongoing \nre search directions that adds two very different kind of parametricity \nto graded types.\n\n(The provocative title should only be taken as a joke. De spite their \napparent similitudes\, this work and Éric Tanter's have vas tly different \nobjectives and involved different issues and techniques. I n particular\, \nnotice that gradual and graded types are fundamentally di fferent.) URL:https://chocola.ens-lyon.fr/events/meeting-2018-11-15/sessions/177/ END:VEVENT BEGIN:VEVENT SUMMARY:Éric Tanter - Abstracting Gradual Typing: Principles and Applicat ion to Gradual Parametricity DTSTART:20181115T110000 DTEND:20181115T123000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-11-15/sessions/176/ CATEGORIES: DESCRIPTION:Gradual typing enables programming languages to seamlessly com bine\n dynamic and static checking. Language researchers and designers h ave\n extended a wide variety of type systems to support gradual typing. \n These efforts consistently demonstrate that designing a satisfactory\ n gradual counterpart to a static type system is challenging\, and this\ n challenge only increases with the sophistication of the type system.\n Gradual type system designers need more formal tools to help them\n c onceptualize\, structure\, and evaluate their designs. Based on an\n und erstanding of gradual types as abstractions of static types\, we have\n developed systematic foundations for gradual typing based on abstract\n interpretation\, called Abstracting Gradual Typing (AGT for short).\n Gr adual languages designed with the AGT approach satisfy\, by\n constructi on\, the established criteria for gradually-typed languages.\n In this t alk\, I will give a brief introduction to AGT in a simply-typed\n settin g\, and will then discuss recent work on a gradual counterpart of\n Syst em F that enforces relational parametricity\, even in the presence\n of imprecise types. URL:https://chocola.ens-lyon.fr/events/meeting-2018-11-15/sessions/176/ END:VEVENT BEGIN:VEVENT SUMMARY:Henning Basold - Foundations for Corecursive Proof Search with Hor n Clauses DTSTART:20180920T153000 DTEND:20180920T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-09-20/sessions/172/ CATEGORIES: DESCRIPTION:Coinduction is a powerful definition\, programming and reasoni ng method\nthat can be applied in a variety of situations\, such as automa ta theory\,\nreactive systems\, modal logic\, potentially infinite data\,\ nnon-terminating computations etc. Typically\, coinduction is understood\n as the fact that bisimilarity implies equality in the denotational\nsemant ics. However\, coinduction can be extended to other predicates\nand relati ons on state-based systems\, thereby providing for general\ncoinductive pr ogramming and reasoning techniques.\n\nI will present in this talk foundat ions for recursive proof search in\ncoinductive Horn clause specifications \, aka coinductive logic programs.\nSuch specifications have a wide range of applications: coinductive\nprogramming\, type class resolution\, type c hecking and more. Because of\napplications like type class resolution\, we will focus on constructive\nmethods for proof search. In particular\, we will discuss a first-order\nintuitionistic sequent calculus with recursion for coinductive\npredicates\, a system of coinductive uniform proofs that will enable\nproof search\, and we will study the relation of these proof system to\neach other and to complete Herbrand models. URL:https://chocola.ens-lyon.fr/events/meeting-2018-09-20/sessions/172/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Geoffroy - Connecting degrees of parallelism and Boolean algebras through classical realizability DTSTART:20180920T140000 DTEND:20180920T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-09-20/sessions/173/ CATEGORIES: DESCRIPTION:Non-fully abstract models of PCF and related systems\n typic ally contain so-called non-sequential functions : for\n example\, Scott' s model of continuous functions has parallel or\, while\n Berry's stable functions have Gustave's function. Using constructs\n which come from K rivine's classical relizability (notably the\n characteristic Boolean al gebra Gimel 2)\, we show how these\n non-sequential functions and the qu estion of their relative strength\n (in terms of their ability to emulat e one-another) can be connected to\n the theory of Boolean algebras. URL:https://chocola.ens-lyon.fr/events/meeting-2018-09-20/sessions/173/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Streicher - How Unique are Ground Models DTSTART:20180920T103000 DTEND:20180920T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-09-20/sessions/174/ CATEGORIES: DESCRIPTION:Guided by basic topos theory we discuss the notion of "ground\ nmodel" and how unique it is. We describe a few negative results and finis h\nwith discussing why the question is open for classical realizability. URL:https://chocola.ens-lyon.fr/events/meeting-2018-09-20/sessions/174/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Padovani - Mailbox Types for Unordered Interactions DTSTART:20180517T153000 DTEND:20180517T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-05-17/sessions/168/ CATEGORIES: DESCRIPTION:We present a behavioral type system for reasoning on protocol\ nconformance in networks of processes that communicate through\nunordered mailboxes. This communication model is the one adopted by\nconcurrent obje cts and actors.\n\nIn sharp contrast with other behavioral types (session types in\nparticular)\, the type of a mailbox specifies which patterns of\ nmessages are supposed to be stored in - or retrieved from - a\nmailbox\, but not in which order. This allows the description of\nmailboxes concurre ntly accessed by several processes\, abstracting\naway from the state and behavior of the processes using them.\n\nThere seem to be analogies betwee n mailbox types and linear logic\nformulas\, as well as between the typing rules and the proof rules of\nclassical linear logic. With this seminar w e seek to initiate a\ndeeper investigation of these analogies.\n URL:https://chocola.ens-lyon.fr/events/meeting-2018-05-17/sessions/168/ END:VEVENT BEGIN:VEVENT SUMMARY:Florian Faissole - Synthetic topology in homotopy type theory for probabilistic programming DTSTART:20180517T140000 DTEND:20180517T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-05-17/sessions/170/ CATEGORIES: DESCRIPTION:The ALEA Coq library formalizes discrete measure theory\nusing a variant of the Giry monad\, as a submonad of the CPS monad:\n(A -> [0\, 1]) -> [0\,1]. This allows one to use Moggi's monadic \nmeta-language\nto give an interpretation of a language\, Rml\, into type theory. Rml is\na f unctional language with a primitive for probabilistic choice. This\nformal ization was the semantical basis for the Certicrypt system for \nverifying \nsecurity protocols. We improve on the formalization by using homotopy \n type\ntheory which provides e.g. quotients and functional extensionality. \nMoreover\,\nhomotopy type theory allows us to use synthetic topology to present a \ntheory\nwhich also includes "continuous" data types\, like [0\ ,1]. We also get a\nconstructive formalization of probabilistic programmin g.\n URL:https://chocola.ens-lyon.fr/events/meeting-2018-05-17/sessions/170/ END:VEVENT BEGIN:VEVENT SUMMARY:Tarmo Uustalu - A Coalgebraic View of Bar Recursion and Bar Induct ion DTSTART:20180517T103000 DTEND:20180517T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-05-17/sessions/157/ CATEGORIES: DESCRIPTION:We reformulate the bar recursion and induction principles in t erms of\nrecursive and wellfounded coalgebras. Bar induction was originall y\nproposed by Brouwer as an axiom to recover certain classically valid\nt heorems in a constructive setting. It is a form of induction on\nnon-wellf ounded trees satisfying certain properties. Bar recursion\,\nintroduced la ter by Spector\, is the corresponding function definition\nprinciple.\n\nW e give a generalization of these principles\, by introducing the notion\no f barred coalgebra: a process with a branching behaviour given by a\nfunct or\, such that all possible computations terminate.\n\nCoalgebraic bar rec ursion is the statement that every barred coalgebra\nis recursive\; a recu rsive coalgebra is one that allows definition of\nfunctions by a coalgebra -to-algebra morphism. One application of this\nprinciple is tabulation of continuous functions: Ghani\, Hancock and\nPattinson defined a type of we llfounded trees that represent\ncontinuous functions on streams. Bar recur sion allows us to prove that\nevery stably continuous function can be tabu lated to such a tree\,\nwhere by stability we mean that the modulus of con tinuity is its own\nmodulus.\n\nCoalgebraic bar induction states that ever y barred coalgebra is\nwellfounded\; a wellfounded coalgebra is one that a dmits proof by a\nform of induction.\n\nThis is joint work with Venanzio C apretta\, University of Nottingham\, \npublished in Proc. of FoSSaCS 2016. Time permitting\, I might also \ndiscuss our related ongoing work. URL:https://chocola.ens-lyon.fr/events/meeting-2018-05-17/sessions/157/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamie Vicary - Practical higher-dimensional algebra DTSTART:20180412T150000 DTEND:20180412T160000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-04-05/sessions/169/ CATEGORIES: DESCRIPTION: I report progress towards a new definition of ∞-category\nw hich provides a practical environment for direct computation\, and\ndemons trate an early version of the computer implementation.\n URL:https://chocola.ens-lyon.fr/events/meeting-2018-04-05/sessions/169/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Simon Lemay - Differential Algebras for Differential Categori es DTSTART:20180412T133000 DTEND:20180412T143000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-04-05/sessions/171/ CATEGORIES: DESCRIPTION:Differential categories were introduced by Blute\, Cockett\, a nd Seely to categorify Ehrhard and Regnier's differential linear logic and the differential lambda calculus. Since then\, differential categories ha ve lead to abstract formulations of many notions involving differentiation such as the directional derivative\, differential forms\, smooth manifold s\, De Rham cohomology\, etc. Therefore\, if the theory of differential ca tegories wishes to champion itself as axiomatizing the fundamentals of dif ferentiation: differential algebras should fit naturally in this story. In this talk\, we give an overview of the story of differential categories a nd introduce T-differential algebras\, which are generalization of differe ntial algebras for differential categories. We also discuss free and cofre e T-differential algebras\, and power series for differential categories.\ n URL:https://chocola.ens-lyon.fr/events/meeting-2018-04-05/sessions/171/ END:VEVENT BEGIN:VEVENT SUMMARY:Glynn Winskel - Distributed Probabilistic Strategies DTSTART:20180412T103000 DTEND:20180412T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-04-05/sessions/162/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/meeting-2018-04-05/sessions/162/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Mimram - Mechanized tools for higher categories DTSTART:20180315T153000 DTEND:20180315T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-03-15/sessions/166/ CATEGORIES: DESCRIPTION:Weak higher categories generalize the traditional notion of ca tegory by\ncomprising higher-dimensional cells and using those in order to provide\nwitnesses for structural axioms. Due to their very general natur e\, they are\ndifficult to manipulate and even to define. In this talk\, w e will present two\nrecently developed (theoretical and software) tools in order to assist the\nmathematician working with those structures. Firstly \, we will describe a type\ntheory whose models are precisely the globular categories\, thus providing a\nproof assistant in order to ensure the val idity of coherence laws in those\ncategories. Secondly\, we will generaliz e higher-dimensional rewriting techniques\nto Gray categories (a semi-stri ct variant of tricategories) in order to obtain\ncoherence results for alg ebraic structures in low dimensional weak categories.\n URL:https://chocola.ens-lyon.fr/events/meeting-2018-03-15/sessions/166/ END:VEVENT BEGIN:VEVENT SUMMARY:Bérénice Delcroix-Oger - Why operads can be seen as enhanced spe cies and what they are used for. DTSTART:20180315T140000 DTEND:20180315T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-03-15/sessions/167/ CATEGORIES: DESCRIPTION:Species have been introduced by Joyal in the 80s and are defin ed as functors (usually from the category of finite sets and bijections to itself)\, endowed with some operations. An operad can then be seen as a s pecies enhanced with a natural transformation. After an explanation\, with examples\, of these definitions\, I will give some examples illustrating the power of these notions\, especially concerning freeness of algebras.\n URL:https://chocola.ens-lyon.fr/events/meeting-2018-03-15/sessions/167/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcelo Fiore - An Algebraic Combinatorial Approach to the Abst ract Syntax of Opetopic Structures DTSTART:20180315T103000 DTEND:20180315T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-03-15/sessions/165/ CATEGORIES: DESCRIPTION: The starting point of the talk will be the identification o f structure\n common to tree-like combinatorial objects\, exemplifying t he situation\n with abstract syntax trees (as used in formal languages) and with\n opetopes (as used in higher-dimensional algebra). The emergin g\n mathematical structure will be then formalized in a categorical\n setting\, unifying the algebraic aspects of the theory of abstract\n syn tax and the theory of opetopes. This realization conceptually allows\n o ne to transport viewpoints between these\, now bridged\, mathematical\n theories and I will explore it here in the direction of\n higher-dimensi onal algebra\, giving an algebraic combinatorial framework\n for a gener alisation of the slice construction for generating opetopes.\n The techn ical work will involve setting up a microcosm principle for\n near-semir ings and subsequently exploit it in the cartesian closed\n bicategory of generalised species of structures. Connections to\n (cartesian and sym metric monoidal) equational theories\, type theory\,\n lambda calculus\, and algebraic combinatorics will be mentioned in\n passing.\n URL:https://chocola.ens-lyon.fr/events/meeting-2018-03-15/sessions/165/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Ehrhard - Stable and measurable functions on positive cones : a model of probabilistic functional languages with continuous types DTSTART:20180208T153000 DTEND:20180208T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-02-08/sessions/163/ CATEGORIES: DESCRIPTION:\nJoint work with Michele Pagani and Christine Tasson\n\nThe P robabilistic Coherence Space (PCS) model provides a denotational \nsemanti cs for probabilistic functional languages (with full recursion \nand recur sive types) where programs are interpreted as power series with \nnon-nega tive real coefficients. It has interesting properties (such as a \nFull Ab straction property)\, but seems to be essentially limited to \ndiscrete pr obabilities. To overcome this limitation\, we replace PCSs \nwith positive cones\, which generalize them quite naturally\, and power \nseries with S cott-continuous functions which are "stable" in a sense \nthat we will exp lain. A typical object of this new model is the cone of \nfinite measures on the real line which seems impossible to represent as \na PCS. Raphaëll e Crubillé has shown recently that this extension of the \nPCS model is c onservative.\n URL:https://chocola.ens-lyon.fr/events/meeting-2018-02-08/sessions/163/ END:VEVENT BEGIN:VEVENT SUMMARY:Justin Hsu - From Couplings to Probabilistic Relational Program Lo gics DTSTART:20180208T140000 DTEND:20180208T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-02-08/sessions/164/ CATEGORIES: DESCRIPTION:Many program properties are relational\, comparing the behavio r \nof a program (or even two different programs) on two different inputs. \nWhile researchers have developed various techniques for verifying such \nproperties for standard\, deterministic programs\, relational properties \nfor probabilistic programs have been more challenging. In this talk\, I \nwill survey recent developments targeting a range of probabilistic \nre lational properties\, with motivations from privacy\, cryptography\, \nmac hine learning. The key idea is to meld relational program logics with \nan idea from probability theory\, called a probabilistic coupling. The \nlog ics allow a highly compositional and surprisingly general style of \nanaly sis\, supporting clean proofs for a variety of probabilistic \nrelational properties.\n URL:https://chocola.ens-lyon.fr/events/meeting-2018-02-08/sessions/164/ END:VEVENT BEGIN:VEVENT SUMMARY:Prakash Panangaden - Quantitative Equational Logic DTSTART:20180208T103000 DTEND:20180208T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2018-02-08/sessions/161/ CATEGORIES: DESCRIPTION:Equational reasoning is a central part of mathematics. The tr aditional\ntheory links the equational logic and monads on the category of sets.\nMore precisely\, one can define an algebraic theory by giving a se t of\noperations and equations. One can then show that the collection of\ nalgebras defined by these equations form the algebras for a monad on the\ ncategory of sets. One has classical theorems like the completeness and\n variety theorems of Birkhoff. We consider a modified notion of equation\n where the equality symbol is annotated with a real number so we can\nwrite s =_e t with the interpretation that the terms "s" and "t" are\nwithin "e " of each other. We develop the metatheory and obtain\nanalogues of Birkh off's theorem. Furthermore\, we show that this\nextended notion of equati onal definition yields algebras of monads on\nthe category of metric space s. What makes the theory interesting is the\nfact that well known metric spaces of probability distributions can be\ndefined by such equations.\n\n This is joint work with Radu Mardare and Gordon Plotkin. URL:https://chocola.ens-lyon.fr/events/meeting-2018-02-08/sessions/161/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Krivine - Incremental Update for Graph Rewriting DTSTART:20171214T153000 DTEND:20171214T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-12-14/sessions/160/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/meeting-2017-12-14/sessions/160/ END:VEVENT BEGIN:VEVENT SUMMARY:Kenji Maillard - F*\, from practice to theory DTSTART:20171214T140000 DTEND:20171214T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-12-14/sessions/158/ CATEGORIES: DESCRIPTION:F* is a programming language as well as a proof-assistant putt ing a strong\nemphasis on practical verification of effectful programs. In order to enable the\nverification of security critical programs such as c ryptographic primitives\n(HACL*) or protocols (TLS in MiTLS)\, F* provides a rich logic with dependent\ntypes and universes\, an effect-based weakes t precondition calculus and an\nsmt-automation backend. In this presentati on\, we will present how these\ningredients are used in actual program ver ification and then give an account of\ntheir metatheoretical aspects.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-12-14/sessions/158/ END:VEVENT BEGIN:VEVENT SUMMARY:François Pottier - Looking back on Mezzo: experience and metathe ory DTSTART:20171214T103000 DTEND:20171214T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-12-14/sessions/159/ CATEGORIES: DESCRIPTION:Mezzo is (a proposal for) a programming language equipped with an expressive\ntype-and-permission system. Like ML\, it is a high-level p rogramming \nlanguage\,\nequipped with algebraic data types\, first-class functions\, polymorphism\,\ngarbage collection\, etc. Its main innovation\ , in comparison with ML\, is its\naffine type-and-permission system\, whic h does not just describe the \nstructure\nof data\, but controls who has p ermission to read or write\, and allows types\n(and permissions) to evolve over time. In this talk\, I would like to give an\ninformal overview of M ezzo's main design principles\, followed with a more\ntechnical look at Me zzo's metatheory. The proof of type soundness\, which has\nbeen verified i n Coq\, is first carried out for a core affine \nlambda-calculus\,\nthen e xtended with three independent features\, namely affine references\,\nlock s\, and adoption-and-abandon.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-12-14/sessions/159/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Seiller - Towards a geometric theory of computation(al comp lexity) DTSTART:20171109T153000 DTEND:20171109T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-11-16/sessions/156/ CATEGORIES: DESCRIPTION:The purpose of this talk is to explain a new approach to compl exity theory\nbased on (dynamic) semantics of linear logic\, whose aim is to enable\ntechniques and invariants from ergodic theory (e.g. l^2-Betti n umbers of a\ncountable Borel equivalence relation) to be used in computati onal complexity.\n\nThe origins of the techniques can be traced to Girard' s “geometry of\ninteraction” (GoI) program using von Neumann algebras and the recent\nGoI-inspired results in complexity. However\, this approac h reaches its full\nstrength when using the more combinatorial setting of Interaction Graphs\nmodels of (fragments of) linear logic. Using technique s akin to game semantics\n(with a bit of measure theory)\, we are able to characterise (predicate)\ncomplexity classes as the set of programs/proofs interpretations of type\nPred[m] := Nat ⇒ Bool. These models are parame trised by a group of\nmeasure-preserving maps m (equivalently\, by a measu rable group action) and\nprovide the first sketches of a conjectured corre spondence between measurable\ngroup/monoid actions and complexity constrai nts.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-11-16/sessions/156/ END:VEVENT BEGIN:VEVENT SUMMARY:Jules Chouquet - A result concerning the size of proof-nets\, and two applications DTSTART:20171109T140000 DTEND:20171109T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-11-16/sessions/152/ CATEGORIES: DESCRIPTION:We study the behaviour of the cut elimination in differential linear logic proof nets (without exponential boxes). \n \nSometimes\, we w ant to consider parallel reduction\, that fires as much cuts as wanted in the net\, but doing so\, we are not able to bound the loss of size in one step of reduction. We propose a method (adapted from a Lionel Vaux techniq ue in lambda calculus) where\, recovering a kind of geometric invariant in proof nets\, allows us to manage this loss of size. We are then able\, wi th well-chosen informations\, to bound the size of all possible antireduct s of a given net.\n\nThis result leads to others\, since the notion of inv ariance we're dealing with can be applied to infinite sets of structures\, like the Taylor expansions of nets. In this setting\, we deduce from the geometrical considerations above\, an interesting finiteness result having at least two nice applications : one concerning the simulation of the exp onential cut-elimination in MELL\; one concerning a normalization by evalu ation method in connected MELL proof-nets. \n URL:https://chocola.ens-lyon.fr/events/meeting-2017-11-16/sessions/152/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Fontanella - Realizability: from Curry-Howard to forcing DTSTART:20171109T103000 DTEND:20171109T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-11-16/sessions/151/ CATEGORIES: DESCRIPTION:Realizability studies the computational content of proofs by d efining a\ncorrespondence between the formulas of a logical system and pro grams in such a\nway that knowledge of the “realizers” (i.e. the progr ams associated with the\nformula) gives information about the proof of the formula. The Curry-Howard\nisomorphism establishes a correspondence betwe en proofs of intuitionistic\nlogic formulas and programs seen as lambda-te rms. The scope of Realizability\nwas later extended to classical logic tha nks to the work by Griffin on typing\noperators. Thanks to Krivine\, resea rch in realizability further evolved to\nencompass proofs in set theory. T he technique developed by Krivine generalizes\nthe method of forcing in se t theory\, in fact forcing models are special cases\nof realizability mode ls. This talk\nis meant as a gentle introduction to Forcing from the point of view of\nclassical realizability.