Proof search for programming in Intuitionistic Linear Logic (Extended Abstract)

Abstract

Introduction Linear logic (denoted LL) [6] is a powerful and expressive logic with connections to a variety of topics in computer science as logic programming, concurrency or functional programming. From the logical side, LL combines the constructive content of Intuitionistic Logic with the symmetries of Classical Logic and from the computation side, it offers a control on resource management and evaluation order. Concerning functional programming, applications of LL to computation can be seen through the Curry-Howard isomorphism in which propositions are interpreted as types, proofs as programs and proof normalization process as computation. Works have been recently devoted to term assignment for intuitionistic linear logic (ILL) [3, 12] and full LL [1] with proposals of linear lambda calculi having important properties as subject-reduction or substitution property. Having natural deduction and sequent calculus proof systems of ILL (that are proved equivalent), we can invest