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Journal of Logic and ComputationVolume 30, Issue 8, 2021, Pages 1567-1608

Kripke-style semantics and completeness for full simply typed Lambda calculus(Article)

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  • aFaculty of Technical Sciences, University of Novi Sad, Novi Sad, 21000, Serbia
  • bMathematical Institute SASA, Belgrade, 11000, Serbia

Abstract

Full simply typed lambda calculus is the simply typed lambda calculus extended with product types and sum types. We propose a Kripke-style semantics for full simply typed lambda calculus. We then prove soundness and completeness of type assignment in full simply typed lambda calculus with respect to the proposed semantics. The key point in the proof of completeness is the notion of a canonical model. © The Author(s) 2020.

Author keywords

CompletenessCurry-Howard correspondenceKripke-style semanticsLambda calculus

Indexed keywords

Engineering controlled terms:Differentiation (calculus)Semantics
Engineering uncontrolled termsCanonical modelingKeypointsKripke-style semanticsProduct typesSimply typed lambda calculusSoundness and completeness
Engineering main heading:Calculations
  • ISSN: 0955792X
  • CODEN: JLCOE
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1093/LOGCOM/EXAA055
  • Document Type: Article
  • Publisher: Oxford University Press

  Kašterović, S.; Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia;
© Copyright 2021 Elsevier B.V., All rights reserved.

Cited by 2 documents

Ghilezan, S. , Kašterović, S.
Semantics for Combinatory Logic With Intersection Types
(2022) Frontiers in Computer Science
Dudenhefner, A. , Urzyczyn, P.
Kripke Semantics for Intersection Formulas
(2021) ACM Transactions on Computational Logic
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