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-11-16/sessions/151/ END:VEVENT BEGIN:VEVENT SUMMARY:Damiano Mazza - A Tour Around Polyadic Approximations DTSTART:20171012T153000 DTEND:20171012T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-12-10/sessions/154/ CATEGORIES: DESCRIPTION:The notion of polyadic approximation originates in Girard's ve ry first \npaper on linear logic\, where it is proved that intuitionistic (and \nclassical) theorems may be approximated arbitrarly well by purely l inear \ntheorems\, i.e.\, theorems in what is technically called multiplic ative \nadditive linear logic (or the internal language of symmetric monoi dal \nclosed categories with finite products and coproducts). We will exp ore \nthe consequences of taking this idea seriously\, in particular exten ding \nit all the way up to cut-elimination/computation sequences (rather than \njust formulas/types or proofs/programs). The resulting theory\, wh ich is \ndeveloped in the context of higher multicategories\, is quite ric h and \nhas far reaching applications\, inspiring in particular a type-the oretic \nproof of the Cook-Levin theorem (the result stating that SAT is \ nNP-complete). URL:https://chocola.ens-lyon.fr/events/meeting-2017-12-10/sessions/154/ END:VEVENT BEGIN:VEVENT SUMMARY:Luc Pellissier - Linear approximations\, intersection types and th e Grothendieck construction DTSTART:20171012T140000 DTEND:20171012T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-12-10/sessions/153/ CATEGORIES: DESCRIPTION:\nGeneral (intuitionistic or classical) proofs can be approxim ated arbitrarily\nwell by linear proofs\, that is\, proofs that use each o f their premises exactly\nonce. In this work\, we show that such linear ap proximations give rise\, through\nan adapted Grothendieck construction\, t o intersection type systems for any\nlogical system that can be embed mean ingfully into linear logic.\n\nWe recover in this way all well-known inter section type systems\, capturing\ndifferent notions of normalization for v arious languages\, and give a blueprint\nto compute new ones.\n\nJoint wor k with Damiano Mazza and Pierre Vial.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-12-10/sessions/153/ END:VEVENT BEGIN:VEVENT SUMMARY:André Joyal - Opérades et 2-géométrie algébrique DTSTART:20171012T103000 DTEND:20171012T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-12-10/sessions/155/ CATEGORIES: DESCRIPTION:Plusieurs notions de base de l'algèbre commutative\net de la géométrie algébrique ont un analogue en théorie des catégories. \nCes analogies sont utiles pour comprendre certains résultats de la théorie des opérades. \nPar exemple\, on sait que la bi-catégorie des bimodules entre opérades symétriques\nest cartésienne fermée (Fiore-Gambino-Hyla nd-Wynskel\, Gambino-Joyal). Ce résultat signifie essentiellement \nque l e 2-schéma associé à une opérade est exponentiable.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-12-10/sessions/155/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Blot - An interpretation of system F through bar recursio n DTSTART:20170629T153000 DTEND:20170629T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-06-15/sessions/150/ CATEGORIES: DESCRIPTION:\n\nThere are two possible computational interpretations of se cond-order\narithmetic: Girard's system F or Spector's bar recursion and i ts\nvariants. While the logic is the same\, the programs obtained from the se\ntwo interpretations have a fundamentally different computational\nbeha vior and their relationship is not well understood. We make a step\ntoward s a comparison by defining the first translation of system F into\na simpl y-typed total language with a variant of bar recursion. This\ntranslation relies on a realizability interpretation of second-order\narithmetic. Due to Gödel's incompleteness theorem there is no proof of\ntermination of sy stem F within second-order arithmetic. However\, for\neach individual term of system F there is a proof in second-order\narithmetic that it terminat es\, with its realizability interpretation\nproviding a bound on the numbe r of reduction steps to reach a normal\nform. Using this bound\, we comput e the normal form through primitive\nrecursion. Moreover\, since the norma lization proof of system F proceeds\nby induction on typing derivations\, the translation is compositional.\nThe flexibility of our method opens the possibility of getting a more\ndirect translation that will provide an al ternative approach to the\nstudy of polymorphism\, namely through bar recu rsion.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-06-15/sessions/150/ END:VEVENT BEGIN:VEVENT SUMMARY:Marie Kerjean - Smooth models of Differential Linear Logic DTSTART:20170629T140000 DTEND:20170629T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-06-15/sessions/149/ CATEGORIES: DESCRIPTION:While Linear Logic has been from the start strongly tied to al gebra\, it \nis only the later introduction of Differential Linear Logic ( DiLL) that \nsuggested similar ties with analysis. DiLL extends Linear Log ic with \ndifferentiation\, an operation which extracts a linear proof fro m a \nnon-linear one. In this talk\, I will present several models of DiLL \ninterpreting formulas as topological vector spaces and proofs as smooth \nfunctions\, thus strenghtening the analogy with (functional) analysis.\ nI will explain a work with Y. Dabrowski highlighting how with a well \nch osen Mackey duality and under a specific completeness assumption\, the \nm ultiplicative disjunction of LL corresponds to epsilon product of \nSchwar tz. As opposed to the purely algebraic case\, we can identify this \nconne ctive with a well-known mathematical object.\nI will present a classical p olarized model of a version of DiLL without \npromotion\, where formulas a re interpreted as nuclear spaces and where \nexponentials are interpreted as spaces of distributions. This models \nargues for a smooth Differential Linear Logic which\, I will explain\, \nhints for a type theory of differ ential equations.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-06-15/sessions/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Gaboardi - A semantic account of metric preservation in pres ence of probabilities. DTSTART:20170629T103000 DTEND:20170629T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-06-15/sessions/148/ CATEGORIES: DESCRIPTION:Program sensitivity measures how robust a program is to small changes in its input\, and is a fundamental notion in domains ranging from differential privacy to cyber-physical systems. A natural way to formaliz e program sensitivity is in terms of metric preservation with respect to t he metrics on the input and output spaces: requiring that an r-sensitive f unction maps inputs that are at distance d to outputs that are at distance at most r*d. \nI will present some recent work where we started the study of program sensitivity and metric preservation from a denotational point of view. I will introduced metric CPOs\, a novel semantic structure for re asoning about computation on metric spaces\, by endowing CPOs with a compa tible notion of distance. This structure is useful for reasoning about met ric properties of programs\, and specifically about program sensitivity an d metric preservation. I will then discuss how to extend this structure to account for metrics over probability distributions. In particular\, I wil l discuss how these metrics can be used to guarantee programs differential ly private.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-06-15/sessions/148/ END:VEVENT BEGIN:VEVENT SUMMARY:Christine Tasson - Probabilistic Call by Push Value DTSTART:20170511T153000 DTEND:20170511T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-05-11/sessions/147/ CATEGORIES: DESCRIPTION:We introduce a probabilistic extension of Levy’s Call-By-Pus h-Value. This\nextension consists simply in adding a “flipping coin” b oolean closed atomic expression.\nThis language can be understood as a maj or generalization of Scott’s PCF encompassing\nboth call-by-name and cal l-by-value and featuring recursive (possibly lazy) data types. We\ninterpr et the language in the previously introduced denotational model of probabi listic coherence spaces\, a categorical model of full classical Linear Log ic\, interpreting data types as\ncoalgebras for the resource comonad. We p rove adequacy and full abstraction\, generalizing\nearlier results to a mu ch more realistic and powerful programming language.\n\nThis is joint work with Thomas Ehrhard. URL:https://chocola.ens-lyon.fr/events/meeting-2017-05-11/sessions/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Marie Pédrot - An Effectful Way to Eliminate Addiction to Dependence DTSTART:20170511T140000 DTEND:20170511T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-05-11/sessions/140/ CATEGORIES: DESCRIPTION: \nWe define a syntactic monadic translation of type theory\,\ ncalled the weaning translation\, that allows for a large range of effects \nin dependent type theory\, such as exceptions\, non-termination\,\nnon-d eterminism or writing operation. Through the light of a\ncall-by-push-valu e decomposition\, we explain why the traditional\napproach fails with type dependency and justify our approach.\nCrucially\, the construction requir es that the universe of algebras\nof the monad forms itself an algebra. Th e weaning translation\napplies to a version of the Calculus of Inductive C onstructions\nwith a restricted version of dependent elimination\, dubbed Baclofen Type\nTheory\, which we conjecture is the proper generic way to m ix effects and\ndependence. This provides the first effectful version of C IC\, which can\nbe implemented as a Coq plugin.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-05-11/sessions/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Blain Levy - Contextual isomorphisms DTSTART:20170511T103000 DTEND:20170511T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-05-11/sessions/139/ CATEGORIES: DESCRIPTION:\nWhat is the right notion of "isomorphism" between types\, in a simple type theory? The traditional answer is: a pair of terms that are inverse\, up to a specified congruence. We firstly argue that\, in the p resence of effects\, this answer is too liberal and needs to be restricted \, using Fuehrmann's notion of thunkability in the case of value types (as in call-by-value)\, or using Munch-Maccagnoni's notion of linearity in th e case of computation types (as in call-by-name). Yet that leaves us with different notions of isomorphism for different kinds of type.\n\nThis sit uation is resolved by means of a new notion of ``contextual'' isomorphism (or morphism)\, analogous at the level of types to contextual equivalence of terms. A contextual morphism is a way of replacing one type with the o ther wherever it may occur in a judgement\, in a way that is preserved by the action of any term with holes. For types of pure $\\lambda$-calculus\ , we show that a contextual morphism corresponds to a traditional isomorph ism. For value types\, a contextual morphism corresponds to a thunkable i somorphism\, and for computation types\, to a linear isomorphism.\n\nThe r esults are most easily formulated in the setting of call-by-push-value\, w hich we briefly introduce during the talk. This is a fine-grained effectf ul calculus that subsumes call-by-value and call-by-name and distinguishes values from computations and value types from computation types. \n URL:https://chocola.ens-lyon.fr/events/meeting-2017-05-11/sessions/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Yves Strub - Proving Differential Privacy via Probabilistic Couplings DTSTART:20170413T153000 DTEND:20170413T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-04-13/sessions/145/ CATEGORIES: DESCRIPTION:Couplings are a powerful mathematical tool for reasoning about pairs\nof probabilistic processes. Recent developments in formal verifica tion\nidentify a close connection between couplings and pRHL\, a relationa l\nprogram logic motivated by applications to provable security\, enabling \nformal construction of couplings from the probability theory\nliterature . However\, existing work using pRHL merely shows existence\nof a coupling and does not give a way to prove quantitative properties\nabout the coupl ing\, needed to reason about mixing and convergence of\nprobabilistic proc esses. Furthermore\, pRHL is inherently incomplete\,\nand is not able to c apture some advanced forms of couplings such as\nshift couplings.\n\nIn th is talk\, after having introduced pRHL\, I will present an\nextension of p RHL\, which explicitly constructs the coupling in a pRHL\nderivation in th e form of a probabilistic product program that\nsimulates two correlated r uns of the original program. Existing\nverification tools for probabilisti c programs can then be directly\napplied to the probabilistic product to p rove quantitative properties\nof the coupling. Moreover\, this extension c an be equipped with a new\nrule for while loops\, where reasoning can free ly mix synchronized and\nunsynchronized loop iterations\, making the logic relatively complete\nfor deterministic programs.\n\nLast\, I will show ho w the notion of couplings can be extended to\napproximate lifting\, a nota tion this captures a compositional\nabstraction for proving differential p rivacy. (Differential privacy is\na promising formal approach to data priv acy\, which provides a\nquantitative bound on the privacy cost of an algor ithm that operates\non sensitive information.)\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-04-13/sessions/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Leventis - Full abstraction of the probabilistic Böhm tree s DTSTART:20170413T140000 DTEND:20170413T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-04-13/sessions/144/ CATEGORIES: DESCRIPTION:A very natural notion of equivalence of programs is the observ ational\n equivalence: two programs are equivalent if they have the sam e behaviour in\n any environment. More specifically in the lambda-calcu lus two terms M and N\n are equivalent if for every context C\, the ter ms C[M] and C[N] are either\n both solvable or both unsolvable. Respect ing this equivalence is an\n important property of some models of the l ambda-calculus\, called the full\n abstraction. It is well known that t he model of infinitely extensional Böhm\n trees is fully abstract. The question we are interested in is what becomes\n of these notions when we introduce probabilistic choice in the calculus.\n\nThe solvability has a natural extension\, which is the convergence\n probability\, hence tw o terms are observationally equivalent if they have\n the same converge nce probability under any context. There is also a simple\n way to defi ne probabilistic Bohm trees\, as we can associate to any term a\n subpr obability distribution over head normal forms. But it is not obvious\n that these generalizations of the deterministic notions are still\n equ ivalent. In this talk we will show how to prove that probabilistic Böhm\n trees actually form a model\, and how to get a separability result to ensure\n this model is fully abstract.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-04-13/sessions/144/ END:VEVENT BEGIN:VEVENT SUMMARY:Jérémie Chalopin - Un contre-exemple à la conjecture de Thiagar ajan sur les structures d'évènements régulières DTSTART:20170413T103000 DTEND:20170413T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-04-13/sessions/146/ CATEGORIES: DESCRIPTION:On présente un contre-exemple à la conjecture de Thiagarajan (1996 et 2002)\naffirmant que les structures d'évènements régulières correspondent exactement\nà celles obtenues comme dépliages des réseaux de Petri 1-safe finis.\nLes structures d'évènements\, les automates de trace sont des modèles\nfondamentaux pour la théorie de la concurrence. Il existe des interprétations\nélégantes de ces structures comme des ob jets combinatoires et géométriques\, et\non peut reformuler la conjectur e dans ce cadre. Plus précisément\, les domaines\ndes structures d'évè nements correspondent exactement aux graphes médians\npointés et aux com plexes cubiques CAT(0) pointés.\nUne condition nécessaire pour que la co njecture de Thiagarajan soit vérifiée\nest que les domaines des structur es d'évènements régulières admettent un joli\nétiquetage régulier (r egular nice labelling). Pour réfuter cette conjecture\,\non décrit le do maine d'une structure d'évènement régulière qui n'admet pas de\ntel é tiquetage. Notre contre-exemple est basé sur une construction de Wise\n(1 996 et 2007) d'un complexe de carrés de courbure non-positive dont le\nre vêtement universel est un complexe de carrés CAT(0) contenant un plan mu ni\nd'un pavage apériodique. URL:https://chocola.ens-lyon.fr/events/meeting-2017-04-13/sessions/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Mio - Riesz Modal Logic for Markov Processes DTSTART:20170309T153000 DTEND:20170309T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-03-09/sessions/141/ CATEGORIES: DESCRIPTION:We investigate a modal logic for expressing properties of Mark ov processes whose semantics is real-valued\, rather\nthan Boolean\, and b ased on the mathematical theory of Riesz\nspaces. We use the duality theor y of Riesz spaces to provide a\nconnection between Markov processes and th e logic. This takes\nthe form of a duality between the category of coalgeb ras of the\nRadon monad (modeling Markov processes) and the category of\na new class of algebras (algebraizing the logic) which we call\nmodal Riesz spaces. As a result\, we obtain a sound and complete\naxiomatization of t he Riesz Modal logic.\n\nThis is joint work with Robert Furber and Radu Ma rdare. URL:https://chocola.ens-lyon.fr/events/meeting-2017-03-09/sessions/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Paquet - Concurrent game semantics for Probabilistic PCF and relational collapse DTSTART:20170309T140000 DTEND:20170309T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-03-09/sessions/142/ CATEGORIES: DESCRIPTION:We introduce the concurrent game semantics of Probabilistic PC F (PPCF). \nThe model consists of concurrent strategies based on event str uctures \nwith symmetry\, extending with probability a model of Castellan\ , \nClairambault and Winskel.\n\nWe "collapse" this model to the weighted relational model of PPCF \n(Pagani et al)\, by forgetting the execution hi story of programs\; we \nretain only the states reached by terminated exec utions. Usually such \noperations on strategies are only lax-functorial\, but we will see that \nterms of PPCF satisfy a condition called 'visibilit y'\, which ensures \nthat no deadlock arise in their composition\, and hen ce that the collapse \nto weighted relations is functorial.\n\nBecause pro babilistic relations are fully abstract for PPCF\, we obtain \nvia the col lapse that concurrent games are also (intensionally) fully \nabstract.\n\n (Joint work with Simon Castellan\, Pierre Clairambault & Glynn Winskel)\n\ n URL:https://chocola.ens-lyon.fr/events/meeting-2017-03-09/sessions/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoît Valiron - A Geometry of Interaction for Quantum Computatio n DTSTART:20170309T103000 DTEND:20170309T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-03-09/sessions/143/ CATEGORIES: DESCRIPTION:This tutorial will present a low-level operational model for\n higher-order quantum computation\, using Geometry of Interaction as\nframe work. The plan of the the session is a follows. In a first part\,\nwe shal l see what is quantum computation\, and how a suitably typed\nquantum lamb da-calculus can relate to linear logic. In a second\nindependent part\, we shall recap what is a proof-net\, and describe the\ntwo operational seman tics on proof-nets relevant to this talk: the\nfirst one using graph rewri ting\, the other using tokens flowing in the\ngraph (aka what we call Geom etry of Interaction). In the third and\nlast part of the talk\, we shall d iscuss how to merge the two\nconstructions\, to see how to get a quantum G eometry of\nInteraction. The construction is modular: we shall see how to add\nprobabilistic behavior to proof-nets\, how to augment them with\nregi sters\, and how to deal with the synchronization required for\nquantum com putation. If time permits\, we'll discuss an algebraic\npresentation of me mory using nominal sets that is amenable to other\ncomputational models.\n \nThis presentation will assume basic knowledge of\n\n - sequent calculus\ n - lambda-calculus\n - linear logic\n - (some) notion of linear algebra\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-03-09/sessions/143/ END:VEVENT BEGIN:VEVENT SUMMARY:Olivier Laurent - On the Proof Theory of BCD Intersection Subtypin g DTSTART:20170209T153000 DTEND:20170209T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-02-09/sessions/137/ CATEGORIES: DESCRIPTION:In their 1983 paper\, Barendregt\, Coppo and Dezani-Ciancaglin i defined an intersection type system\, now known under the name BCD. This system relies on a subtyping relation\, and most of the properties of BCD typing are related with properties of BCD subtyping. We thus focus on the study of BCD subtyping.\n\nBy understanding the BCD subtyping relation as a deduction relation\, we propose to look at it from a proof-theoretical point of view.\nWe give a sequent calculus presentation IS of BCD subtypin g and study its core properties: cut-elimination\, sub-formula property\, rule inversions\, beta condition\, etc.\nThanks to a Girard's style transl ation of IS\, we prove that BCD subtyping can be seen as a fragment of Lam bek's calculus.\nFinally we address ongoing work on the computational comp lexity of BCD subtyping\, as well as alternative presentations and possibl e extensions. URL:https://chocola.ens-lyon.fr/events/meeting-2017-02-09/sessions/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Scherer - Full abstraction for language design DTSTART:20170209T140000 DTEND:20170209T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-02-09/sessions/138/ CATEGORIES: DESCRIPTION:A transformation between languages is fully abstract if it\npr eserves observational equivalence. Full abstraction has been\nproposed as a desirable formal property of compilers:\na fully-abstract compiler guara ntees that the semantics of the\nlow-level target language does not leak i nto source programs.\n\nAbstraction leaks are also usability issues. Multi -language\nprogramming systems are widely used\, but often exhibit\nunfort unate\, unplanned interactions. We propose to use full\nabstraction for *l anguage design*: if the embedding of a single\nlanguage into the multi-lan guage system is fully abstract\, we\nknow that it interacts gracefully wit h the other languages of the\nsystem.\n\nWe demonstrate our approach by a case study\, of a proposed\nmulti-language design that combines a simple M L language with\na linear language with linear mutable state. We prove tha t\nprogrammers knowing only the ML side of the story will not have\nbad su rprises when interacting with code that may\, internally\,\nuse the linear language.\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-02-09/sessions/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Danko Ilic - Exp-log normal form of types and formulas DTSTART:20170209T103000 DTEND:20170209T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/meeting-2017-02-09/sessions/136/ CATEGORIES: DESCRIPTION:In this lecture\, we will look at the decomposition of the arr ow type\n(i.e. intuitionistic implication) in terms of unary exponentiatio n and\nlogarithm\, and show some applications of it.\n\nWe will start by r ecalling the notion of type isomorphism\, reviewing\nthe meta-theoretic fa cts that hold of it in presence of disjoint union\ntypes.