Encoding linear logic with interaction combinators

  • Authors:

  • Ian Mackie;Jorge Sousa Pinto

  • Affiliations:

  • CNRS (UMR 7650), LIX, École Polytechnique, 91128 Palaiseau Cedex, France;Departamento de Informática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal

  • Venue:
  • Information and Computation
  • Year:
  • 2002

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Abstract

The purpose of this paper is to demonstrate how Lafont's interaction combinators, a system of three symbols and six interaction rules, can be used to encode linear logic. Specifically, we give a translation of the multiplicative, exponential, and additive fragments of linear logic together with a strategy for cut-elimination which can be faithfully simulated. Finally, we show briefly how this encoding can be used for evaluating λ-terms. In addition to offering a very simple, perhaps the simplest, system of rewriting for linear logic and the λ-calculus, the interaction net implementation that we present has been shown by experimental testing to offer a good level of sharing in terms of the number of cut-elimination steps (resp. β-reduction steps). In particular it performs better than all extant finite systems of interaction nets.