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....of this paper was released as a technical report [Abr90] I have benefited from comments and corrections from a number of people, particularly Phil 3 Wadler, Anne Troelstra, Ian Mackie, and especially Yves Lafont. My thanks also to Ugo Solitro and Silvio Valentini for bringing their papers [Sol89, Val89] to my attention. 2 Intuitionistic Logic and Functional Programming This section essentially reviews standard material, although the style of presentation of the operational semantics, and the assignment of terms to proofs in the sequent calculus, are neither as widely known as they deserve to ....

U. Solitro. A typed calculus based on a fragment of linear logic. Theoretical

.... concurrent programming [1] The point is to better understand what a proof is in LL consisting in a particular graph named proof net [6, 9] But before considering the computational aspect and the synthesis of programs from proof nets using, for example, an adequate refinement of typed calculus [15], one should be able to mechanize the construction of proofs, having in mind that propositional linear logic is undecidable [13] In this paper, we give an algorithm to mechanize the construction of a proof net for a given sequent in multiplicative linear logic International Conference ....

U. Solitro. A typed calculus based on a fragment of linear logic. Theoretical Computer Science, 68:333--342, 1989.

.... programming [1] The point is to better understand what a proof is in linear logic consisting in a particular graph named proof net [6, 10] But before considering the computational aspect and the synthesis of programs from proof nets, for example using an adequate refinement of typed calculus [16], one should be able to mechanize the construction of proofs in linear logic. We know that propositional linear logic is undecidable [14] but it is not the case for multiplicative part of it. In this paper, we give an algorithm to mechanize the construction of a proof net for a given sequent in ....

U. Solitro. A typed calculus based on a fragment of linear logic. Theoretical Computer Science, 68:333--342, 1989.

....same type. The relationship between proof nets and processes have already been studied in the literature. Abramsky interprets proofs as processes and consider a cutelimination as communication paradigm [1] Similar typed calculi based on linear logic where developed also by Solitro and Valentini [11, 13]. Yuxi Fu [5] 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 [3] implements the cut elimination of linear logic in the ....

....q = M ] 4 Types We want to introduce here the types for calculus. The basic idea is that the type of a process like ( x)fj t 1 ; t n jg is a multiset A 1 ; An which can be a linear sequent. We know from literature that linear logic can provide a type environment. Resuming [11], in Table 1 we propose the sequent calculus for MLL, the multiplicative subsystem of linear logic, enriched with the encoding in calculus. In the quoted paper, it is proved that the encoding is natural, i.e. there is an isomorphism between proof and the corresponding terms with respect to ....

U. Solitro. A typed calculus based on a fragment of linear logic. Theoretical Computer Science, 68(3):333-342, 1989.

....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 ....

....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] The basic idea is to have an untyped calculus (called calculus) as simple as possible that embodies functional ....

U. Solitro. A typed calculus based on a fragment of linear logic. Theoretical Computer Science, 68(3):333--342, 1989.

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