\n\nWe shall then show that it makes sense to use the transformation\naᵇ=exp(b·log(a)) i n the context of types by defining a normal form for\nthe type language { →\,×\,+} and applying it to obtain a simplification\nof the standard ax ioms of η-equality for the {→\,×\,+}-typed λ-calculus.\n\nWe shall en d by hinting at proof theoretic applications. In\nparticular\, we shall sh ow how to extend the type normal form to the\nfirst-order quantifiers and define a constructive arithmetical\nhierarchy of formulas resembling the c lassical arithmetical hierarchy.\n\n\n\n \n\n\n URL:https://chocola.ens-lyon.fr/events/meeting-2017-02-09/sessions/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Blot - Hybrid realizability for intuitionistic and classi cal choice DTSTART:20161013T153000 DTEND:20161013T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-10-13/sessions/135/ CATEGORIES: DESCRIPTION:In intuitionistic realizability like Kleene's or Kreisel's\, t he axiom\nof choice is trivially realized. It is even provable in Martin-L \\"of's\nintuitionistic type theory. In classical logic\, however\, even t he\nweaker axiom of countable choice proves the existence of non-computabl e \nfunctions. This logical strength comes at the price of a complicated\n computational interpretation which involves strong recursion schemes\nlike bar recursion. We take the best from both worlds and define a\nrealizabil ity model for arithmetic and the axiom of choice which\nencompasses both i ntuitionistic and classical reasoning. In this model\ntwo versions of the axiom of choice can co-exist in a single proof:\nintuitionistic choice and classical countable choice. We interpret\nintuitionistic choice efficient ly\, however its premise cannot come from\nclassical reasoning. Conversely \, our version of classical choice is\nvalid in full classical logic\, but it is restricted to the countable\ncase and its realizer involves bar rec ursion. Having both versions\nallows us to obtain efficient extracted prog rams while keeping the\nprovability strength of classical logic.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-10-13/sessions/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Peressotti - Coalgebraic Semantics of Self-Referential Behav iours DTSTART:20161013T140000 DTEND:20161013T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-10-13/sessions/134/ CATEGORIES: DESCRIPTION:We investigate the semantics of systems which can refer to the mselves\,\ne.g.\, by “passing around" systems of the same kind as values (hence\npotential observables). For this reason\, we refer to these syste ms as\nself-referential. Instances of this scenario are higher-order calcu li\nlike the λ-calculus\, the calculus of higher-order communicating\nsys tems (CHOCS)\, the higher-order π-calculus (HOπ)\, HOcore\, etc. It is\n well known that higher-order systems pose unique challenges and are\ndiffi cult to reason about. Many bisimulations and proof methods have\nbeen prop osed also in recent works. This ongoing active effort points\nout that a d efinition of abstract self-referential behaviour is still\nelusive.\n\nWe address these difficulties by providing an abstract\ncharacterisation of s elf-referential behaviours as self-referential\nendofunctors\, i.e. functo rs whose definition depends on their own\nfinal coalgebra. The constructio n of these functors is not trivial\,\nsince they must be defined at once w ith their own final coalgebra and\ndue to the presence of both covariant a nd contravariant dependencies\n(e.g. arising from higher-order inputs). We provide such a\nconstruction.\n\nSimilarly defined endofunctors arise fro m considering as object\nsystems (i.e.\, those which can be values) only c ertain subclasses of\nsystems (usually via some syntactic restriction) or a syntactic representations (cf. higher-order process algebras): self-refe rential endofunctors are\nshown to be universal among them. Universality r enders\nself-referential endofunctors a touchstone for similar behavioural \nfunctors and offers the mathematical structure for assessing soundness\n and completeness of other models via properties of the associated\nunivers al morphisms.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-10-13/sessions/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Laird - Weighted Models for Computation and Communication DTSTART:20161013T103000 DTEND:20161013T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-10-13/sessions/133/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2016-10-13/sessions/133/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Hyvernat - Using the Size-Change Principle for checking tot ality of recursive definitions DTSTART:20160922T153000 DTEND:20160922T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-09-22/sessions/131/ CATEGORIES: DESCRIPTION:The Size-Change Principle (SCP) is a simple algorithm giving a partial \ntermination test for recursive definitions. It is particularly well \nsuited for functional languages with inductive types where recursiv e \nfunctions are given by pattern matching (Caml / Coq) or equations \n(H askell / Agda).\n\nIf term constructors are lazy\, the SCP also gives (by duality) a partial \nproductivity test for recursive functions involving c oinductive types. \nThis is what is used in Agda.\n\nUnfortunately\, when inductive and coinductive types are nested\, this \ntest is unsound: there are "well typed" and terminating recursive \ndefinitions producing terms in empty types. Such definitions make Agda \ninconsistant.\n\nBy using ide as from L. Santocanale about circular proof and parity \ngames\, I'll show how the SCP can be used to check "totality" of \nrecursive definitions to make sure the definition denote actual objects \nin their type. URL:https://chocola.ens-lyon.fr/events/seminaire-2016-09-22/sessions/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Guilhem Jaber - SyTeCi: Symbolic\, Temporal and Circular reasonin g for automatic proofs of contextual equivalence DTSTART:20160922T140000 DTEND:20160922T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-09-22/sessions/132/ CATEGORIES: DESCRIPTION: Circular reasoning for automatic proofs\n of contextual eq uivalence\n Operational Techniques (Kripke Logical Relations and\n Env ironmental/Open/Parametric Bisimulations) have matured enough to\n becom e now formidable tools to prove contextual equivalence of\n effectful hi gher-order programs. However\, it is not yet possible to\n automate such proofs -- the problem being of course in general\n undecidable.\n\n I n this talk\, we will see how to take the best of these techniques to\n design an automatic procedure which is able many non-trivial examples\n of equivalence\, including most of the examples from the literature.\n T he talk will describe the main ingredients of this method:\n\n - Symboli c reduction to evaluate of programs\,\n\n - Transition systems of heap i nvariants\, as used with Kripke Logical\n Relations\,\n\n - Temporal l ogic to abstract over the control flow between the program\n and its env ironment\,\n\n - Circular proofs to automate the reasoning over recursiv e functions.\n Using them\, we will see how we can reduce contextual equ ivalence to the\n problem of non-reachability in some automatically gene rated transition\n systems of invariants.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-09-22/sessions/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Henning Basold - Dependent Inductive-Coinductive Types: Category T heoretical and Syntactic Perspectives DTSTART:20160922T103000 DTEND:20160922T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-09-22/sessions/130/ CATEGORIES: DESCRIPTION:Dependent types have been pioneered by Per Martin-Löf as a fo rmal\nframework to carry out intuitionistic mathematics. The major feature of\ndependent type theories is that definitions\, computations and proofs are\ngiven in the same language. Moreover\, correctness checking of proof s\namounts to type-checking\, which is well understood. The latter require s\nthough that the associated reduction relation is strongly normalising o n\nall terms a type can depend on\, so to obtain an actual algorithm for\n type checking.\n\nMost formal type systems with dependent types allow the use of inductive\ntypes\, among other base types\, to carry out actually i nteresting\nmathematics. Inductive types have been studied vastly in this context\,\nand we know precisely how to incorporate them into dependent ty pe\nsystems with a strongly normalising reduction relation. On the other\n hand\, in computer science\, but also in mathematics\, we frequently\nenco unter (possibly) infinite computations that are nevertheless\nwell-defined . The concept that emerged to accommodate infinite\ncomputations is that o f coinductive types. The really interesting\nexamples arise though from th e mix of inductive and coinductive types\,\nwhich has hardly been investig ated in the context of dependent type\ntheories.\n\nIn this talk\, I will present first a category theoretical perspective on\ndependent type theori es that are solely based on mixed\ninductive-coinductive types. Such theor ies allow us to encode\nintuitionistic logic as inductive or coinductive t ypes. Vice versa\, we\nalso show that dependent inductive-coinductive type s can be constructed\nin categories with enough structure just from non-de pendent inductive\ntypes. We then use this high level perspective to set u p a syntactic\ncalculus with inductive-coinductive types. For this calculu s we will\nprove that its associated reduction relation preserves types an d is\nstrongly normalising. Finally\, if time permits\, we might discuss f uture\ndirections of how to internalise bisimilarity on coinductive types into\nthe calculus\, while retaining decidable type checking.\n\nThe categ ory theoretical view is based on a paper I presented at\nFICS 2015\, where as the calculus and its properties are joint work with\nHerman Geuvers pre sented at LICS 2016.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-09-22/sessions/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Streicher - Effective Spectral Theorem for Bounded Self Ad joint Operators (tbc) DTSTART:20160609T153000 DTEND:20160609T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-06-09/sessions/129/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2016-06-09/sessions/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Brunerie - Examples of closed natural numbers in homotop y type theory DTSTART:20160609T140000 DTEND:20160609T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-06-09/sessions/127/ CATEGORIES: DESCRIPTION:Homotopy type theory (HoTT) is usually presented as Martin-Lö f’s\ndependent type theory together with Voevodsky’s univalence axiom and\nvarious other axioms for higher inductive types. In particular\, the\ npresence of axioms makes it non-constructive in that one can find\nclosed terms of type ℕ which do not reduce to canonical natural\nnumbers. But with Thierry Coquand’s constructive cubical model\, it\nbecomes possible to compute with univalence and higher inductive\ntypes. In this talk\, I will present various examples of such closed\nnatural numbers that we woul d like to compute\, extracted from the\nproof of π₄(S³)=ℤ/2ℤ in Ho TT that I recently completed.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-06-09/sessions/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Thierry Coquand - Une justification de l’axiome d’univalence DTSTART:20160609T103000 DTEND:20160609T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-06-09/sessions/128/ CATEGORIES: DESCRIPTION:\nLes travaux de Voevodsky suggèrent une extension de la thé orie des types dependents qui résout certains problèmes de modularité ( égalité extensionelle et quotients). Un problème est que la justificati on de cette extension est développée en utilisant le tiers-exclu et l’ axiome du choix. Nous présentons un modele de cette extension dans un cad re constructif\, et qui peut s’écrire avec avantage directement comme u ne théorie des types. \n\nDes travaux récents de Christian Sattler (Lee ds) montrent comment on peut utiliser ces idées pour décrire une structu re de modele similaire a la structure\nde modele sur les ensembles simplic iaux\, mais ou l’on n’utilise jamais le tiers-exclu et l’axiome du choix. \n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-06-09/sessions/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Hirschowitz - A sheaf-based approach to concurrent innocent st rategies DTSTART:20160512T153000 DTEND:20160512T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-05-12/sessions/123/ CATEGORIES: DESCRIPTION:This talk is an introduction to a sheaf-based approach to prog ramming\nlanguage semantics\, developed since 2011 with Clovis Eberhart\, Damien\nPous and Thomas Seiller.\n\nIn a sense\, the intersection of presh eaf models and innocent game\nsemantics is boolean presheaves on traces wi th the prefix ordering.\nIn the same sense\, our approach takes the union. It proceeds in two\nmain layers.\n\nThe high-level layer essentially imp lements the idea that if one\nconsiders a rich enough notion of play\, the n the innocence of game\nsemantics may be encoded as a sheaf condition. R ichness here means\nsufficient sensitivity to causality information. The sheaf condition\nmeans that any play is covered by its views\, for the top ology-like\nsense of `covered' provided by Grothendieck topologies. We wil l sketch\nour general notion of playground and how each playground gives r ise to\na family of categories of innocent strategies.\n\nThe low-level la yer is concerned with the construction of relevant\nplaygrounds. In the fi rst installments of our approach\, we constructed\nplaygrounds for CCS and the pi-calculus\, by hand. In recent work with\nClovis\, we started to ge neralise the process. I will illustrate this\nby constructing a candidate playground for the original HO games\,\nwhich will turn out to also illust rate an important limitation of the\ncurrent approach. URL:https://chocola.ens-lyon.fr/events/seminaire-2016-05-12/sessions/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Castellan - The parallel intensionally fully abstract model for PCF DTSTART:20160512T140000 DTEND:20160512T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-05-12/sessions/122/ CATEGORIES: DESCRIPTION:In this talk\, we introduce a new way to compose innocent stra tegies (a\nsemantic representation of normal terms of PCF) based on the wo rk of\nRideau-Winskel on concurrent games on event structures.\n\nThis new framework can also deal with a notion of "concurrent innocent\nstrategies " that can be composed and still form a model of PCF where\nterm evaluatio n features some parallelism. We show that\, similarly to\nHyland and Ong's original construction\, the quotient of this model by\ncontextual equival ence is fully abstract for PCF\, conveying the\nintuition that PCF terms c annot observe the fact that they are evaluated\nin parallel or sequentiall y.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-05-12/sessions/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrzej Murawski - Contextual approximation and higher-order proce dures DTSTART:20160512T103000 DTEND:20160512T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-05-12/sessions/121/ CATEGORIES: DESCRIPTION:We investigate the complexity of deciding contextual approxima tion\n(refinement) in finitary Idealized Algol\, a prototypical language\n combining higher-order types with state. Earlier work in the area\nestabli shed the borderline between decidable and undecidable cases\,\nand focusse d on the complexity of deciding approximation between terms\nin normal for m.\n\nIn contrast\, in this paper we set out to quantify the impact of\nlo cally declared higher-order procedures on the complexity of\nestablishing contextual approximation in the decidable scenarios. We\nshow that the obv ious decision procedure based on exhaustive\nbeta-reduction can be beaten. Further\, by classifying redexes by\nlevels\, we give tight bounds on the complexity of contextual\napproximation for terms that may contain redexe s up to level k\,\nnamely\, (k-1)-EXPSPACE-completeness.\n\nInterestingly\ , the bound is obtained by selective beta-reduction:\nredexes from level 3 onwards can be fired without losing optimality\,\nwhereas redexes of leve l up to 2 are handled by a dedicated decision\nprocedure based on game sem antics and a variant of pushdown automata.\n\nThis is joint work with Rank o Lazic\, presented at FoSSaCS 2016.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-05-12/sessions/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Simon - Autour des structures NIP et du lemme de régularit é de Szemeredi DTSTART:20160310T153000 DTEND:20160310T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-03-10/sessions/125/ CATEGORIES: DESCRIPTION:Je présenterai les structures NIP : structures dans lesquelle s les \nfamilles d'ensembles définissables sont de VC-dimension finie. \nJ'expliquerai ensuite en quoi elles sont liées à des résultats de \n régularité pour des familles particulières de graphes.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-03-10/sessions/125/ END:VEVENT BEGIN:VEVENT SUMMARY:Julien Melleray - An introduction to the theory of Borel complexit y of classification problems. DTSTART:20160310T140000 DTEND:20160310T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-03-10/sessions/124/ CATEGORIES: DESCRIPTION:\nAbstract: A common theme in mathematics is to try and find c omplete \ninvariants for various classification problems (typically\, one tries to \nunderstand isomorphism between some mathematical structures). O ne would \nthen like to know whether the invariants used are as simple as possible\; \nnamely\, one would like to know the precise complexity of the \nclassification problem under consideration.\nThere are many ways to add ress this type of question\; I will try to \nmotivate and explain the poin t of view of Borel complexity\, focusing on \nclassification problems indu ced by a group action\, hoping to give an \nidea of the overall picture an d of some open problems. The talk will be \nintroductory and the speaker w ill aim at making it as self-contained as \npossible.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-03-10/sessions/124/ END:VEVENT BEGIN:VEVENT SUMMARY:Laurent Regnier - Réalisabilité classique\, vers de nouveaux mod èles de ZF ? DTSTART:20160310T103000 DTEND:20160310T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-03-10/sessions/126/ CATEGORIES: DESCRIPTION:Realisability was originally designed by Kleene in order to bu ild models of\nintuitionistic arithmetic (Heyting Arithmetic) as a kind of synthesis between\nGödel's Dialectica interpretation and Brouwer-Heyting -Kolmogorov\ninterpretation. Indeed the basic idea is to extend the notion of justifications\nof mathematical statements from (formal) proofs to pro grams thus defining the\nnotion of a formula justified (proved) by a progr am.\n\nKleene used (indices of) recursive functions for his programs\, but rapidly\nrealisability was adapted to other formalisms\, mostly based on lambda-calculus.\nAlso realisability was soon seen to be also extendable t o classical theories\,\nbut not as a primitive notion since one has to use a Gödel's like\nnot-not-translations to transfer the semantics from intu itionnistic to\nclassical logic.\n\nIt is thus not a small achievement tha t Krivine at the end of the nineties\ncould define a direct notion of real isability for classical logic. In a first\nstep the semantics was defined for higher order arithmetic\, then further\nextended to full set theory by finding realisers for each axioms of\nZF. Interestingly enough these real isers are all very simple programs\, but the\none for the extensionality a xiom which implements a real algorithm (essentialy\na while loop).\n\nThe so-called classical realisability thus allows to define new semantics for\ narithmetic\, analysis and now set theory in which the truth value of a fo rmula\nis the set of its realisers. Krivine has shown that this constructi on can be\nseen as an extension of Cohen's forcing\, but with some very ne w properties (eg\,\ncontrarily to forcing\, ordinals are not preserved bet ween the base model and\nthe realisability model) that are almost all yet to be discovered and\nunderstood...\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-03-10/sessions/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Tabareau - Enlarge your Coq using Forcing. DTSTART:20160211T153000 DTEND:20160211T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-02-11/sessions/119/ CATEGORIES: DESCRIPTION:\nWe will study forcing translations of proofs in dependent ty pe theory\, through\nthe Curry-Howard correspondence. Based on a call-by-p ush-value decomposition\,\nwe will synthesize two simply-typed translation s: i) one call-by-value\,\ncorresponding to the translation derived from t he presheaf construction as\nstudied in a previous pa- per\; ii) one call- by-name\, whose intuitions already\nappear in Krivine and Miquel’s work.  \n\nFocusing on the call-by-name translation\, we will adapt it to the d ependent\ncase and prove that it is compatible with the definitional equal ity of our\nsystem\, thus avoiding coherence problems. This allows us to u se any category as\nforcing conditions\, which is out of reach with the ca ll-by-value translation.\nOur construction also exploits the notion of sto rage operators in order to\ninterpret dependent elimination for inductive types. This is a novel example of\na dependent theory with side-effects\, clarifiying how dependent elimination for\ninductive types must be restric ted in a non-pure setting. Being implemented as\na Coq plugin\, this work gives the possibility to formalize easily consistency\nresults\, for insta nce the consistency of the negation of Voevodsky’s univalence\naxiom.\n\ nFinally\, if time allows\, we will see how the forcing translation could give\nrise to a computational of the univalence axiom using the category o f cubes as\nforcing conditions and interpreting the cubical type theory of Coquand et al. \n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-02-11/sessions/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Boulier - Model structure in Homotopy Type Theory DTSTART:20160211T140000 DTEND:20160211T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-02-11/sessions/120/ CATEGORIES: DESCRIPTION:Homotopy Type Theory is conjectured to be the internal languag e of (∞\,1)-topoi. In particular\, the category of contexts of HoTT is a n (∞\, 1)-category. This (∞\, 1)-cateory can be presented as a categor y with weak equivalences\, where weak equivalences are given by the now cu stomary type theoretic equivalences. But we can add more structure: namely we can define what are fibrations and cofibrations in type theory\, so th at the category of contexts be a model category. This was done by Gambino and Garner [GG] and Lumsdaine [Lum] and we will start by presenting their work.\n\nNext we will consider moving to a two level type system like the one considered by Thorsten Altenkirch\, to formalize those notions interna lly. Indeed\, a strict equality satisfying UIP allows to formalize what is a strict category and a model structure over it.\n \nLast\, we will see how the model structure justify some homotopy colimit calculations from s trict colimits.\n\n\n[Lum] Lumsdaine\, P. L. (2011). Model structures from higher inductive types. http://peterlefanulumsdaine.com/research/Lumsdain e-Model-strux-from-HITs.pdf.\n\n[GG] Gambino\, N.\, & Garner\, R. (2008). The identity type weak factorisation system. Theoretical Computer Science\ , 409(1)\, 94-109.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-02-11/sessions/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Thorsten Altenkirch - What is a category? (in univalent type theor y) DTSTART:20160211T103000 DTEND:20160211T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-02-11/sessions/118/ CATEGORIES: DESCRIPTION:\nCategory theory is one of the main tools in theoretical comp uter \nscience. Univalent type theory allows us to represent ordinary cate gory \ntheory in a very straightforward way but we need to assume that the \nhom-types are **sets** in the sense of univalent type theory\, that is \ntheir equalities are mere propositions. In my talk I a going to explore \nhow we can lift this limitation and how we can define \n(\\omega\,1)-cat egories in a 2-level type theory. The 2-level theory is \nnecessary becaus e we have to distinguish between **strict** and **weak** \nequality and co nsequently between **types** and **pretypes**. One \napplication of this a pproach is a generic theory of higher inductive \ntypes.