We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the Curry-Howard isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluation and storage allocation, while maintaining the logical content of programs as proofs, and computation as cut-elimination.

. In this paper, we consider the multiplicative fragment of linear logic (MLL) from an automated deduction point of view. Before to use this new logic to make logic programming or to program with proofs, a better comprehension of the proof construction process in this framework is necessary. We propose a new algorithm to construct automatically a proof net for a given sequent in MLL and its proofs of termination, correctness and completeness. It can be seen as an implementation oriented way to consider automated deduction in linear logic. 1 Introduction Computer scientists can consider logic with two points of view: it can be an external reference to which they report during their activity, for example, to make correctness proofs of programs or it can be integrated as an internal tool for programming. In this work, we consider the second one. Intuitionism [16] has given at first a logical tool to approach programming in this connection. Centered around a constructive vision of truth, ...

this paper to an interaction mechanism inspired to the computational behaviour of proof nets, a deduction system of linear logic [7]. In this setting the conclusion of a derivation is the type of the corresponding proof net. The computational mechanism is cut elimination that can only occur between terms with the same type. The relationship between proof nets and processes have already been studied in the literature. Abramsky interprets proof as processes and consider a cut-elimination as communication paradigm [1]. Similar typed calculi based on linear logic where developed also by Solitro and Valentini [13, 14]. Yuxi Fu [6] studies a computational model in which the role of process and proofs is reversed with respect to the Abramsky's view. The corresponding paradigm is thus communication as cut-elimination for classical proofs. Bellin and Scott implements the cut-elimination of linear logic in the -calculus. We here push forward the work in [13, 14] where : : : . Our approach differ from the one mentioned above in that we move from the mentioned calculi for linear logic and borrow some ideas from cham by Berry and Boudol [3].