Representation and duality of the untyped λ-calculus in nominal lattice and topological semantics, with a proof of topological completeness

Murdoch J. Gabbay, Michael J. Gabbay

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5 Citations (Scopus)
196 Downloads (Pure)

Abstract

We give a semantics for the λ-calculus based on a topological duality theorem in nominal sets. A novel interpretation of λ is given in terms of adjoints, and λ-terms are interpreted absolutely as sets (no valuation is necessary).
Original languageEnglish
JournalANNALS OF PURE AND APPLIED LOGIC
Early online date8 Oct 2016
DOIs
Publication statusE-pub ahead of print - 8 Oct 2016

Keywords

  • Nominal algebras
  • Fresh-finite limits
  • Lambda-calculus
  • Spectral spaces
  • Lattices and order
  • Variables
  • Nominal techniques
  • Mathematical foundations
  • Fraenkel–Mostowski set theory

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