\n\nThis is based on ongoing work with Paolo Capriotti\, Gabe Dijkstra\, \nFrederik Forsberg and Nicolai Kraus.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-02-11/sessions/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Lionel Vaux - A characterization of strong normalizability as a fi niteness structure via the Taylor expansion of λ-terms\, with applicati ons. DTSTART:20160114T153000 DTEND:20160114T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-01-14/sessions/117/ CATEGORIES: DESCRIPTION:In the folklore of differential linear logic and its denotatio nal\n models\, a common intuition is that the structure of finiteness spa ces\,\n introduced by Ehrhard\, semantically reflects the strong normaliz ation\n property of cut-elimination.\n \n We make this intuition formal in the context of λ-calculus by\n introducing a finiteness structure on resource λ-terms\, which is\n such that a λ-term is strongly normalizi ng iff the support of its\n Taylor expansion is finitary.\n \n This str ucture is a refinement of the one introduced by Ehrhard in his\n LICS 201 0 paper: for the latter\, we also prove that any strongly\n normalizing λ-term has a finitary Taylor expansion (this was\n already known for the terms of system F)\, but the converse does not\n hold. As was already th e case in Ehrhard's work\, the proofs do not rely\n on any uniformity pro perty\, hence this approach is valid for\n non-deterministic extensions o f the λ-calculus as well.\n \n One application of this work is the exis tence of a normal form for\n the Taylor expansion of any strongly normali zable term.\n We will moreover give a brief overview of our work in progr ess\,\n allowing to extend our results to (must) normalizability and (mus t)\n head normalizability : this is the next step in a line of work aimi ng\n at a generalization of results by Ehrhard and Regnier [TCS vol. 403\ ,\n 2008\; CiE 2006] that were previously limited to a uniform setting. \ n\n (Joint work with Michele Pagani and Christine Tasson.) URL:https://chocola.ens-lyon.fr/events/seminaire-2016-01-14/sessions/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphaëlle Crubillé - Metrics Reasoning about lambda-terms DTSTART:20160114T140000 DTEND:20160114T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-01-14/sessions/116/ CATEGORIES: DESCRIPTION:Terms of Church's lambda-calculus can be considered equivalent along\n many different definitions\, but context equivalence is certainl y the\n most direct and universally accepted one. However\, this definiti on\n has the drawback of being based on an universal quantification over\ n all contexts. In order to give handier characterisations\,\n coinducti ve methodologies have been developped since 1990 by\n Abramsky (among oth ers) for deterministic computations\, and later by\n Lassen for non-deter ministic ones\, with new and exciting results\n appearing recently also f or probabilistic languages: applicative\n bisimilarity\, a coinductively defined notion of equivalence for\n functional programs\, has been shown to be sound\, and sometime even\n fully abstract\, for probabilistic lamb da-calculi. In the\n probabilistic case\, however\, equivalence can be se en as too\n discriminating: terms which have totally unrelated behaviours are\n treated the same as terms which behave very similarly. We study th e\n problem of evaluating the distance between lambda-terms. A natural\n generalisation of context equivalence\, is shown to be characterised\n in a restricted affine setting by a notion of trace distance\, and to\n b e bounded from above by a coinductively defined distance based on\n the K antorovich metric on distributions. A different\, again\n fully-abstract\ , tuple-based notion of trace distance is shown to be\n able to handle no ntrivial examples\, and to allow a generalisation to\n the non-affine cas e.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2016-01-14/sessions/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Staton - Algebraic effects\, linearity\, and quantum programmi ng languages DTSTART:20160114T103000 DTEND:20160114T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2016-01-14/sessions/115/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2016-01-14/sessions/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Yves Guiraud - Théorie de Squier et application aux monoïdes d'A rtin DTSTART:20151203T153000 DTEND:20151203T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-12-03/sessions/113/ CATEGORIES: DESCRIPTION:\nUn monoïde ayant une présentation par un système de réé criture convergent fini\na un problème du mot décidable. Dans les année s 1980\, Jantzen s'interroge sur\nla réciproque : un monoïde de type fin i ayant un problème du mot décidable\nadmet-il toujours une présentatio n convergente finie ? Squier a répondu\nnégativement à cette question e n établissant une connexion entre des propriétés\nalgorithmiques des sy stèmes de réécriture\, comme la terminaison et la\nconfluence\, et des invariants algébriques\, comme l'homologie ou l'homotopie.\n\nDans cet ex posé\, je présenterai le résultat initial de Squier\, dans le\nformalis me contemporain de la réécriture de dimension supérieure. Puis je\nmont rerai comment\, avec Stéphane Gaussent et Philippe Malbos\, nous avons ad apté\nle théorème de Squier pour étudier des propriétés homotopiques des monoïdes de\ntresses et de leur généralisation\, les monoïdes d'A rtin.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-12-03/sessions/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Rodolphe Lepigre - A call-by-value realizability model for PML DTSTART:20151203T140000 DTEND:20151203T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-12-03/sessions/112/ CATEGORIES: DESCRIPTION:We present a new type system with support for proofs of progra ms in a\ncall-by-value language with control operators. The proof mechanis m relies\non observational equivalence of (untyped) programs. It appears i n two type\nconstructors\, which are used for specifying program propertie s and for\nencoding dependent products. The main challenge arises from the lack of\nexpressiveness of dependent products due to the value restrictio n. To\ncircumvent this limitation we relax the syntactic restriction and o nly\nrequire equivalence to a value. The consistency of the system is obta ined\nsemantically by constructing a classical realizability model in thre e\nlayers (values\, stacks and terms). URL:https://chocola.ens-lyon.fr/events/seminaire-2015-12-03/sessions/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonas Frey - Toposes from Krivine realizability with side effects DTSTART:20151203T103000 DTEND:20151203T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-12-03/sessions/114/ CATEGORIES: DESCRIPTION:To start\, I will give an introduction to the categorical appr oach to\nKrivine realizability\, and in particular explain how Krivine\nre alizability gives rise to toposes using Hyland\, Johnstone and Pitts'\n"tr ipos-to-topos construction". Krivine realizability is parametric\nover the concept of "pole"\, and I will explain how to obtain new poles\nby augmen ting the syntax with side effects for I/O. To conclude I\nwill discuss po tential links to algorithmic complexity theory\, based\non work in progres s in collaboration with Jakob Grue Simonsen.\n\n\n**__This talk will be gi ven in Salle des Thèses\, ground floor__** (we will be in Amphi B in the afternoon). URL:https://chocola.ens-lyon.fr/events/seminaire-2015-12-03/sessions/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Jacques Lévy - The cost of usage in the lambda-calculus DTSTART:20151105T153000 DTEND:20151105T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-11-05/sessions/111/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2015-11-05/sessions/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Scherer - Multi-focusing the lambda-calculus. DTSTART:20151105T140000 DTEND:20151105T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-11-05/sessions/109/ CATEGORIES: DESCRIPTION:In this talk\, I would like to present applications of maximal \nmulti-focusing to programming languages problems -- in the\nsimply-typed lambda-calculus with both negative types\n(such has functions) and positi ve types (such as sums). Focusing seems\nto be a key ingredient in extendi ng existing intuitions on beta-eta\nequivalence from the purely negative f ragment (functions and pairs) to\na more diverse system with types of both polarities. I will present\nfocusing and multi-focusing (for propositiona l intuitionistic logic\,\nthat is the simply-typed lambda-calculus)\, and its use to enumerate\ncanonical inhabitants of a type (in particular testi ng whether a type\nhas a unique inhabitant) and to test typed program equi valence\n(even in presence of the empty type).\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-11-05/sessions/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Bob Atkey - Type systems for programming with coinductive data typ es DTSTART:20151105T103000 DTEND:20151105T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-11-05/sessions/110/ CATEGORIES: DESCRIPTION:(title to be confirmed) URL:https://chocola.ens-lyon.fr/events/seminaire-2015-11-05/sessions/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Beniamino Accattoli - Proof nets and the lambda-calculus 2.0 DTSTART:20151001T153000 DTEND:20151001T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-10-01/sessions/107/ CATEGORIES: DESCRIPTION:The traditional proof nets representation of lambda-calculus d ates\nback to the nineties\, to the work of Danos and Regnier\, and it is\ nnowadays a cornerstone of the linear logic literature.\n\nIn the last few years such a traditional view has been refined\,\nbuilding on a simple so lution to its main issue\, i.e. the different\ngranularities of the evalua tion mechanisms at work in the two systems.\nSuch a solution\, the linear substitution calculus\, is both a\nrefinement of lambda calculus and a gra ph-free presentation of proof\nnets. Its simplicity led to a new wave of s tudies on the topic\, whose\nmain achievement has been the development of a theory of cost models\nfor the lambda calculus.\n\nThe talk will be an i ntroduction to the main ideas at work in the new\nframework\, that are:\n\ n1. an abstract point of view on proof nets\, seen as a rewriting system\n up to a postponable structural equivalence\, and not as a graphical\nlangu age\;\n\n2. a new\, simpler presentation of linear head reduction\, justif ied via\nrewriting and quantitative analyses\;\n\n3. the extension of the theory to abstract machines and processes\,\nthem too seen as abstract pro of nets evaluating via linear head\nreduction\;\n\n4. the use of strong bi simulations to relate terms\, graphs\, machines\,\nand processes in a perf ect way.\n\nBeware: the talk will not be a bland survey of previous work\, nor will\nit present recent results\, in particular not those about cost models.\nIt will rather be an original introduction to basic concepts\,\nq uestioning the status quo\, and stressing the change of perspective. URL:https://chocola.ens-lyon.fr/events/seminaire-2015-10-01/sessions/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Leventis - Theories in Probabilistic lambda-calculus. DTSTART:20151001T140000 DTEND:20151001T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-10-01/sessions/108/ CATEGORIES: DESCRIPTION:Our goal is to extend the notion of lambda-theory to the call- by-name\nprobabilistic lambda-calculus. We will first describe this calcul us without\nusing probabilistic reductions nor specifying a reduction stra tegy\, so that we\ncan give a meaning to the notion of beta-equivalence. W e will then define\nprobabilistic lambda-theories\, as well as the notions of extensionality and\nsensibility for such theories. Lastly we will pres ent a result similar to the\none proved by Martin Hyland in usual lambda-c alculus: there is a maximum\nconsistent extensional sensible lambda-theory \, and it is given by the equality\nof Böhm trees or equivalently by the observational equivalence of terms.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-10-01/sessions/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Ugo de'Liguoro - Intersection types for lambda-calculi with contro l DTSTART:20151001T103000 DTEND:20151001T120000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-10-01/sessions/106/ CATEGORIES: DESCRIPTION:We investigate lambda-calculi extended with control operators from the\npoint of view of intersection type theories. Intersection types are a\nnatural bridge between syntax and semantics and have been extensive ly\nused to characterize computational properties of the untyped\nlambda-c alculus. We aim at extending these techniques and results to\ncalculi with control\, whose semantics is usually given either in terms\nof CPS transl ations or of abstract machines. Building over a\ndenotational model of con tinuations due Streicher and Reus\, that is a\nmodel of several such calcu li (including Felleisen's lambda-C\,\nParigot's lambda-mu\, De Groote and Saurin's Lambda-mu and Krivine's\nlambda/cc)\, and using Abramsky's ideas on domain logic\, we show how\ntype theories and type assignment systems c an be obtained out of\nStreicher and Reus models as well as of the"extensi onal" variant by\nNakazawa and Katsumata\, all inducing filter models in t he sense of\nBarendregt-Coppo-Dezani. We eventually mention some results a bout\nstrongly normalizing terms of Parigot's lambda-mu and the\napproxima tion theorem for De Groote-Saurin's Lambda-mu.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-10-01/sessions/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonino Salibra - Logics via algebras and substitutions DTSTART:20150521T153000 DTEND:20150521T163000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-05-21/sessions/105/ CATEGORIES: DESCRIPTION:In this talk we present a translation of formulas and models o f classical and non-classical logics into factor algebras. The corresponde nce:\n\n * Propositional variables - operator of decompositions\n\n * Logi cal operations - substitutions\n\n * Formulas - algebraic terms\n\n * Mode ls - factor algebras\,\n\nprovides a uniform calculus of provability for a ll the logics which admit the translation. Many examples will be discussed : classical logic\, intuitionistic logic\, linear logic\, many-valued logi cs.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-05-21/sessions/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Arthur Charguéraud - Vérification interactive de programmes imp ératifs\, avec CFML DTSTART:20150521T140000 DTEND:20150521T150000 DTSTAMP:20260612T104321Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-05-21/sessions/104/ CATEGORIES: DESCRIPTION:CFML est un outil qui permet de prouver en Coq la correction f onctionnelle\nde programmes Caml. CFML s'appuie sur la notion de formule c aractéristique\,\nqui permet de décrire la sémantique d'un programme im pératif sous la forme\nd'une formule de la logique d'ordre supérieur. Le s formules \ncaractéristiques\,\nqui sont à la fois correctes et complè tes\, sont de tailles linéaires et\npeuvent être générées automatique ment à partir du code source des \nprogrammes.\n\nElles s'appuient de plu s sur la Logique de Séparation\, qui permet \nd'effectuer\ndes raisonneme nts modulaires\, et intègrent la notion de crédits-temps\, qui\npermet d e vérifier des propriétés de complexité asymptotique. Dans cet\nexpos é\, je présenterai la théorie de CFML et j'illustrerai son utilisation\ nen pratique\, à travers plusieurs exemples.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-05-21/sessions/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Étienne Miquey - Realizability games for the specification proble m DTSTART:20150521T103000 DTEND:20150521T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-05-21/sessions/103/ CATEGORIES: DESCRIPTION:In Krivine classical realizability\, one can understand the tr uth value\nof a formula (that is the set of its realizers) as its defender s\, and\nthe falsity value as the set of its opponents. Following this\nin tuition\, the execution of a process is a match between both players\,\nth at a realizer should win.\n\nIn this talk\, we will explain how to use a n otion of game to give a\nprecise specification of the realizers of a given formula. We will\nfocus on the particular case of arithmetical formulae\, for which our\ndefinition relies on the principle of Coquand's games. In the end\, we\nobtain an equivalence between universal realizers and winnin g\nstrategies (even in presence of non-substitutive instructions such as\n Quote)\, which also directly implies the absoluteness of arithmetical\nfor mulae for classical realizability. URL:https://chocola.ens-lyon.fr/events/seminaire-2015-05-21/sessions/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylvain Salvati - Model construction for higher-order model-checki ng DTSTART:20150409T153000 DTEND:20150409T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-04-09/sessions/100/ CATEGORIES: DESCRIPTION:\nWhen dealing with finite state properties\, it is usual to h ave some\nfinite algebraic structures (e.g. finite monoids in the case of finite\nstate automata on strings) that represent those properties. When d ealing\nwith logical properties of programs that are computed by finite st ate\nautomaton\, the question of what is an "adequate" finite algebraic\ns tructure arises. Having such a structure would entail a sort of\nmodularit y in program verification\, but it also gives some strong\nunderstanding o f how the properties can be checked.\n\nIn the context of higher-order ver ification\, programs are models as\nlambda-terms and it is natural to thin k about denotational domains as\na possible candidate. Finitary Scott doma ins only capture very simple\nproperties of the Bohm trees generated by hi gher-order programs. This\ntalk will illustrate how to enrich Scott domain s so that they can\ncapture wider classes of finite state properties.\n\n( joint work with Igor Walukiewicz)\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-04-09/sessions/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Grellois - Categorical semantics of linear logic and highe r-order model-checking DTSTART:20150409T140000 DTEND:20150409T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-04-09/sessions/101/ CATEGORIES: DESCRIPTION:To model-check a higher-order functional program with recursio n\, one can\nabstract it as a lambda Y-term normalizing to a tree over a s ignature of\nactions\, which approximates the set of behaviours of this pr ogram.\nRunning an alternating parity automaton over this tree is then a w ay to\nensure that it respects a given MSO specification.\n\nA connection between higher-order model-checking and linear logic\nappears naturally wh en one considers the linear typing of lambda-terms.\nInterpreted in the re lational model of linear logic\, the duals of these\ntypes correspond prec isely to the set of alternating automata (without\nparity condition)\, lea ding to a semantic model-checking approach:\nlambda-terms generating trees and alternating tree automata are given\ndual semantics in the relational model\, so that their interaction\ncomputes the set of states from which an automaton accepts the tree\ncomputed by a term. The model-checking prob lem may then be solved by\nchecking that the initial state of the automato n belongs to the result.\n\nIn this talk\, we explain how this theorem can be generalized to\nlambda-terms with recursion\, and to alternating autom ata with a parity\ncondition. This requires us to consider an infinitary v ariant of the\nrelational semantics of linear logic\, and to define a colo ured\nexponential modality over it. We finally devise a fixed point operat or\nverifying directly at the level of denotations the parity condition of \nalternating parity tree automata\, and obtain the desired generalized\ns emantic model-checking theorem.\n\nWe finally recast our approach in a fin itary model of linear logic\,\nprovided by its Scott semantics\, and expla in how it leads to a\ndecidability proof of the higher-order model-checkin g problem.\n\n(joint work with Paul-André Melliès) URL:https://chocola.ens-lyon.fr/events/seminaire-2015-04-09/sessions/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Walukiewicz - Verification of behavioural properties of highe r-order programs DTSTART:20150409T103000 DTEND:20150409T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-04-09/sessions/102/ CATEGORIES: DESCRIPTION:Our objective is to verify behavioural properties of programs\ , as for\nexample "an open stream is eventually closed"\, or "a login func tion is\ncalled infinitely often". We use lambda Y-calculus\, the simply t yped\nlambda-calculus with the fixpoint combinator\, as an intermediate\nl anguage. The approach we pursue consists of two steps: translate a\nprogra m into a term of lambda Y-calculus\, and then analyse the Bohm\ntree of th e resulting term. Thanks to the result of Ong it is\ndecidable if the Bohm tree of a given term satisfies a given property\nexpressed in monadic sec ond-order logic\; this is a classical\nlogic for tree properties that is c apable to express many interesting\nproperties of computations. We solve t he verification problem by a mix\nof automata and semantic techniques\, in particular we construct\nappropriate models of lambda Y calculus.\n\n\nTh e talk will start with the introduction to the verification problem\nfor h igher-order programs. Most type systems for programming languages\nconcent rate on\, some\, safety properties of programs. We will present\nmonadic s econd-order logic (MSOL) on binary trees\, and give\nindications why verif ication of MSOL properties is more complex than\njust for safety propertie s. Next\, we will adapt the notion of\nrecognizability\, the classical not ion from language theory\, to our\nsetting. We will state our main result saying that for every MSOL\nproperty there is a finitary model of the lamb da Y-calculus\nrecognizing this property. Finally\, we will discuss some c orollaries of\nthis theorem concerning verification of programs as well as program\ntransformation\, and program synthesis.\n\nThis is joint work wi th Sylvain Salvati. URL:https://chocola.ens-lyon.fr/events/seminaire-2015-04-09/sessions/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulio Guerrieri - Injectivity of relational semantics for connect ed MELL proof-structures via Taylor expansion DTSTART:20150312T153000 DTEND:20150312T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-03-12/sessions/99/ CATEGORIES: DESCRIPTION:We show that:\n\n(1) the Taylor expansion of a cut-free MELL p roof-structure R with\natomic axioms is the (most informative part of the) relational\nsemantics of R\;\n\n(2) every box-connected MELL proof-struct ure is uniquely determined by\nthe element of order 2 of its Taylor expans ion\;\n\n(3) the relational semantics is injective for box-connected MELL\ nproof-structures.\n\nWe point out that our notion of box-connection is ra ther general: all\nACC or connected proof-structures are box-connected (th e converse does\nnot hold).\n\nThis is joint work with Lorenzo Tortora\nde Falco. Our results are deeply related to a previous work of Lorenzo Torto ra\nde Falco and Daniel de Carvalho\, but is based on a slightly different \nviewpoint.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-03-12/sessions/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Amina Doumane - On the dependencies of logical rules DTSTART:20150312T140000 DTEND:20150312T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-03-12/sessions/98/ CATEGORIES: DESCRIPTION:Many correctness criteria have been proposed since linear logi c was\nintroduced and it is not clear how they relate to each other.