The λ-context Calculus

  • Authors:
  • Murdoch J. Gabbay;Stéphane Lengrand

  • Affiliations:
  • Computer Science Department, Heriot-Watt University, Scotland;School of Computer Science, University of St Andrews, Scotland

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

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Abstract

We present a simple but expressive lambda-calculus whose syntax is populated by variables which behave like meta-variables. It can express both capture-avoiding and capturing substitution (instantiation). To do this requires several innovations, including a key insight in the confluence proof and a set of reduction rules which manages the complexity of a calculus of contexts over the 'vanilla' lambda-calculus in a very simple and modular way. This calculus remains extremely close in look and feel to a standard lambda-calculus with explicit substitutions, and good properties of the lambda-calculus are preserved.