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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 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)
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)