\nWe p resent proof-nets and their correctness criteria from the\nperspective of dependency\, as introduced by Mogbil and Jacobé de\nNaurois.\n\nMore prec isely\, we introduce a new correctness criterion\, called\nDepGraph\, and show that together with Danos' contractibility criterion\nand Mogbil and N aurois criterion\,\nthey form the three faces of a notion of dependency wh ich is crucial\nfor correctness of proof-structures.\n\nFinally\, we extra ct the logical meaning of the dependency relation and\nshow that it allows to recover and characterize some constraints on\nthe ordering of inferenc es which are implicit in the proof-net.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-03-12/sessions/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Ehrhard - Un critère de correction de Christian Rétoré DTSTART:20150312T103000 DTEND:20150312T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-03-12/sessions/97/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2015-03-12/sessions/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Polonski - Toward extensional type theory with decidable ty pe-checking DTSTART:20150205T153000 DTEND:20150205T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-02-05/sessions/96/ CATEGORIES: DESCRIPTION:We report our work on a new treatment of equality in dependent type theory.\n\nLarge-scale formalization of mathematics in type theory i s greatly\nimpededed by the intensional character of type-theoretic equali ty.\nFor a variable n:Nat\, the terms n+1 and 1+n are equal but not\nconve rtible. Consequently\, if B(n) is a dependent type over N (eg.\nR^n)\, th en B(n+1) and B(1+n) are isomorphic but not equal\; thus there\nis no auto matic way to transfer properties from one type to another.\nThe terms S=(\ \n.n+1) and S'=(\\n.1+n) of type Nat->Nat are not even\nequal propositiona lly\, thus there is no explicit isomorphism between\ntypes B(S) and B(S') when B(f) is a type dependent over Nat->Nat.\nMartin-Lof defined extension al type theory by reflecting the equality\nproofs (terms of the identity t ype) into the conversion relation.\nUnfortunately\, this renders type-chec king and proof-checking\nundecidable\, undermining a major motivation for working in type\ntheory.\n\nVoevodsky recently proposed the Univalence Axi om which solves the\nproblem of extensionality\, but\, without a computati onal justification\,\nleads to the failure of canonicity\, another crucial metatheoretic\nproperty. Coquand et al have recently provided this missi ng piece by\nbuilding a model of univalence in constructive metatheory.\n\ nWe propose an alternative\, syntax-based approach to extensionality.\nIn this approach\, the equality type is initially defined externally\,\nas a logical relation on the term model of type theory\, which in turn\nis defi ned by induction on type structure. The relation is then\nreflected into the language by extending the syntax. This results in\na 1-dimensional th eory\; in order to have equality as a type\nconstructor that can be iterat ed (so that we can write p\,q :\nEq(A\,a\,b)\, pi : Eq(Eq(A\,a\,b)\,p\,q)\ , etc.)\, the reflection operation\nmust itself be internalized. We show how this can be done in a\nconsistent way\, and verify some basic properti es of the resulting\nsystem.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-02-05/sessions/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Anupam Das - Theories of bounded arithmetic for deep inference pro of systems DTSTART:20150205T140000 DTEND:20150205T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-02-05/sessions/95/ CATEGORIES: DESCRIPTION:We give uniform versions of propositional logic deep inference systems \nin the setting of 'bounded arithmetic'\, relating the size of \ npropositional proofs to forms of proof-theoretic strength in fragments \n of arithmetic.\n\nThis continues the recent program of studying the comple xity of deep \ninference proofs by bringing it in line with the standards of mainstream \nproof complexity. It is also inspired by previous work whe re proofs of \nthe propositional pigeonhole principle in the minimal deep inference \nsystem\, KS\, were constructed using rather abstract uniform t emplates\, \nsuggesting the need for such an approach.\n\nTo minimise prer equisites we work in the setting of monotone proofs \nrepresented as rewri ting derivations\, isolating fragments of so-called \n'analytic' deep infe rence. For the same reason we construct our \narithmetic theories by adapt ing the well studied IDelta_0 of Parikh\, \nParis\, Wilkie and others\, al though similar theories could be designed \nusing the more modern second-o rder setting of Zambella\, Cook and Nguyen.\n\nAlong the way we require a blend of tools from bounded arithmetic \n(correspondence with propositiona l proofs)\, deep inference (efficient \nnormalization of propositional tra nslations)\, and descriptive complexity \n(taming the closure functions of least fixed point operators used to \nsimulate deep inference).\n URL:https://chocola.ens-lyon.fr/events/seminaire-2015-02-05/sessions/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Jörg Endrullis - Clocked lambda-calculus DTSTART:20150205T103000 DTEND:20150205T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2015-02-05/sessions/94/ CATEGORIES: DESCRIPTION:*(This talk will be given in room B1\, fourth floor)* URL:https://chocola.ens-lyon.fr/events/seminaire-2015-02-05/sessions/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Kazushige Terui - Some topics on hypersequents DTSTART:20141204T153000 DTEND:20141204T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-12-04/sessions/90/ CATEGORIES: DESCRIPTION:Hypersequent calculus\, introduced by Arnon Avron\,\nis an ext ension of the ordinary sequent calculus\nthat deals with disjunctions of s equents.\nHistorically it has been a tool for studying intermediate logics and\nmany-valued logics (so-called *fuzzy* logics)\,\nbut it is interesti ng in its own right\nas a proof system with a well-behaved cut-elimination procedure.\n\nIn this talk\, I will discuss some aspects of hypersequents \, that could be\nhopefully meaningful to those who are not interested in fuzzy logics at all.\nThe topics include:\n\n* Brouwer's fixed point theor em and cut-elimination: a potential link.\n\n* Algebraic cut-elimination a la Maehara and Okada: success and failure.\n\n* Takeuti-Titani's density rule: elimination and algebraic interpretation. URL:https://chocola.ens-lyon.fr/events/seminaire-2014-12-04/sessions/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Geoffroy - Classical realizability models of ZF\, ∇2\, and the model of threads DTSTART:20141204T140000 DTEND:20141204T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-12-04/sessions/89/ CATEGORIES: DESCRIPTION:Classical realizability is a rewrite of Kleene's realizability in\norder to make it compatible with classical reasoning\, following the\ ndiscovery by T. Griffin of a connection between classical reasoning\nand control operators. J.-L. Krivine used classical realizability\nsemantics t o construct novel models of standard set theory (ZF).\n\nI will explain ho w classical realizability semantics work\, how to\nconstruct classical rea lizability models of ZF\, and how they differ\nfrom forcing models. Notabl y\, each classical realizability model\ncontains a characteristic boolean algebra ∇2\, of mysterious structure\nand weird cardinality. Specificall y\, I will focus on the model of\nthreads\, which showcases these differen ces.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-12-04/sessions/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Levy - Transition systems over games DTSTART:20141204T110000 DTEND:20141204T123000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-12-04/sessions/88/ CATEGORIES: DESCRIPTION:We describe a framework for game semantics combining operation al and denotational accounts. A game is a bipartite graph of\n“passive ” and “active” positions\, or a categorical variant with morphisms b etween positions.\n\nThe operational part of the framework is given by a l abelled\ntransition system in which each state sits in a particular positi on of\nthe game. From a state in a passive position\, transitions are labe lled\nwith a valid O-move from that position\, and take us to a state in\n the updated position. Transitions from states in an active position\nare l ikewise labelled with a valid P-move\, but silent transitions are\nallowed \, which must take us to a state in the same position.\n\nThe denotational part is given by a “transfer” from one game\nto another\, a kind of p rogram that converts moves between the two\ngames\, giving an operation on strategies. The agreement between\nthe two parts is given by a relation c alled a “stepped bisimulation”.\n\nThe framework is illustrated by an example of substitution\nwithin a lambda-calculus.\n\n(Joint work with Sam Staton) URL:https://chocola.ens-lyon.fr/events/seminaire-2014-12-04/sessions/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Baptiste Jeannin - Semantic Foundations for Networks DTSTART:20141113T153000 DTEND:20141113T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-11-13/sessions/93/ CATEGORIES: DESCRIPTION:Recent years have seen growing interest in high-level language s for\nprogramming networks. But the design of these languages has been\nl argely ad hoc\, driven more by the needs of applications and the\ncapabili ties of network hardware than by foundational principles. The\nlack of a s emantic foundation has left language designers with little\nguidance in de termining how to incorporate new features\, and\nprogrammers without a mea ns to reason precisely about their code.\n\nIn this talk we introduce NetK AT\, a new network programming language that\nis based on a solid mathemat ical foundation and comes equipped with a\nsound and complete equational t heory. We describe the design\nof NetKAT\, including primitives for filter ing\, modifying\, and\ntransmitting packets\; union and sequential composi tion operators\; and\na Kleene star operator that iterates programs. We sh ow that NetKAT\nis an instance of a canonical and well-studied mathematica l structure\ncalled a Kleene algebra with tests KAT and prove that its\neq uational theory is sound and complete with respect to its\ndenotational se mantics. Finally\, we present practical applications of\nthe equational th eory including syntactic techniques for checking\nreachability\, proving n on-interference properties that ensure\nisolation between programs\, and e stablishing the correctness of\ncompilation algorithms. URL:https://chocola.ens-lyon.fr/events/seminaire-2014-11-13/sessions/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucca Hirschi - Partial order reduction for the applied pi-calculu s DTSTART:20141113T140000 DTEND:20141113T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-11-13/sessions/92/ CATEGORIES: DESCRIPTION:Process algebras provide convenient languages for representing concurrent\ncomputation\, and they have been used successfully to model c omplex systems\nsuch as security protocols. However\, their naive interlea ving semantics \ngives\nrise to exponentially many states that are essenti ally the same. This is\nproblematic\, for instance\, when model-checking s ecurity protocols.\nWe solve this problem on a large fragment of the appli ed pi-calculus\nby providing reduced transition systems that optimally eli minate redundant\ntraces\, and which are still adequate for on-the-fly mod el-checking of\nreachability and (in the action-deterministic case) trace equivalence \nproperties.\n\nTechnically\, we rely on basic trace theory b ut also on focusing from\nproof theory.\n\n(Joint work with Baelde & Delau ne.)\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-11-13/sessions/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Dimitri Ara - Street's orientals and Mac Lane's coherence theorem DTSTART:20141113T103000 DTEND:20141113T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-11-13/sessions/91/ CATEGORIES: DESCRIPTION:In this talk\, I will present some elements of the homotopy th eory of strict\nn-categories\, insisting on Street's orientals. The n-th o riental is a strict\nn-category shaped on the n-simplex. We will see that these objects govern\nhigher associativities and in particular that Mac La ne's coherence theorem \ncan be rephrased in terms of the combinatorics of low dimensional orientals. \nUsing this setting and homotopical methods\, I will sketch a proof of\nMac Lane's coherence theorem. (This talk is bas ed on joint work with Georges\nMaltsiniotis.) URL:https://chocola.ens-lyon.fr/events/seminaire-2014-11-13/sessions/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Flavien Breuvart - De la caractérisation des modèles de H* DTSTART:20141016T153000 DTEND:20141016T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-10-16/sessions/86/ CATEGORIES: DESCRIPTION:Je ferai une présentation rallongée de l'article LICS du mê me nom.\n\nIl s'agit de donner une caractérisation\, pour une classe impo rtante de\nmodèles du lambda-calcul non typé\, de la pleine adéquation pour la\nnormalisation de tête (i.e. pour H*). On montrera en effet qu'il est\npour cela nécessaire et suffisant d'être hyperimmune. L'hyperimmun ité\nest une notion que nous introduirons qui demande à ce que les\ncomp ortements mal fondés du modèle ne soient pas capturables par des\nfoncti ons récursives.\n\nCe résultat sera notamment utilisé comme prétexte e t exemple pour\nl'introduction d'un outil central dans ma thèse: les lamb da-calculs avec\ntests. Il s'agit d'enrichir le lambda-calcul non typé av ec des\nopérateurs directement issus du modèle dénotationnel impliqué afin de\nrendre celui-ci pleinement adéquat pour notre nouvelle syntaxe.\ nIntuitivement\, ces opérateurs vont internaliser un processus \nd'infér ence de type possiblement divergent qui tente de typer l'arbre de \nBöhm d'un terme.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-10-16/sessions/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Paulin Jacobé de Naurois - Reachability in Vector Addition with S tates and Split/Join Transitions DTSTART:20141016T140000 DTEND:20141016T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-10-16/sessions/85/ CATEGORIES: DESCRIPTION:We define Vector Addition with States and Split/Join Transitio ns\, a new \nmodel that extends VASS. Non-negative reachability in this mo del without \njoin transitions is known to be equivalent to the decidabili ty of MELL\, \nand to be TOWER-hard. As a first step towards a reachabilit y result\, we \ndefine a suitable notion of covering graph for the model\, and prove its \nfiniteness and effective constructibility.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-10-16/sessions/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylvain Schmitz - Complexity in propositional substructural logics and counter systems DTSTART:20141016T103000 DTEND:20141016T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-10-16/sessions/87/ CATEGORIES: DESCRIPTION:The ties between propositional linear logic on the one hand an d \nextensions of vector addition systems on the other hand have long been \nknown\, as they lie for instance at the heart of Lincoln et al.'s 1992 \nundecidability proof. With Ranko Lazić we recently revisited these \nc onnections with an eye on complexity issues\, which allowed us to prove \n tight complexity bounds on provability in affine and contractive \nfragmen ts of linear logic. Our work also yields a new Tower lower bound \non pro vability in MELL\, for which decidability is still open.\n\nWork presented at CSL-LICS 2014\; full paper available on arXiv: \n.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-10-16/sessions/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Valeria Vignudelli - On the Discriminating Power of Higher-order L anguages DTSTART:20140925T153000 DTEND:20140925T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-09-25/sessions/84/ CATEGORIES: DESCRIPTION:We compare the discriminating power of higher-order sequential and concurrent\nlanguages (lambda-calculi\, CCS-like calculi\, Higher-Ord er pi-calculi)\, possibly\nenriched with refusal or passivation operators. The comparison is carried out\nby defining a testing scenario where conte xts of these languages are used to\ndistinguish first-order processes\, wh ich may be either ordinary\nnondeterministic processes or probabilistic pr ocesses.\n\nThe hierarchies of contextual/testing equivalences so obtained allow us both to\ncompare different languages and to investigate the inte rplay between higher-order constructs\, concurrency and probabilistic syst ems. \n\n(Joint work with Marco Bernardo and Davide Sangiorgi). URL:https://chocola.ens-lyon.fr/events/seminaire-2014-09-25/sessions/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Ulrich Schöpp - On the Relation of Interaction Semantics to Conti nuations and Defunctionalization DTSTART:20140925T140000 DTEND:20140925T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-09-25/sessions/83/ CATEGORIES: DESCRIPTION:In Game Semantics\, the Geometry of Interaction and related ap proaches\nto programming language semantics\, programs are modelled by int eractive\nprocesses. Such interactive semantic models have been used in th e\ndesign of new compilation methods\, e.g. for hardware synthesis or for\ nprogramming with sublinear space. This talk is about how such\nsemantical ly motivated non-standard compilation methods relate to more\nstandard tec hniques in the compilation of functional programming\nlanguages\, namely c ontinuation passing and defunctionalization. The\ninterpretation of the la mbda-calculus in a model of computation by\ninteraction is related to a ca ll-by-name CPS-translation followed by a\ndefunctionalization procedure th at takes into account control-flow\ninformation. I will describe the relat ion first for the linear\nlambda-calculus\, then extend this to the simply -typed lambda-calculus\nand consider extensions\, such as recursion.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-09-25/sessions/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Ugo Dal Lago - Towards a Coinductive Characterization of Computati onal Indistinguishability DTSTART:20140925T103000 DTEND:20140925T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-09-25/sessions/82/ CATEGORIES: DESCRIPTION:Computational indistinguishability is one of the most central concepts \nin modern cryptography\, and many other definitions (e.g. \npse udorandomness\, security of cryptographic schemes) can be formulated \nin terms of CI. We present the results of a study directed towards \ngiving a direct and precise characterization of computational \nindistinguishabili ty in an higher-order functional language for \npolynomial time computabil ity\, in which tools from implicit \ncomputational complexity and coinduct ion both play a central role.\nThis is joint work with Alberto Cappai. URL:https://chocola.ens-lyon.fr/events/seminaire-2014-09-25/sessions/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Fanny He - A characterization of the Taylor Expansion of λ-terms DTSTART:20140403T153000 DTEND:20140403T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-04-03/sessions/81/ CATEGORIES: DESCRIPTION:The Taylor expansion of λ-terms\, as introduced by Ehrhard an d Regnier\,\nexpresses a λ-term as a series of multi-linear terms\, which capture bounded\ncomputations. Normal forms of Taylor expansions give a n otion of infinitary\nnormal forms\, refining the notion of Böhm trees in a quantitative setting.\nWe give the algebraic conditions over a set of no rmal simple terms which\ncharacterize the property of being the normal for m of the Taylor expansion of a λ-term. From this full completeness result \, we give further conditions which semantically describe normalizable and total λ-terms.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-04-03/sessions/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Bernardi - Mutually testing processes DTSTART:20140403T140000 DTEND:20140403T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-04-03/sessions/80/ CATEGORIES: DESCRIPTION:In the standard testing theory of DeNicola-Hennessy one proc ess is considered to be a refinement of another if every test guaranteed by the former is also guaranteed by the latter. In the domain of web serv ices this has been recast\, with processes viewed as servers and tests as clients. In this way the standard refinement preorder between servers is determined by their ability to satisfy clients. \n\nBut in this setting th ere is also a natural refinement preorder between clients\, determined by their ability to be satisfied by servers. In more general settings where there is no distinction between clients and servers\, but all processes ar e peers\, there is a further refinement preorder based on the mutual satis faction of peers.\n\n\nIn this talk we are concerned with the behavioural characterisations of the server and the client preorders.\nAcceptance sets are enough to capture the server preorder\, but not the client one. To ch aracterise the client preorder we introduce the notion of "usability"\, an d combine it with the one of acceptance sets. This is enough to characteri se also the peer preorder.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-04-03/sessions/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmanouel Beffara - A logical view on scheduling in concurrency DTSTART:20140403T103000 DTEND:20140403T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-04-03/sessions/79/ CATEGORIES: DESCRIPTION:This paper elaborates on a new approach of the question of the proof-theoretic study of concurrent interaction called "proofs as schedul es". Observing that proof theory is well suited to the description of conf luent systems while concurrency has non-determinism as a fundamental featu re\, we develop a correspondence where proofs provide what is needed to ma ke concurrent systems confluent\, namely scheduling. In our core logical s ystem (a variant of multiplicative linear logic)\, processes and scheduler s appear explicitly as proofs in different fragments of the proof language and cut elimination between them does correspond to execution of a concur rent system. This separation of roles suggests new insights for the denota tional semantics of processes and new methods for the translation of π-ca lculi into prefix-less formalisms (like solos)\, as the operational counte rpart of a translation between logical systems. URL:https://chocola.ens-lyon.fr/events/seminaire-2014-04-03/sessions/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Férée - A game semantics approach to complexity DTSTART:20140313T153000 DTEND:20140313T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-03-13/sessions/77/ CATEGORIES: DESCRIPTION:There are numerous notions of computability for non-standard s tructures\, like higher order functions or real number computations. Howev er\, most of their\nunderlying computational model lack a natural notion o f complexity. Indeed\, if we understand well what the complexity of a firs t order or even second order\nfunctions is\, it is far from being the case for other\, more complex objects.\n \nI will describe a few existing comp utational models\, especially for higher order functions\, to see why they are not complexity-friendly. Then\, I will propose a\ngeneral framework b ased on game semantics to define meaningful notions of size and complexity for quite general objects and provide several examples to\nillustrate it. URL:https://chocola.ens-lyon.fr/events/seminaire-2014-03-13/sessions/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Marie Pédrot - Can Dialectica break bricks? DTSTART:20140313T140000 DTEND:20140313T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-03-13/sessions/78/ CATEGORIES: DESCRIPTION:The Dialectica translation is a logical transformation describ ed by\nGödel in 1958\, but designed in the 30's. At the end of the 80's\, it was\ngiven a categorical counterpart\, which happened to be compatible with\nthe usual decomposition of intuitionistic logic into linear logic.\ nStill\, it was lacking a true Curry-Howard interpretation.