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A denotational semantics for the symmetric interaction combinators

  • DAMIANO MAZZA (a1)
Abstract

The symmetric interaction combinators are a variant of Lafont's interaction combinators. They enjoy a weaker universality property with respect to interaction nets, but are equally expressive. They are a model of deterministic distributed computation and share the good properties of Turing machines (elementary reductions) and of the λ-calculus (higher-order functions and parallel execution). We introduce a denotational semantics for this system, which is inspired by the relational semantics for linear logic, and prove an injectivity and full completeness result for it. We also consider the algebraic semantics defined by Lafont, and prove that the two are strongly related.

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Danos, V. and Regnier, L. (1989) The structure of multiplicatives. Archive for Mathematical Logic 28 181203.
Ehrhard, T. (2005) Finiteness spaces. Mathematical Structures in Computer Science 15 (4)615646.
Fernández, M. and Mackie, I. (2003) Operational equivalence for interaction nets. Theoretical Computer Science 297 (13) 157181.
Girard, J.-Y. (1987a) Linear logic. Theoretical Computer Science 50 (1)1102.
Girard, J.-Y. (1987b) Multiplicatives. In: Lolli, G. (ed.) Logic and Computer Science: New Trends and Applications, Rendiconti del Seminario Matematico dell'Università e Politecnico di Torino 1134.
Girard, J.-Y. (1989) Geometry of interaction I: interpretation of System F. In: Proceedings of the Logic Colloquium '88, North Holland 221–260.
Gonthier, G., Abadi, M. and Lévy, J.-J. (1992) The geometry of optimal lambda reduction. In: Conference Record of the Nineteenth ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 92), ACM Press 1526.
Lafont, Y. (1990) Interaction nets. In: Conference Record of POPL'90, ACM Press 95108.
Lafont, Y. (1995) From proof nets to interaction nets. In: Girard, J.-Y., Lafont, Y. and Regnier, L. (eds.) Advances in Linear Logic, Cambridge University Press 225247.
Lafont, Y. (1997) Interaction combinators. Information and Computation 137 (1)69101.
Lippi, S. (2002) Encoding left reduction in the lambda-calculus with interaction nets. Mathematical Structures in Computer Science 12 (6)797822.
Mackie, I. and Pinto, J. S. (2002) Encoding linear logic with interaction combinators. Information and Computation 176 (2)153186.
Mazza, D. (2006) Observational equivalence for the interaction combinators and internal separation. In: Mackie, I. (ed.) Proceedings of TERMGRAPH 2006. Electronic Notes in Theoretical Computer Science 7–16.
Pagani, M. (2007) Proofs, denotational semantics and observational equivalence in Multiplicative Linear Logic. Mathematical Structures in Computer Science 17 (2)341359.
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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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