BEGIN:VCALENDAR
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-TIMEZONE:Europe/Paris
BEGIN:VEVENT
SUMMARY:Victor Arrial - Genericity Through Stratification
DTSTART:20240523T151500
DTEND:20240523T161500
DTSTAMP:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192910Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192911Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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:20240521T192912Z
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