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A Note on Logical PERs and Reducibility. Logical Relations Strike Again!

Author Jean Gallier

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Jean Gallier
  • University of Pennsylvania, Philadelphia, PA, USA

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Jean Gallier. A Note on Logical PERs and Reducibility. Logical Relations Strike Again!. In The Provenance of Elegance in Computation - Essays Dedicated to Val Tannen. Open Access Series in Informatics (OASIcs), Volume 119, pp. 7:1-7:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/OASIcs.Tannen.7

Abstract

We prove a general theorem for establishing properties expressed by binary relations on typed (first-order) λ-terms, using a variant of the reducibility method and logical PERs. As an application, we prove simultaneously that β-reduction in the simply-typed λ-calculus is strongly normalizing, and that the Church-Rosser property holds (and similarly for βη-reduction).

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Type theory
  • Theory of computation → Complexity theory and logic
Keywords
  • Typed lambda-calculus
  • reducibility
  • logical relations
  • per’s
  • strong normalization
  • Church-Rosser property

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