\n\nWe will fil l this hole by presenting the computational content of\nDialectica by mean s of an untyped lambda-calculus translation. We will\nshow that this trans lation has a really simple explanation as soon as we\nput our source term in the Krivine abstract machine\, except for a\ndisturbing detail\, seemin gly deeply rooted in linear logic. We will also\nshow how our presentation can be naturally applied to a\ndependently-typed system almost without ad aptation\, thus giving a\nhindsight on how linear dependent types may be b uilt (or not).\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-03-13/sessions/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoît Valiron - Towards a formal analysis of quantum algorithms DTSTART:20140313T103000 DTEND:20140313T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-03-13/sessions/76/ CATEGORIES: DESCRIPTION: The field of quantum algorithms is vibrant. Nevertheless\, th ere is\n currently a lack of programming languages for describing and\n formalizing quantum computation on a practical scale\, i.e.\, not just\n at the level of toy problems. We address this issue by introducing\n Quip per\, a scalable\, expressive\, functional\, higher-order quantum\n progr amming language. Quipper has been used to program a diverse set\n of non- trivial quantum algorithms\, and is able to generate quantum\n gate repre sentations using trillions of gates. \n \n In this talk\, I will present the setting and the current (limited)\n semantics for quantum computatio n. I will introduce Quipper and\n discuss what is currently missing\, tha t is\, a linear type system to\n capture the non-duplicability of quantum data. From there I will\n present two uses for this type-system: (1) an denotational semantics\n for all of quantum computation\, and (2) resourc e estimation for\n quantum algorithms.\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2014-03-13/sessions/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Giuseppe Castagna - Polymorphic Functions with Set-Theoretic Types DTSTART:20140213T140000 DTEND:20140213T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-02-13/sessions/73/ CATEGORIES: DESCRIPTION:We present a calculus with higher-order polymorphic functions\ , recursive types with arrow and product type constructors and set-theoret ic type connectives (union\, intersection\, and negation). In a first part we define and study the explicitly-typed version of the calculus in which type instantiation is driven by explicit instantiation annotations. In pa rticular\, we define an explicitly-typed lambda-calculus with intersection types and an efficient evaluation model for it. In the second part\, we d efine a local type inference system that allows the programmer to omit exp licit instantiation annotations\, and a type reconstruction system that al lows the programmer to omit explicit type annotations. This work provides the theoretical foundations and technical machinery needed to design and i mplement higher-order polymorphic functional languages for semi-structured data. URL:https://chocola.ens-lyon.fr/events/seminaire-2014-02-13/sessions/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilles Barthe - Verified implementations of cryptographic standar ds DTSTART:20140213T113000 DTEND:20140213T123000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-02-13/sessions/72/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2014-02-13/sessions/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Luke Ong - Functions\, Concurrency and Automatic Verification DTSTART:20140213T100000 DTEND:20140213T110000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2014-02-13/sessions/74/ CATEGORIES: DESCRIPTION:We study the automatic verification of asynchronous message-pa ssing\n concurrent programs. This talk will begin with a survey of a rec ent\n project [1]\, Soter\, to verify safety properties of Erlang progra ms by\n abstract interpretation and infinite-state model checking\, and a\n discussion of the lessons learn. The rest of the talk will focus on an\n approach to address a source of imprecision of the Soter approach. Â\n We study the reachability problem of concurrent pushdown systems th at\n communicate via unbounded and unordered message buffers\, a model o f\n computation for Erlang programs. Our goal is to relax the common\n restriction that messages can only be retrieved by a pushdown process\n when its stack is empty. We introduce a new class of Asynchronously\n P artially Commutative Pushdown Systems with a mild shape constraint on\n the stacks for which the coverability problem is decidable. Stacks that\n fit the shape constraint may reach arbitrary heights\; further a process \n may execute any communication action (be it process creation\, messag e\n send or retrieval) whether or not its stack is empty. This class\n extends previous computational models studied in the setting of\n async hronous procedural calls\, and enables the safety verification of a\n la rge class of recursively-defined message-passing programs.\n This is joi nt work with Jonathan Kochems and Emanuele D'Osualdo.\n [1] [1]http://mj olnir.cs.ox.ac.uk/soter URL:https://chocola.ens-lyon.fr/events/seminaire-2014-02-13/sessions/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Hyeonseung Im - A modal logic internalizing normal proofs DTSTART:20131212T160000 DTEND:20131212T170000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-12-12/sessions/71/ CATEGORIES: DESCRIPTION:In the proof-theoretic study of logic\, the notion of normal p roof has been understood and investigated\nas a metalogical property. Usua lly we formulate a system of logic\, identify a class\nof proofs as normal proofs\, and show that every proof in the system reduces to a correspondi ng\nnormal proof. This paper develops a system of modal logic that is capa ble of expressing\nthe notion of normal proof within the system itself\, t hereby making normal proofs an inherent\nproperty of the logic. Using a mo dality △ to express the existence of a normal proof\, the system\nprovid es a means for both recognizing and manipulating its own normal proofs. We develop the\nsystem as a sequent calculus with the implication connective ⊃ and the modality △\, and prove the\ncut elimination theorem. From t he sequent calculus\, we derive two equivalent natural deduction systems.\ n\nJoint Work with Sungwoo Park (Pohang)\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-12-12/sessions/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Guy McCusker - Weighted relational models of typed lambda-calculi DTSTART:20131212T143000 DTEND:20131212T153000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-12-12/sessions/70/ CATEGORIES: DESCRIPTION:The category Rel of sets and relations yields one of the simpl est denotational semantics of Linear Logic. Rel can be viewed as the bipro duct completion of the Boolean ring. We consider the generalization of thi s construction to arbitrary continuous semirings\, producing categories th at provide cpo-enriched models of linear logic akin to Rel\, and investiga te models of PCF in their co-Kleisli categories. These models contain quan titative information\, provided by the elements of the semiring R. Specifi c instances of R allow us to compare programs not only with respect to “ what they can do”\, but also “in how many steps” or “in how many d ifferent ways” (for non-deterministic PCF) or even “with what probabil ity” (for probabilistic PCF).\n\nJoint work with Jim Laird (Bath) and Gi ulio Manzonetto and Michele Pagani (LIPN\, Paris-Nord) URL:https://chocola.ens-lyon.fr/events/seminaire-2013-12-12/sessions/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Padovani - Ticket entailment is decidable DTSTART:20131212T110000 DTEND:20131212T123000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-12-12/sessions/69/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2013-12-12/sessions/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Neelakantan R. Krishnaswami - Types for Higher-Order Functional Re active Programming DTSTART:20131114T153000 DTEND:20131114T170000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-11-14/sessions/68/ CATEGORIES: DESCRIPTION:Functional reactive programming (FRP) is an elegant approach t o\ndeclaratively specify reactive systems. However\, the powerful\nabstrac tions of FRP have historically made it difficult to predict and\ncontrol t he resource usage of programs written in this style.\n\nIn this talk\, I d escribe a new language for higher-order reactive\nprogramming. This langua ge generalizes and simplifies work on functional reactive programming\, su pporting the use of higher-order abstractions such as first-class function s and streams of streams.\n\nFurthermore\, the type system can be understo od (via the Curry-Howard correspondence) as a proof system for a variant o f linear temporal logic\, and the type discipline also permits a simple an d provably efficient implementation strategy.\n\nTime permitting\, I will also discuss some preliminary work on denotational models for this calculu s. URL:https://chocola.ens-lyon.fr/events/seminaire-2013-11-14/sessions/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Beniamino Accattoli - Toward a New Theory of Exponential Proof- Nets DTSTART:20131114T140000 DTEND:20131114T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-11-14/sessions/66/ CATEGORIES: DESCRIPTION:Despite being one of the most successful outcomes of linear lo gic\, the theory of proof-nets for Multiplicative and Exponential Linear L ogic (MELL) is not fully satisfactory. In this talk I will discuss two of its shortcomings\, the need of explicit boxes\, and the elaborated reasoni ng behind its proof of strong normalization. \nIn the first part I will sh ow how switching to a polarized version of MELL allows to internalize boxe s\, so that they are induced by the proof itself\, instead of being explic itly added to the graph. These "implicit boxes" are canonical and enjoy a correctness criterion which is a natural extension of Laurent's criterion for Polarized MELL. Moreover\, they induce new cut-elimination rules.\n\nI n the second part I will focus on the new dynamics recasted in the usual\, non-polarized setting with explicit boxes. I will introduce a notion of s ubstitution for proof nets and use it to revisit the proof of strong norma lization\, organizing it along three abstract principles. The new dynamics admits a very simple proof of these principles (and thus of strong normal ization)\, while the ordinary dynamics does not.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-11-14/sessions/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominic Hughes - Is linear logic two-thirds wrong (for classical f irst-order logic)? DTSTART:20131114T103000 DTEND:20131114T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-11-14/sessions/67/ CATEGORIES: DESCRIPTION:Linear logic decomposes classical logic into multiplicatives\, additives\nand exponentials. Multiplicative proof nets are remarkably ele gant\;\nadditive and exponential nets have struggled in comparison. Could this\nstruggle mean that additives and exponentials are simply the wrong w ay to\ndecompose classical logic?\n\nI present a decomposition of classica l first-order logic which retains\nmultiplicatives at its core and replace s additives and exponentials with a\nnaive notion: a function f is the ide al parallel representation of\ncontraction and weakening. Contraction occu rs when f(x)=f(y) and weakening\noccurs outside the image of f.\n\nThe app roach clarifies the units: the positive multiplicative unit is\nretained a nd the three problematic units are rejected. Quantifiers are\nbroadly simi lar to those in multiplicative proof nets.\n\n[Note: additives and exponen tials are interesting and elegant in their own\nright\; here I reject them only from the perspective of decomposing\nclassical first-order logic.] URL:https://chocola.ens-lyon.fr/events/seminaire-2013-11-14/sessions/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Mio - Semantic Foundations of Quantitative (real-valued) Lo gics based on Functional Analysis DTSTART:20131017T153000 DTEND:20131017T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-10-17/sessions/65/ CATEGORIES: DESCRIPTION:Several notions of bisimulation for Probabilistic Nondetermini stic Transition Systems (PNTS) have been proposed in the literature. We de velop the theory of what we call "Upper-Expectation bisimilarity" using st andard results of linear algebra and functional analysis and provide stron g mathematical foundations for real-valued modal logics for PNTS's. URL:https://chocola.ens-lyon.fr/events/seminaire-2013-10-17/sessions/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Aloïs Brunel - Composing forcing and classical realizability: the monitoring calculus DTSTART:20131017T140000 DTEND:20131017T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-10-17/sessions/64/ CATEGORIES: DESCRIPTION:In this talk\, I will present the monitoring calculus\, which is the result of a new forcing program transformation. It's a lambda calcu lus with a state that is able to monitor the execution of programs (this " monitoring" being a parameter of the machine). This mechanism is similar t o what happens in Miquel's KFAM (Krivine Forcing Abstract Machine).\n\nBas ed on this calculus\, I define the notion of Forcing Computational Algebra (FCA)\, which internalizes the composition of linear forcing with a more usual biorthogonality-based realizability. As we will see\, by considering different FCAs\, we obtain realizability frameworks for various programmi ng languages (for example featuring higher-order references\, recursive ty pes\, bounded-time/space execution\, streams\, etc.)\, all sharing a commo n soundness result.\n\nI will also show how the well-known technique of it erated forcing corresponds in our framework to a certain construction on F CAs\, allowing us to combine different programming features in a modular w ay.\n\nThe ultimate goal of this work is to obtain a general\, modular\, a lgebraic framework in which we design and combine realizability models for all kind of programming languages. URL:https://chocola.ens-lyon.fr/events/seminaire-2013-10-17/sessions/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Brunerie - Homotopy type theory and homotopy groups of s pheres DTSTART:20131017T103000 DTEND:20131017T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-10-17/sessions/63/ CATEGORIES: DESCRIPTION:I will give an overview of homotopy type theory (HoTT)\, a fie ld combining abstract homotopy theory with dependent type theory. I will t hen explain the problem of computing homotopy groups of spheres and how it relates to homotopy type theory. URL:https://chocola.ens-lyon.fr/events/seminaire-2013-10-17/sessions/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Pagani - Probabilistic Coherence Spaces are Fully Abstract for Probabilistic PCF DTSTART:20130926T153000 DTEND:20130926T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-09-26/sessions/62/ CATEGORIES: DESCRIPTION:Probabilistic coherence spaces PCOH yield a semantics of highe r-order probabilistic computation\, interpreting types as convex sets and programs as power series. We prove that the equality of interpretations in PCOH characterizes the operational indistinguishability of programs in PC F with a random primitive.\n\nThis is the first result of full abstraction for a semantics of probabilistic PCF. The key ingredient relies on the re gularity of power series and introduces\, in denotational semantics\, tech niques coming from Calculus.\n\nAlong the way to the theorem\, we design a weighted intersection type assignment system giving a logical presentatio n of PCOH.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-09-26/sessions/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Basaldella - An interactive semantics for classical proofs DTSTART:20130926T140000 DTEND:20130926T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-09-26/sessions/61/ CATEGORIES: DESCRIPTION:The aim of this talk is to present a semantics for proofs in c lassical logic.\n\nClassical logic: We use a variant of the proof-system i ntroduced by Tait\n(1968)\, a system which is often used for analyzing the proof-theory of\nclassical arithmetic and its fragments. The language of this logic consists of\ninfinitary propositional formulas\, and the proof- system for this language is\nformulated through a sequent calculus with in finitary rules of inference.\n\nProofs: The target of our analysis is not the derivability predicate “the\nformula A is derivable”\, but the mor e subtle relation “p is a proof of the\nformula A”\, that we abbreviat e as “p der A.” In order to define this relation\,\nwe need to formali ze the concept of “formula-free proofs”\, i.e\, proofs that\ndoes not depend (too much) on the formulas they prove. To understand the idea\nbehi nd this concept\, consider the untyped λ-calculus. By the Curry-Howard\nc orrespondence\, λ-terms can be seen as a “formula-free” formalization of\nnatural deduction proofs for the implicational fragment of intuitioni stic\npropositional logic. Hence\, “p der A” can be read as “the unt yped λ-term p has\n(simple) type A in the Curry-style type assignment.” Here we use a similar\nidea: we define a class of objects that we call te sts which play the role of\nthe untyped λ-terms\, and in order to define p der A\, we use Tait’s normal\nrules as type assignment.\n\nSemantics: Our semantics is deeply inspired by Girard’s ludics (2001). As in\nuntyp ed λ-calculus β-reduction can be seen as natural deduction normalization \n“without types”\, we similarly define a “formula-free” cut-elimi nation\nprocedure which works with tests\, that we call interaction. By an alyzing the\nproperties of interaction\, we define another relation “p i nt A” between tests\nand formulas with the following meaning: “the res ult of the interaction\nbetween the test p and the counter-tests for A ter minates.” We finally show a\nsoundness-and-completeness theorem: “p de r A” if and only if “p int A”. URL:https://chocola.ens-lyon.fr/events/seminaire-2013-09-26/sessions/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Raffalli - Nullstellensatz and Positivestellensatz from cut-elimination DTSTART:20130926T103000 DTEND:20130926T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-09-26/sessions/60/ CATEGORIES: DESCRIPTION:\nWe give here an effective proof of Hilbert's nullstellensatz and\nKrivine-Stengle's positivestellensatz using the cut elimination theo rem for\nsequent calculus. The proof is very similar to the current techn iques in\nconstructive algebraic geometry by Henri Lombardi\, but seems mo re modular.\n\nIn the case of the positive stellensatz\, we think we prove a more general\nresult than the original one\, thanks to a new notion of justification of\npositiveness: PBDD (polynomial binary decision diagram). It allows both to\nrecover Krivine-Stengle's justification\, but also ano ther one which seems to\nrequire lower degree.\n\nWe apply the same techni ques to the nullstellensatz for differentially closed\nfield and show that the proof is almost unchanged.\n\nRemark: here we do not provide bound\, but an effective algorithm (implemented\nin OCaml) to build the wanted alg ebraic equality. Nevertheless\, we discuss how\nbound could probably be ob tained. We also do not deal effectively with the\naxiom of algebraic/real closure. Those are eliminated using standard model\ntheory.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-09-26/sessions/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Silva - Coalgebra: applications in automata theory and p rogramming language design DTSTART:20130516T153000 DTEND:20130516T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-05-16/sessions/59/ CATEGORIES: DESCRIPTION: We give a brief introduction to the coalgebraic method and show two\n recent\n developments that attest its generality and useful ness.\n\n We first show a new proof of Brzozowski's minimization\n alg orithm and discuss generalizations resulting from this new\n perspective .\n\n We then present CoCaml\, a functional programming language extendi ng\n OCaml\,\n which allows us to define functions on coinductive data types\n parameterized by\n an equation solver. We provide compelling e xamples that attest to the\n usefulness of\n the new programming const ructs.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-05-16/sessions/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Marie Madiot - A pi-calculus with preorders DTSTART:20130516T140000 DTEND:20130516T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-05-16/sessions/57/ CATEGORIES: DESCRIPTION:The fusion calculi are a simplification of the pi-calculus in\ nwhich input and output are symmetric and restriction is the only\nbinder. We highlight a major difference between these calculi and\nthe pi-calcul us from the point of view of types\, proving some\nimpossibility results f or subtyping in fusion calculi. We propose a\nmodification of fusion calc uli in which the name equivalences\nproduced by fusions are replaced by na me preorders\, and with a\ndistinction between positive and negative occur rences of names. The\nresulting calculus allows us to import subtype syst ems\, and related\nresults\, from the pi-calculus. We examine the consequ ences of\nthe modification on behavioural equivalence (e.g.\, context-free \ncharacterisations of barbed congruence) and expressiveness (e.g.\,\nfull abstraction of the embedding of the asynchronous\npi-calculus). URL:https://chocola.ens-lyon.fr/events/seminaire-2013-05-16/sessions/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrzej Murawski - Deconstructing general references via game sema ntics DTSTART:20130516T103000 DTEND:20130516T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-05-16/sessions/58/ CATEGORIES: DESCRIPTION:We investigate the game semantics of general references throug h the fully\nabstract game model of Abramsky\, Honda and McCusker (AHM)\, which\ndemonstrated that the visibility condition in games corresponds to the extra\nexpressivity afforded by higher-order references with respect t o integer\nreferences. First\, we prove a stronger version of the visible factorisation\nresult from AHM\, by decomposing any strategy into a visibl e one and\na single strategy corresponding to a reference cell of type uni t -> unit\n(AHM accounted only for finite strategies and its result involv ed\nunboundedly many cells).\n\nWe show that the strengthened version of t he theorem implies universality\nof the model and\, consequently\, we can rely upon it to provide semantic\nproofs of program transformation results . In particular\, one can prove that\nany program with general references is equivalent to a purely functional\nprogram augmented with a single unit -> unit reference cell and a single\ninteger cell. We also propose a synt actic method of achieving such a\ntransformation.\nFinally\, we provide a type-theoretic characterisation of terms in which\nthe use of general refe rences can be simulated with an integer reference\ncell or through purely functional computation\, without any changes to\nthe underlying types.\n\n This is joint work with Nikos Tzevelekos (Queen Mary\, University of Londo n)\,\npresented at FOSSACS'13 earlier this year.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-05-16/sessions/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Munch-Maccagnoni - When composition is not associative DTSTART:20130411T153000 DTEND:20130411T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-04-11/sessions/55/ CATEGORIES: DESCRIPTION:Strict and lazy composition (in the presence of\nevaluation or der) do not associate. The\nphenomenon was observed multiple times in\nsem antics (programming\, proof theory).\n\nNon-associativity is not only ubiq uitous but\nalso characterises by itself notions of\ncomputation with non- trivial evaluation\norder\, as we will see. URL:https://chocola.ens-lyon.fr/events/seminaire-2013-04-11/sessions/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Colin Riba - Forcing MSO on Infinite Words in Weak MSO DTSTART:20130411T140000 DTEND:20130411T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-04-11/sessions/54/ CATEGORIES: DESCRIPTION:We propose a forcing-based interpretation of\nmonadic second-o rder logic (MSO) on !