Réunion ANR Récré, 11 avril 2013

Programme

10:30 – 12:00

Nicolas Tabareau (INRIA, Inventeurs du monde numérique)

Invited talk: Univalence for free, not yet ...

We present an internalization of the 2-groupoid (or rather groupoidoid) interpretation of the calculus of construction that allows to realize proof irrelevance, reasoning modulo and a weak form of the univalence axiom. As an example, we show that in our setting, the type of Church integers is equal to the inductive type of natural numbers.

• slides

14:00 – 15:00

Colin Riba (ENS Lyon)

Invited talk: Forcing MSO on Infinite Words in Weak MSO

We propose a forcing-based interpretation of monadic second-order logic (MSO) on !-words in Weak MSO (WMSO). The interpretation is purely syntactic and compositional. We show that a formula with parameters is true in MSO if and only if its interpretation is true in WMSO. We also show that a closed formula is true in MSO if and only if its interpretation is provable under some axioms which hold for WMSO, but without axiomatizing it. We use model-theoretic arguments. Our approach is inspired from point-free topology: infinite words, seen as topological points, are approximated by filters of bounded segments. We devise forcing conditions such that the corresponding generic filters approximate Ramseyan factorizations of infinite words modulo satisfaction of formulas of a given quantifier depth. Our interpretation parallels some approaches to Mc- Naughton?s Theorem (equivalence between non-deterministic B¨uchi automata and deterministic Rabin automata) but the obtained formulas do not by themselves describe deterministic automata.

15:30 – 16:30

Guillaume Munch-Maccagnoni (Univ. Paris 7)

Invited talk: When composition is not associative

Strict and lazy composition (in the presence of evaluation order) do not associate. The phenomenon was observed multiple times in semantics (programming, proof theory).

Non-associativity is not only ubiquitous but also characterises by itself notions of computation with non-trivial evaluation order, as we will see.