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- Charles Grellois, Paul-André Melliès
- FoSSaCS
- 2015

In this paper, we construct an infinitary variant of the relational model of linear logic, where the exponential modality is interpreted as the set of finite or countable multisets. We explain how to interpret in this model the fixpoint operator Y as a Conway operator alternatively defined in an inductive or a coinductive way. We then extend the relational… (More)

- Charles Grellois, Paul-André Melliès
- CSL
- 2015

In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church encoding of a higher-order recursion scheme (HORS) comes together with a dual Church encoding of an alternating tree… (More)

- Charles Grellois, Paul-André Melliès
- MFCS
- 2015

In this paper, we explain how the connection between higherorder model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem originally established by Carayol and Serre using collapsible pushdown automata. The main idea is to start from an infinitary and colored relational… (More)

- Charles Grellois
- 2016

- Charles Grellois, Paul-André Melliès
- ITRS
- 2014

In recent work, Kobayashi observed that the acceptance by an alternating tree automaton A of an infinite tree T generated by a higher-order recursion scheme G may be formulated as the typability of the recursion scheme G in an appropriate intersection type system associated to the automaton A . The purpose of this article is to establish a clean connection… (More)

- Charles Grellois, Paul-André Melliès
- ArXiv
- 2015

- Ugo Dal Lago, Charles Grellois
- ESOP
- 2017

- Charles Grellois
- ArXiv
- 2011

Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general class of monads called monads with arities, so that not only algebraic theories can be computed from a proper set of… (More)

- Ugo Dal Lago, Charles Grellois
- ArXiv
- 2017

We introduce a system of monadic affine sized types, which substantially generalise usual sized types, and allows this way to capture probabilistic higher-order programs which terminate almost surely. Going beyond plain, strong normalisation without losing soundness turns out to be a hard task, which cannot be accomplished without a richer, quantitative… (More)

- Charles Grellois
- 2014

This article presents two different ways of model-checking higher-order recursion schemes, both relying on game semantics. A given recursion scheme is translated to another, which is its computational extent, in the sense that β-reduction paths called traversals in the new generated tree are isomorphic to branches of the former tree. Then, the two… (More)