A Calculus for Interaction Nets Based on the Linear Chemical Abstract Machine

  • Authors:
  • Ian Mackie;Shinya Sato

  • Affiliations:
  • LIX, CNRS UMR 7161, École Polytechnique, 91128 Palaiseau Cedex, France;Himeji Dokkyo University, Faculty of Econoinformatics, 7-2-1 Kamiohno, Himeji-shi, Hyogo 670-8524, Japan

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2008

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Abstract

Interaction nets are graph rewriting systems which are a generalisation of proof nets for classical linear logic. The linear chemical abstract machine (CHAM) is a term rewriting system which corresponds to classical linear logic, via the Curry-Howard isomorphism. We can obtain a textual calculus for interaction nets which is surprisingly similar to linear CHAM based on the multiplicative fragment of classical linear logic. In this paper we introduce a framework based on the linear CHAM to model interaction net reduction. We obtain a textual calculus for interaction nets that is closer to the graphical representation than previous attempts.