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Computational Interpretations of Linear Logic
 Theoretical Computer Science
, 1993
"... We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the CurryHoward isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluati ..."
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Cited by 320 (3 self)
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We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the CurryHoward 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 cutelimination.
A Procedure for Automatic Proof Nets Construction
, 1992
"... 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 propos ..."
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Cited by 12 (8 self)
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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.
A Non Functional Calculus: Linear Logic and Concurrency
, 2000
"... 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 ..."
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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 cutelimination 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 cutelimination for classical proofs. Bellin and Scott implements the cutelimination 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].
Functional Features of a Calculus for Logic and Concurrency
, 2000
"... We propose a simple untyped calculus inspired by the proofs encodings of the Linear Logic by Girard. The basic elements of our calculus are multiset of terms sharing a workspace and their dynamic behaviour is dened by a reduction semantics in the style of the Chemical Abstract Machine. We addres ..."
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We propose a simple untyped calculus inspired by the proofs encodings of the Linear Logic by Girard. The basic elements of our calculus are multiset of terms sharing a workspace and their dynamic behaviour is dened by a reduction semantics in the style of the Chemical Abstract Machine. We address the issue of treating concurrency via a model of computation whose basic step can be interpreted as cutelimination.