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Communication Dans Un Congrès Année : 2016

Relational type-checking for MELL proof-structures. Part 1: Multiplicatives

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Relational semantics for linear logic is a form of non-idempotent intersection type system, from which several informations on the execution of a proof-structure can be recovered. An element of the relational interpretation of a proof-structure R with conclusion Γ acts thus as a type (refining Γ) having R as an inhabitant. We are interested in the following type-checking question: given a proof-structure R, a list of formulae Γ, and a point x in the relational interpretation of Γ, is x in the interpretation of R? This question is decidable. We present here an algorithm that decides it in time linear in the size of R, if R is a proof-structure in the multiplicative fragment of linear logic. This algorithm can be extended to larger fragments of multiplicative-exponential linear logic containing λ-calculus.
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hal-01324001 , version 1 (01-06-2016)

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Giulio Guerrieri, Luc Pellissier, Lorenzo Tortora de Falco. Relational type-checking for MELL proof-structures. Part 1: Multiplicatives. Eighth Workshop on Intersection Types and Related Systems, Jun 2016, Porto, Portugal. ⟨hal-01324001⟩
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