-words in Weak MSO\n(WMSO). The interpretation is pur ely syntactic and compositional.\nWe show that a formula with parameters i s true in MSO if and\nonly if its interpretation is true in WMSO. We also show that a\nclosed formula is true in MSO if and only if its interpretati on is\nprovable under some axioms which hold for WMSO\, but without\naxiom atizing it.\nWe use model-theoretic arguments. Our approach is inspired\nf rom point-free topology: infinite words\, seen as topological points\,\nar e approximated by filters of bounded segments. We devise\nforcing conditio ns such that the corresponding generic filters\napproximate Ramseyan facto rizations of infinite words modulo\nsatisfaction of formulas of a given qu antifier depth.\nOur interpretation parallels some approaches to Mc-\nNaug hton?s Theorem (equivalence between non-deterministic\nB¨uchi automata an d deterministic Rabin automata) but the\nobtained formulas do not by thems elves describe deterministic\nautomata. URL:https://chocola.ens-lyon.fr/events/seminaire-2013-04-11/sessions/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Tabareau - Univalence for free\, not yet ... DTSTART:20130411T103000 DTEND:20130411T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-04-11/sessions/56/ CATEGORIES: DESCRIPTION:We present an internalization of the 2-groupoid (or rather gro upoidoid)\ninterpretation of the calculus of construction that allows to r ealize\nproof irrelevance\, reasoning modulo and a weak form of the unival ence\naxiom. As an example\, we show that in our setting\, the type of Chu rch\nintegers is equal to the inductive type of natural numbers. URL:https://chocola.ens-lyon.fr/events/seminaire-2013-04-11/sessions/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmanuel Beffara - Proofs as schedules DTSTART:20130314T153000 DTEND:20130314T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-03-14/sessions/53/ CATEGORIES: DESCRIPTION:This work proposes a new interpretation of the logical content s of programs in the context of concurrent interaction\, wherein proofs co rrespond to valid executions of a processes. A type system based on linear logic is used\, in which a given process has many different types\, each typing corresponding to a particular way of interacting with its environme nt and cut elimination corresponds to executing the process in a given int eraction scenario. A completeness result is established\, stating that eve ry lock-avoiding execution of a process in some environment corresponds to a particular typing. Besides traces\, types contain precise information a bout the flow of control between a process and its environment\, and proof s are interpreted as composable schedulings of processes. In this interpre tation\, logic appears as a way of making explicit the flow of causality b etween interacting processes.\n\nJoint work with [Virgile Mogbil](http://w ww-lipn.univ-paris13.fr/~mogbil/). URL:https://chocola.ens-lyon.fr/events/seminaire-2013-03-14/sessions/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Chung-Kil Hur - The Power of Parameterization in Coinductive Proof DTSTART:20130314T140000 DTEND:20130314T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-03-14/sessions/51/ CATEGORIES: DESCRIPTION:In this talk\, I will present a very simple principle for reas oning\nabout coinduction\, which we call parameterized coinduction. More\n precisely\, it is a theorem about the greatest fixed point of a\nmonotone function on a complete lattice. This theorem is as simple as\nthe Tarski's fixed-point theorem but provides a more useful reasoning\nprinciple.\n\nI n a different point of view\, the principle captures a semantic notion\nof "guarded proof" in coinduction. Thus we implemented a new tactic\n"pcofix " replacing Coq's primitive tactic "cofix" and avoiding its\nsyntactic gua rdedness checking of proof terms.\n\nYou can find the Coq library 'Paco' t hat provides the tactic 'pcofix' at\n\n[http://plv.mpi-sws.org/paco](http: //plv.mpi-sws.org/paco)\n\nThis is joint work with Georg Neis\, Derek Drey er and Viktor Vafeiadis.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-03-14/sessions/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Robin Cockett - Linear types as a semantics for concurrency: passi ng messages and defining protocols DTSTART:20130314T103000 DTEND:20130314T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-03-14/sessions/52/ CATEGORIES: DESCRIPTION:Linear logic has since its inception been viewed as being clos ely\nconnected to concurrency. However\, making this connection explicit\ nhas been difficult as it lacked two key features of concurrent\nprograms: the ability to pass messages and the ability to define\nprotocols. Messag es consist of data from the sequential world which\ncan be passed along ch annels from one process to another\, while\nprotocols are types which des cribe patterns of interactions.\n\nThe talk will describe the semantics of these facilities in terms of a\nCurry-Howard-Lambek correspondence betwee n the proof theory (the logic\nof message passing)\, the categorical seman tics (linear categories)\,\nand the term logic (a concurrent programming l anguage).\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-03-14/sessions/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Seiller - Espace Logarithmique et Permutations DTSTART:20130215T153000 DTEND:20130215T160000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/47/ CATEGORIES: DESCRIPTION:Suite à son travail récent utilisant des algèbres de von Ne umann\, Girard a proposé une nouvelle approche pour l'étude des classes de complexité. Cette méthode utilise la construction du produit croisé entre une algèbre et un groupe agissant sur celle-ci. Cette construction consiste à internaliser les automorphismes externes représentés par le groupe\, et Girard propose de caractériser les classes de complexité par des ensembles d'opérateurs engendrés par ces internalisations.\n\nNous avons étudié\, avec Clément Aubert\, le cas de l'action du groupe des p ermutations des entiers naturels sur un produit tensoriel. Dans un premier travail\, nous avons montré que dans ce cas la méthode proposée par Gi rard permet d'obtenir une caractérisation de la classe co-NL (le complém entaire de l'ensemble des langages décidables par une machine de Turing n on-déterministe en espace logarithmique). Afin de prouver ce résultat\, nous avons défini la notion de machine à pointeurs qui s'avère être un e nouvelle caractérisation de co-NL par des machines abstraites. Plus ré cemment\, nous avons étendu ce travail en définissant un ensemble d'opé rateurs caractérisant exactement la classe L (LogSpace).\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul-André Melliès - Logique tensorielle et principe de chiralit é DTSTART:20130215T143000 DTEND:20130215T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/46/ CATEGORIES: DESCRIPTION:Dans cet exposé\, j'expliquerai comment utiliser le principe de chiralité\npour décomposer la négation tensorielle en constituants élémentaires.\nL'analyse débouchera sur une présentation purement comb inatoire\nde la notion de catégorie de dialogue. Les combinateurs que j'o btiens\nsont les suivants: (1) une négation involutive\, (2) une adjoncti on\nentre foncteurs de contrôle L et R\, (3) une paire de combinateurs\na xiome - coupure\, et (4) une paire de lois distributives en chiralité. \n J'expliquerai au moyen de diagrammes de cordes comment\nchacun de ces comb inateurs raffine le combinateur lui correspondant\nen logique linéaire. M on exposé s'appuiera en grande partie\nsur les articles 4 et 5 que je viens de mettre en ligne.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Baptiste Midez - Quelques aspects combinatoires du lambda-cal cul avec ressources DTSTART:20130215T140000 DTEND:20130215T143000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/45/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Yves Lafont\, Pierre Rannou - Réécriture de diagrammes convergen te pour l'algèbre linéaire DTSTART:20130215T120000 DTEND:20130215T123000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/44/ CATEGORIES: DESCRIPTION:La réécriture de diagrammes\, inspirée par les travaux d'Al bert Burroni sur les catégories monoïdales\,\ngénéralise à la fois la réécriture de mots (pour les monoïdes) et la réécriture de termes (p our les théories algébriques du premier ordre).\nLa confluence et la ter minaison de tels systèmes de réécriture ont d'abord été étudiées pa r Yves Lafont\, puis Yves Guiraud\,\nnotamment dans le cadre de l'algèbre linéaire sur le corps fini à 2 éléments.\nUne généralisation de ce calcul pour un corps K quelconque\, apparentée au calcul matriciel\, a é té étudiée par Pierre Rannou.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Flavien Breuvart - Une bien étrange caractérisation de l'adéqua tion complète dans les domaines de Scott DTSTART:20130215T110000 DTEND:20130215T113000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/42/ CATEGORIES: DESCRIPTION:Il existe une vaste littérature traitant de résultats d'adé quation complète (c'est à dire la correspondance entre la congruence dé notationnelle et la congruence observationnelle) pour une multitude de cou ple modèle-langage. Mais l'adéquation complète en tant qu'objet a rarem ent été étudiée\, à l'exception notable du langage PCF\, pour lequel Milner a caractérisé la classe des modèles complétement adéquats\, q ui sont ceux dont les éléments compacts sont définissables. Même dans le cas du lambda-calcul\, s'il existe des conditions nécessaires (extensi onnalité) ou suffisantes (stratification)\, aucune caractérisation n'a été donnée. Je vais donc expliquer comment\, dans une classe de modèle suffisamment restreinte\, la caractérisation de l'adéquation complète pour le lambda-calcul se trouve être surprenamment complexe.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre-Louis Curien - Revisiting the categorical interpretation of dependent type theory DTSTART:20130215T103000 DTEND:20130215T110000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/41/ CATEGORIES: DESCRIPTION:(travail en commun avec Richard Garner (Macquarie University\ , Sydney) et Martin Hofmann (Ludwig-Maximilian's-Universität\, München) \n\nWe relate Hofmann's and Curien's interpretations of Martin-Löf's type theory\, which were both designed to cure a mismatch between syntax and s emantics in Seely's original interpretation in locally cartesian closed c ategories. As an outcome\, we obtain a new proof of the coherence theorem that Curien had proved\, which implied that Seely's interpretation in the end was sound.\n\n(exposé en français)\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-02-15/sessions/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulio Manzonetto - Loader and Urzyczyn are Logically Related DTSTART:20130214T153000 DTEND:20130214T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-02-14/sessions/49/ CATEGORIES: DESCRIPTION:In simply typed λ-calculus with one ground type the following theorem due to Loader holds. (i) Given the full model F over a finite set \, the question whether some element f∈F is λ-definable is undecidable. In the λ-calculus with intersection types based on countably many atoms\ , the following is proved by Urzyczyn. (ii) It is undecidable whether a ty pe is inhabited. Both statements are major results presented in Barendregt -Dekkers-Statman'12. We show that (i) and (ii) follow from each other in a natural way\, by interpreting intersection types as continuous functions logically related to elements of F. From this\, and a result by Joly on λ -definability\, we get that Urzyczyn's theorem already holds for intersect ion types with at most two atoms. URL:https://chocola.ens-lyon.fr/events/seminaire-2013-02-14/sessions/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Guilhem Moulin - Type Theory in Colors DTSTART:20130214T140000 DTEND:20130214T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-02-14/sessions/50/ CATEGORIES: DESCRIPTION:Dependent type-theory is becoming the standard way to\nformali ze mathematics\, at the same time as displacing traditional\nplatforms for high-insurance programming.\n\nHowever\, current implementations of type- theory are not always\nsatisfactory in the sense that some "obvious truth" are impossible to\nprove\, making type-theory awkward to use for many app lications\, both in\nformalization and programming.\n\nWe propose an exten sion of type-theory with colored terms\, a notion of\ncolor erasure\, and an interpretation of colored types as predicates.\nThat leads to a more po werful type-theory: Some proofs and definitions\ncan now be trivially deri ved hence can be omitted\; Beside\, some\nparametricity results can be int ernalized. (Joint work with\nJean-Philippe Bernardy.) URL:https://chocola.ens-lyon.fr/events/seminaire-2013-02-14/sessions/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonino Salibra - From Lambda Calculi to Universal Algebra and To pology: Back and Forth DTSTART:20130214T103000 DTEND:20130214T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-02-14/sessions/40/ CATEGORIES: DESCRIPTION:Answering a question by Honsell and Plotkin\, we show that the re\nare two equations between lambda terms\, the so-called subtractive\neq uations\, consistent with lambda calculus but not\ncontemporaneously satis fied in any Scott continuous model.\n\nWe also relate the subtractive equa tions to the open problem of\nthe order-incompleteness of lambda calculus\ , by studying the\nconnection between the notion of absolute unorderabilit y in a\nspecific point and a weaker notion of subtractivity\, namely\nn-su btractivity\, for partially ordered algebras. Finally we study\nthe relati on between n-subtractivity and relativized separation\nconditions in topol ogical algebras\, obtaining an incompleteness\ntheorem for a general topol ogical semantics of lambda calculus.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-02-14/sessions/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Barbara Petit - Geometry of types DTSTART:20130117T153000 DTEND:20130117T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-01-17-1/sessions/38/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2013-01-17-1/sessions/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Alastair F. Donaldson - GPUVerify: a Verifier for GPU Kernels DTSTART:20130117T140000 DTEND:20130117T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-01-17-1/sessions/39/ CATEGORIES: DESCRIPTION:I will describe GPUVerify\, a collaboration between Imperial\n College London and Microsoft Research Redmond on the design and\n imp lementation of a technique and tool for analysing concurrent\n software written to run on graphics processing units (GPUs).\nGPUVerify checks the kernel functions that execute across cores of a\n GPU architecture and a ttempts to detect\, or verify absence of\, two\n kinds of defects: data races and barrier divergence. \nTo scale to\n large numbers of threads\, GPUVerify exploits the relatively simple\n nature of the GPU programmin g model in a way that allows verification\n of massively parallel kernel s to be reduced to a sequential program\n verification task. \nIn this t alk I will describe the defects that\n GPUVerify checks for\, present so me details of the verification\n technique\, and discuss open problems i n this area.\n \n This is joint work with:\n\n - Adam Betts\, Nathan Ch ong\, Peter Collingbourne*\, Jeroen Ketema\, Paul\n Thomson (Imperial)\n \n - Shaz Qadeer (Microsoft)\n\n (*) now at Google URL:https://chocola.ens-lyon.fr/events/seminaire-2013-01-17-1/sessions/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Pagani - Syntax vs Semantics: a quantitative bridge DTSTART:20130117T103000 DTEND:20130117T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2013-01-17-1/sessions/37/ CATEGORIES: DESCRIPTION:Since its inception\, various models of Linear Logic have been defined\nin categories of vector spaces (more generally modules) and line ar\nfunctions. These models provide semantics of quite expressive\nhigher- order functional programming languages\, where the\ndenotation of a progra m is given by a matrix.\n\nA natural question then arises -- What is the c omputational meaning of\nthe scalars appearing in\nsuch matrices?\, Can w e recover from them some operational behavior\nthat is hidden\nin the stan dard (domain based) semantics?\n\nDanos & Ehrhard give a first positive an swer in the specific case of\nprobabilistic coherence spaces. We address t he question in a more\ngeneral setting\, providing a general construction of adequate models\nparametrized by a continuous semiring of scalars. We s how how specific\ninstances of such a semiring allow to compare programs n ot only with\nrespect to "what they can do"\, but also in "how many steps" or "with\nwhat resources"\nor in "how many ways" (for non-determistic cal culi) or "with what\nprobability" (for probabilistic calculi).\n\n(This is a joint work with Jim Laird (Bath)\, Giulio Manzonetto (Paris\n13) and Gu y McCusker (Bath))\n URL:https://chocola.ens-lyon.fr/events/seminaire-2013-01-17-1/sessions/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Antoine Madet - Complexité Implicite de Lambda-Calculs Concurrent s (soutenance de thèse) DTSTART:20121206T150000 DTEND:20121206T173000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-12-06/sessions/36/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2012-12-06/sessions/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Gérard Boudol - Relaxed Semantics of Concurrent Programs DTSTART:20121206T133000 DTEND:20121206T143000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-12-06/sessions/31/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2012-12-06/sessions/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Hennessy - A theory of communicating transactions DTSTART:20121206T101500 DTEND:20121206T111500 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-12-06/sessions/30/ CATEGORIES: DESCRIPTION:We propose a novel language construct called communicating tra nsactions\,\nobtained by dropping the isolation requirement from classical transactions\,\nwhich can be used to model automatic error recovery in di stributed systems.\nWe extend CCS with this construct and give a simple se mantics for the extended\ncalculus\, called TransCCS. We develop a sound a nd complete theory for both\nmay- and fair-testing\, which we believe are the appropriate notions to capture\nsafety and liveness in TransCCS. We ex hibit the usefulness of our theory by\nproving illuminating laws and simpl e but non-trivial examples.\n\nJoint work with Edsko de Vries and Vasileio s Koutavas URL:https://chocola.ens-lyon.fr/events/seminaire-2012-12-06/sessions/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Kreuzer - Non-principal ultrafilters\, program extractio n and higher order reverse mathematics DTSTART:20121115T153000 DTEND:20121115T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-11-15/sessions/34/ CATEGORIES: DESCRIPTION:We investigate the strength of the existence of a non-principa l\nultrafilters over fragments of higher order arithmetic. \n\nLet (U) be the statement that a non-principal ultrafilter on N exists\nand let ACA_0^ w be the higher order extension of ACA_0\n(arithmetical comprehension).\n\ nWe show that ACA_0^w+(U) is \\Pi^1_2-conservative over ACA_0^w\nand thus that ACA_0^w+(U) is conservative over PA.\n\nMoreover\, we provide a progr am extraction method and show that from a\nproof of a strictly Pi^1_2 stat ement \\forall f \\exists g A_qf(f\,g)\nin ACA_0^w+(U)$ a realizing term in Gödel's system T can be\nextracted. This means that one can extract a term t\, such that\n\\forall f A_qf(f\,t(f)). URL:https://chocola.ens-lyon.fr/events/seminaire-2012-11-15/sessions/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Lionel Rieg - A case study of forcing in classical realisability: Herbrand's theorem\, proof and extracted algorithm DTSTART:20121115T140000 DTEND:20121115T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-11-15/sessions/35/ CATEGORIES: DESCRIPTION:We give here a new proof of Herbrand's theorem in PAω : we us e a forcing\ntransformation to add a Cohen real to PAω. This new real all ows us to avoid\nusing the fan theorem and requiring an order on atomic fo rmulas.\nWe then take a look at the program extracted from this new proof using\nKrivine's translation of forcing into classical realizability.\nBec ause of the clever uses (i.e. only in the forcing universe) of classical\n logic in the proof\, the extracted program does not backtrack the tree it\ nbuilds\, contrary to a classical proof without forcing.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-11-15/sessions/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Louis Krivine - Some examples of realizability models of ZF DTSTART:20121115T103000 DTEND:20121115T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-11-15/sessions/33/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2012-11-15/sessions/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Raffalli - Realisability\, call-by-value and Ramsey the orem DTSTART:20121011T153000 DTEND:20121011T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-10-11/sessions/24/ CATEGORIES: DESCRIPTION:First\, we will look at programs extracted from proofs of the\ ninfinite tape lemma (also called Stolzenberg's principle\, which\nsays th at a partition of N in two has at least one infinite\npart). We will show how a specific axiom on streams allow the\nextraction of an efficient pro gram.\n\nUsing this first program\, we will extract programs for Ramsey\nt heorem (not only for pairs) and as an application\, we will get a\nprogram for the ``happy ending problem'' (for all N\, in any\ninfinite set of poi nts\, we can find N points which are the\nvertices of a convex polygon).\n \nAll those extracted programs are SML program using CallCC. To\nprove tha t those SML programs are indeed correct\, we will\nintroduce call-by-value realizability and see that it is a\npromising variation of classical real izability.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-10-11/sessions/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Seiller - Interaction Graphs DTSTART:20121011T140000 DTEND:20121011T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-10-11/sessions/25/ CATEGORIES: DESCRIPTION:Geometry of Interaction (GoI) is a kind of semantics of linear logic proofs that aims at accounting for the dynamical aspects of cut-eli mination. We present here a parametrized construction of a GoI for Multipl icative Additive Linear Logic (MALL) in which proofs are represented by fa milies of directed weighted graphs. This construction is founded on a geom etrical identity between sets of cycles which generalizes the three-term a djunctions which sustain usual GoI constructions. Moreover we show how one can obtain\, for each value of the parameter\, a denotational semantics f or MALL from this GoI. Finally\, we will explain how this setting is relat ed to Girard's various constructions: two particular choices of the parame ter respectively give a combinatorial version of the latest GoI in the hyp erfinite factor and a refined version of older GoIs. Our construction henc e shows how Girard's various constructions relate to each other by unveili ng the unique geometrical identity sustaining them.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-10-11/sessions/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Bernardo Toninho - Linear Logic: A logical foundation for concurre nt computation DTSTART:20121011T103000 DTEND:20121011T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-10-11/sessions/26/ CATEGORIES: DESCRIPTION:Linear logic has long been heralded as a potential model for c oncurrency:\nfrom Girard's original paper\, to Abramsky's computational in terpretation\, \nreiterated by Bellin and Scott. More recently\, an interp retation for\nintuitionistic linear logic has been given by Caires and Pfe nning\nwhere propositions are viewed as session types - a well established \ntyping discipline for concurrency - proofs as processes and proof \nred uction as inter-process communication.