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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)

In this paper, we construct an infinitary variant of the rela-tional 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… (More)

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)

In this paper, we explain how the connection between higher-order 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 push-down automata. The main idea is to start from an infinitary and colored relational… (More)

- Charles Grellois
- 2016

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)

The verification of higher-order recursive programs is a challenging issue, for which model-checking techniques have been considered. Programs are abstracted using higher-order recursion schemes (HORS); and a recursion scheme G can be understood as a simply-typed λ-term with fixpoint operators Y , over a set Σ = a, b, c. .. of free variables of order at… (More)

The model-checking problem for higher-order recursive programs, expressed as higher-order recursion schemes (HORS), and where properties are specified in monadic second-order logic (MSO) has received much attention since it was proven decidable by Ong ten years ago. Every HORS may be understood as a simply-typed λ-term G with fixpoint operators Y whose free… (More)

- Charles Grellois
- 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)

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