A semantic characterisation of the correctness of a proof net

  • Authors:
  • Christian Retoré

  • Affiliations:
  • Projet Calligramme, INRIA-Lorraine & CRIN-C.N.R.S., 615 rue du Jardin Botanique, B.P. 101, F-54602 Villers lèès Nancy Cedex, France. Email: retore@loria.fr

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 1997
  • Linear logic

    Theoretical Computer Science

  • Interaction nets

    POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

  • Computational interpretations of linear logic

    Theoretical Computer Science - Special volume of selected papers of the Sixth Workshop on the Mathematical Foundations of Programming Semantics, Kingston, Ont., Canada, May 1990

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Abstract

The purpose of this note is to show that the correctness of a multiplicative proof net with mix is equivalent to its semantic correctness: a proof structure is a proof net if and only if its semantic interpretation is a clique, where one given finite coherence space interprets all propositional variables.This is just an example of what can be done with these kinds of semantic techniques; for more information and further results, the reader is referred to Retoré (1994).