\nIn this talk I will detail how thi s interpretation can form a basis to\na logical foundation that captures s everal interesting features of\nconcurrency and concurrent computation. Sp ecifically\, I will detail\nhow one can capture concurrent evaluation stra tegies for functional\ncomputation through canonical logical translations\ ; the relationship\nbetween isomorphisms in linear logic and (typed) proce ss equivalence\; \nhow asynchronous communication can be interpreted logic ally and sketch\nhow the interpretation can be extended to richer typed se ttings such as\ndependent type theories.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-10-11/sessions/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Mimram - The higher-dimensional structure of posets DTSTART:20120510T153000 DTEND:20120510T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-05-10/sessions/22/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2012-05-10/sessions/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcelo Fiore - Lie in Logic DTSTART:20120510T134500 DTEND:20120510T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-05-10/sessions/23/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2012-05-10/sessions/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Paulo Oliva - Some Connections Between Proof Theory and Game Theor y DTSTART:20120510T103000 DTEND:20120510T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-05-10/sessions/21/ CATEGORIES: DESCRIPTION:The semantic interpretation of the logical connectives and qua ntifiers as game\nconstructors is well-known and goes back to Lorenzen in the late 50s. The game\nassociated with a given formula consists of two pl ayers (Player and Opponent) arguing\nabout the validity of the formula\, s o that whenever the formula is provable the Player\nhas a winning strategy .\n\nIn my recent work on functional interpretations such as modified real izability and\nthe dialectica interpretation I have come across two novel connections between\ngame theory and proof theory\, which I would like to discuss in this talk.\n\nThe first is an observation that a functional int erpretation can be seen is a\nhigher-order version of the Lorenzen games\, where the game only has two rounds\nbut the two players are allowed to ch oose higher-order functionals as moves.\nSuch interpretation works not onl y for classical and intuitioinistic logic\, but\nextends nicely to linear logic as well (where it coincides with de Paiva's\ndialectica categories). \n\nThe second connection with game theory comes from recent joint work wi th Martín Escardó\non the computational interpretation of the countable and dependent choice. In there\nwe found that the dialectica interpretatio n of dependent choice can also be viewed\nas a statement about existence o f an optimal play in a way which generalises the notion\nof Nash equilibri um from the more traditional von Neumann Game Theory.\n\nThe aim of the ta lk will be to explain these two connections in detail.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-05-10/sessions/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandre Miquel - Classical realizability models\, parallel-or an d Boolean valued models DTSTART:20120405T153000 DTEND:20120405T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-04-05/sessions/20/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/seminaire-2012-04-05/sessions/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Kerneis - From threads to events through classical program transformations DTSTART:20120405T140000 DTEND:20120405T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-04-05/sessions/18/ CATEGORIES: DESCRIPTION:Threads and events are two common techniques to implement conc urrent programs.\nEvents are often deemed harder to write and understand t han threads\, because\ntheir control flow is scattered across long chains of callbacks. But the\nprogrammer cannot always afford using threads\, du e to resource constraints\n(eg. embedded systems) or language limitation ( eg. javascript). In such cases\,\nit might be desirable to translate threa ds into events automatically.\n\nWe present several styles of event-driven programs and study how to generate\nthem from a threaded description\, in the particular case of C programs. Our\ntranslation steps are made of cl assical and proven transformation techniques\,\nmost notably lambda-liftin g and conversion into continuation-passing style.\n\nThese techniques have been used to implement the CPC translator.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-04-05/sessions/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Zappa Nardelli - Verifying Fence Elimination Optimisatio ns DTSTART:20120405T103000 DTEND:20120405T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-04-05/sessions/19/ CATEGORIES: DESCRIPTION:(avec Viktor Vafeiadis\, et Suresh Jagannathan\, Jaroslav Sevc ik\, Peter Sewell)\n\nA simple compiler optimisation for removing redundan t memory fences in\nprograms running on top of x86 multiprocessors turned out to be\nchallenging to prove correct. In this talk\, I will give a sho rt\noverview of the challenges of the semantic design and verified\ncompil ation of high-level programming languages language above shared\nmemory mu ltiprocessors (focussing on x86 and Power/ARM)\, and will\nconclude by pro ving the fence optimisation correct by introducing a\nnovel simulation tec hnique.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-04-05/sessions/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Bernard Stefani - Reversing (HO)pi DTSTART:20120315T153000 DTEND:20120315T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-03-15/sessions/15/ CATEGORIES: DESCRIPTION:The talk will present recent work dealing with the introductio n of a notion of reversibility in concurrent languages.\nReversibility ref ers to the ability to undo an execution and to revert it to a prior state. Such a facility can be useful for a variety of purposes\, including debug ging\, safe exception handling\, programming atomic operations and transac tions\, and more generally programming recoverable systems. The talk will discuss how to introduce reversibility in a paradigmatic concurrent langua ge\, the higher-order pi-calculus\, and will discuss the subtleties involv ed in defining a semantically sound rollback primitive.\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-03-15/sessions/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Guenot - Nested typing and communication in the lambda-cal culus DTSTART:20120315T140000 DTEND:20120315T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-03-15/sessions/16/ CATEGORIES: DESCRIPTION:In a proof system based on the deep inference methodology (as\ nimplemented in the calculus of structures)\, new decompositions of\ninfer ence steps appear and enrich the possible shapes of proofs. In\nparticular \, the lazy context splitting embodied in the "switch"\nrule is a distinct ive feature of this methodology\, which is related\nin an essential way to the order of inference steps used in a proof\n(which can often be seen as equivalent to a sequent proof\, with a\nparticular interleaving chosen fo r branches).\n\nFrom a Curry-Howard perspective\, we are interested in the \ncomputational meaning of such a decomposition. In this talk\, I will\npr esent a system for intuitionistic logic in the calculus of\nstructures\, a nd show how to use it as a type system for a\nlambda-calculus with explici t substitutions. The switch rule\, seen\nas a typing rule\, introduces a n ew operator performing a\nsynchronisation (that is\, a form of communicati on) between\ndifferent parts of a term. This yields interesting observatio ns and\nquestions\, concerning communication between "subprocesses" of a\n term\, evaluation strategies\, the implementation of functional\nlanguages and the treatment of contexts.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-03-15/sessions/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Dale Miller - Proof certificates as focused sequent proofs DTSTART:20120315T103000 DTEND:20120315T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2012-03-15/sessions/14/ CATEGORIES: DESCRIPTION:Computational logic systems\, such as theorem provers and mode l\ncheckers\, produce evidence of a successful proof in an assortment\nof (often ad hoc) formats. Unfortunately\, the evidence generated by\none pro ver is seldom readable by another prover or even by a future\nversion of i tself. As a result\, provers seldom trust and use proofs\nfrom other prove rs. This situation is made all the more regrettable\ngiven that logic and (formal) proof are certainly candidates for\nuniversally accepted standard s. I will outline some recent work on\ndesigning documents\, called proof certificates\, that satisfy the\nfollowing requirements: (i) They are chec kable by a simple proof\ncheckers\; (ii) They are flexible enough that exi sting provers can\nconveniently produce such certificates from their inter nal evidence\nof proof\; (iii) They are directly related to proofs used wi thin the\nstructural proof theory literature\; and (iv) They permit\ncerti ficates to elide some proof information with the expectation\nthat a proof checker can reconstruct the missing information using\nbounded and struct ured proof search. I shall show how the notion of\nfocus sequent proofs ca n be used to design such proof certificates.\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2012-03-15/sessions/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Herbelin - Proving with side-effects DTSTART:20120112T153000 DTEND:20120112T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/inauguration-recre/sessions/9/ CATEGORIES: DESCRIPTION:From a programming point of view\, control operators are effec tful\noperators whose effects can be cleared by using delimiters at base\n types. From the point of view of logic\, it has been shown that by\ndelimi ting control operators\, i.e. classical logic\, on purely\npositive formul as (an equivalent in predicate logic of\nSigma\\^0\\_1-formulas in arithme tic)\, we obtain a logic that remains\nessentially intuitionistic (in the sense of satisfying the\ndisjunction and existence properties) but whose l ogical strength\nnow constructively captures "axioms" such as Markov's pri nciple or\nthe double negation shift.\n\nThere is no reason to restrict th e delimitation to only control\noperators and indeed\, other kinds of deli mited effects such as\nmemory assigments can be considered too. This conne cts to Cohen's\nforcing what eventually yields an intuitionistic logic abl e to\nprove those axioms that are provably consistent by forcing.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/inauguration-recre/sessions/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Guilhem Jaber - Forcing the Calculus of Constructions to get gener alized inductive types DTSTART:20120112T140000 DTEND:20120112T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/inauguration-recre/sessions/10/ CATEGORIES: DESCRIPTION:In this talk\, I will present an extension of the Calculus of\ nConstructions (the theory behind Coq) which allows to extend\nmodularly t he type system with new constructors and new inference\nrules. The idea is to define a translation between the new system\nand the original one\, fo llowing the idea of Krivine and Miquel to\nstudy the translation of proofs induced by forcing. Our translation\nof forcing is is in fact an internal ization in the type theory of\nthe topos of presheaves of Birkedal et al.\ n\nI will then show how we can use this technique to extend the\ninductive types of Coq with negative occurrences. This will be used\nto formalize r ecent works on Kripke Logical Relations.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/inauguration-recre/sessions/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Streicher - A categorical approach to Krivine's classical r ealizability DTSTART:20120112T104500 DTEND:20120112T121500 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/inauguration-recre/sessions/8/ CATEGORIES: DESCRIPTION:The aim of our presentation is to give an account of Krivine's \nClassical Realizability based on the general categorical approach\nto re alizability developed by Hyland\, van Oosten\, Hofstra et.al.\n\nWe define a notion of abstract Krivine structure (aks) and show how\nit gives rise to an order pca with a filter. The latter induces a\ntripos (a categorical model of higher order logic) which in turn\ngives rise to a Classical Rea lizability Topos.\n\nWe formulate a precise theorem explaining why ordinar y forcing is\nthe commutative case of classical realizability.\n\nIf time allows it we shall also give an account of forcing within\nclassical reali zability considered by Krivine as part of his long\nterm project of realiz ing full ZFC.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/inauguration-recre/sessions/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Olivier Coucharière - Présentation ANR DTSTART:20120112T100000 DTEND:20120112T103000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/inauguration-recre/sessions/7/ CATEGORIES: DESCRIPTION: URL:https://chocola.ens-lyon.fr/events/inauguration-recre/sessions/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Damien Pous - Hopcroft\, Karp\, and up-to techniques DTSTART:20111208T153000 DTEND:20111208T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2011-12-08/sessions/12/ CATEGORIES: DESCRIPTION:(joint work with Filippo Bonchi)\n\nWe present a (hopefully) n ew algorithm for determining if two\nnon-deterministic finite automata are language equivalent. We\nexploit coinductive up-to techniques to improve the standard\nalgorithm by Hopcroft and Karp for deterministic finite auto mata\,\nso as to avoid computing the whole deterministic automata. Althoug h\nthe proposed algorithm remains exponential in worst case (the\nproblem is PSPACE-complete)\, experimental results show that it can\nbe much faste r than the standard algorithm: in most cases\, only a\nvery small portion of the underlying deterministic automata has to\nbe explored.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2011-12-08/sessions/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexis Bernardet - A simple presentation of the effective topos DTSTART:20111208T140000 DTEND:20111208T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2011-12-08/sessions/13/ CATEGORIES: DESCRIPTION:Topos theory can be used to abstract models of higher-order lo gic\nthe same way Heyting algebras can be used for propositional logic.\nA topos is a cartesian closed category that satisfies certain\nproperties ( e.g. the category of sets is a topos)\, but it is\ninteresting to see whet her it also satisfies some of these:\n\n> (1) The internal logic of the to pos has the law of excluded middle\n> (2) Every morphism of the topos is c omputable\n> (3) The topos has an object of natural integers (definition o f\n> Lawvere)\n\nWith these three properties\, the halting problem can be proved\ncomputable\; hence\, a (non-degenerated) topos cannot have the se\nthree properties at the same time:\n\n- With properties (1) and (3)\ , we have classical logic: the\n category of sets is a good example.\n- With properties (1) and (2)\, we have finite logic: the category\n o f finite sets is a good example\n- With properties (2) and (3)\, we have intuitionistic logic.\n\n One of the most famous topos satisfying thes e two properties is\n Hyland's effective topos\, which can be seen as t he universe of\n realisability. While it is quite simple to check that the category\n of sets and the category of finite sets are topos\, prov ing that the\n effective topos is indeed a topos is much harder.\n\n\nW e introduce here an alternative definition of Hyland's effective\ntopos\, based on a realisability framework with two levels of\nabstraction: a low level and a high level. With this definition\,\nthe proof that this framew ork forms a topos is almost as simple as\nproving that the category of set s is a topos. Moreover\, the high\nlevel of the framework can be directly used as a model of\nhigher-order intuitionistic systems.\n\nIndeed\, topos satisfying (2) and (3) are the most interesting ones\nfor computer scienc e because they ensure that a programming\nlanguage based on topos theory c an be given a constructive\nsemantics. In such a programming language\, we can only write\nfunctions that terminate\, as in proof assistants like Co q\, so the\nlanguage cannot be Turing-complete. The main advantage of havi ng a\nprogramming language based on topos theory over more usual\nintuitio nistic systems such as Martin-Loef type theory is the\nnotion of equality: it is extensional\, has proof-irrelevance\, and\nallows the axiom of uniq ue choice.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2011-12-08/sessions/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Christophe Filliâtre - Deductive Program Verification with W hy3 DTSTART:20111208T103000 DTEND:20111208T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2011-12-08/sessions/11/ CATEGORIES: DESCRIPTION:Why3 is the next generation of the Why software verification\n platform. Why3 clearly separates the purely logical specification\npart fr om generation of verification conditions for programs.\nRegarding the form er\, Why3 comes with a new enhanced language of\nlogical specification. It features a rich library of proof task\ntransformations that can be chaine d to produce a suitable input for\na large set of theorem provers\, includ ing SMT solvers\, TPTP\nprovers\, as well as interactive proof assistants. Regarding the\nlatter\, Why3 comes with a powerful programming language f eaturing\nrecursive functions\, local bindings\, pattern matching\, except ions\,\nand records with possibly mutable fields. Aliasing are excluded by \ntype checking to allow the computation of natural verification\nconditio ns through a weakest precondition calculus.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2011-12-08/sessions/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Hetzl - Cut-Elimination and Cut-Introduction DTSTART:20111110T153000 DTEND:20111110T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2011-11-10/sessions/5/ CATEGORIES: DESCRIPTION:Herbrand's theorem states that an existential formula is prova ble\nin classical first-order logic iff a finite disjunction of\ninstances is a propositional tautology. This theorem and\nappropriate extensions of it can be used for representing proofs\nwith and without cuts in a compac t way.\n\nI will speak about this representation and its algorithmic\nadva ntages in certain classes of proofs: 1) it allows\ncut-elimination procedu res without syntactic bureaucracy and 2) it\nmakes it possible to algorith mically reverse cut-elimination: by\nfinding sufficiently similar parts of a cut-free proof and\nidentifying them by introduction of a cut the proof is\nabbreviated.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2011-11-10/sessions/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Thibaut Balabonski - Le λ-lifting vu comme un événement silenci eux DTSTART:20111110T140000 DTEND:20111110T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2011-11-10/sessions/4/ CATEGORIES: DESCRIPTION:L'objectif est de faire le lien entre deux avatars de la rédu ction\noptimale. L'un concerne la réduction faible du λ-calcul\, l'autre la\nrécriture du premier ordre\, et tous deux se démarquent de la\nthé orie générale par une même agréable propriété : on peut les\nimplém enter simplement avec des graphes acycliques.\n\nJe commencerai par prése nter les principes de la réduction optimale\ntels qu'introduits par Lévy \, en insistant sur leurs liens avec les\nnotions d'événement et de caus alité.\n\nOn interprétera ensuite dans ce cadre le λ-lifting\, un proc édé de\ncompilation classique assurant le passage du λ-calcul à la\nr écriture du premier ordre. On verra que cette transformation peut\nêtre vue comme un événement “silencieux”\, causalement transparent\,\net respectueux de l'optimalité\, et on en profitera pour réaliser\nquelques transferts de propriétés.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2011-11-10/sessions/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Varacca - Parallel extrusion in the π-calculus\, or the l imits of stability DTSTART:20111110T103000 DTEND:20111110T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2011-11-10/sessions/6/ CATEGORIES: DESCRIPTION:We had given in 2007 a stable event structures semantics of th e\ninternal π-calculus. To extend this to the full π-calculus\, we\nneed ed to deal with\n\n- the communication of free names\,\n\n- the extrus ion of bound names.\n\n\nFree names pose no particular problems\, but scop e extrusion is\ntricky\, especially if we want to allow parallel extrusion s. After\nyears of trying we came to the conclusion that it is not possibl e\nto satisfactorily model parallel extrusion within the framework of\nsta ble event structures. We propose a semantics that while using\nunstable st ructures\, in a sense is very close to the stable case.\nAdequacy theorems and open questions will be provided in great\nabundance.\n\nThis is joint work with Silvia Crafa and Nobuko Yoshida.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2011-11-10/sessions/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Agathe Chollet\, Laurent Fuchs - Autour de la droite d'Harthong-Re eb DTSTART:20111013T153000 DTEND:20111013T163000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2011-10-13/sessions/3/ CATEGORIES: DESCRIPTION:La représentation d'objets géométriques en informatique gra phique\nsépare la structure (topologie\, relations d'incidence\, d'adjace nce)\nd'un objet et la forme géométrique d'un objet. Pour cette dernièr e\,\nlors du calcul de la forme géométrique\, les résultats des calculs \ngéométriques dépendent très fortement du système numérique utilis é.\nCela est principalement du à la nature du résultat à obtenir (un\n point appartient-il à une droite?) qui\, contrairement aux résultats\nen analyse numérique\, ne peut pas se contenter d'une approximation.\nDiff érents modèles de calculs\, plus ou moins adaptés aux calculs\ngéomét riques\, ont été proposés et tous n'ont pas des bases\nthéoriques soli des. Notre approche se situe dans le cadre de la\ngéométrie discrète do nt le principe est d'étudier une version\ndiscrétisée d'objets continus . Nous proposons une méthode de\ndiscrétisation\, l'arithmétisation\, f ondée sur un modèle discret du\nsystème des nombres réels\, la droite de Harthong-Reeb.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2011-10-13/sessions/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Braibant - De coquets circuits DTSTART:20111013T140000 DTEND:20111013T150000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2011-10-13/sessions/2/ CATEGORIES: DESCRIPTION:We propose a new library to model and verify hardware circuits in\nthe Coq proof assistant. This library allows one to easily build\ncir cuits by following the usual pen-and-paper diagrams. We define a\ndeep-emb edding: we use a (dependently typed) data-type that models\nthe architectu re of circuits\, and a meaning function. We propose\ntactics that ease the reasoning about the behavior of the circuits\,\nand we demonstrate that o ur approach is practicable by proving the\ncorrectness of various circuits : a text-book divide and conquer\nadder of parametric size\, some higher-o rder combinators of\ncircuits\, and some sequential circuits: a buffer\, a nd a register.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2011-10-13/sessions/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Tortora de Falco - Weak normalization\, strong normalizati on and confluence of Linear Logic proof-nets: the semantic point of view DTSTART:20111013T103000 DTEND:20111013T120000 DTSTAMP:20260612T104322Z UID:https://chocola.ens-lyon.fr/events/seminaire-2011-10-13/sessions/1/ CATEGORIES: DESCRIPTION:Following a previous joint work with Daniel de Carvalho and Mi chele\nPagani\, we present a semantic approach to the well-known propertie s\nof cut-elimination of Linear Logic proof-nets (weak and strong\nnormali zation\, confluence). This is a joint ongoing work with\nDaniel de Carvalh o.\n\n\n\n URL:https://chocola.ens-lyon.fr/events/seminaire-2011-10-13/sessions/1/ END:VEVENT END:VCALENDAR