A Modified GoI Interpretation for a Linear Functional Programming Language and Its Adequacy

  • Naohiko Hoshino
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6604)

Abstract

Geometry of Interaction (GoI) introduced by Girard provides a semantics for linear logic and its cut elimination. Several extensions of GoI to programming languages have been proposed, but it is not discussed to what extent they capture behaviour of programs as far as the author knows. In this paper, we study GoI interpretation of a linear functional programming language (LFP). We observe that we can not extend the standard GoI interpretation to an adequate interpretation of LFP, and we propose a new adequate GoI interpretation of LFP by modifying the standard GoI interpretation. We derive the modified interpretation from a realizability model of LFP. We also relate the interpretation of recursion to cyclic computation (the trace operator in the category of sets and partial maps) in the realizability model.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Naohiko Hoshino
    • 1
  1. 1.Research Institute for Mathematical ScienceKyoto universityJapan

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