[1807.01871v1] Formalization in Constructive Type Theory of the Standardization Theorem for the Lambda Calculus using Multiple Substitution
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Computer Science > Logic in Computer Science

arXiv:1807.01871v1 (cs)
[Submitted on 5 Jul 2018]

Title:Formalization in Constructive Type Theory of the Standardization Theorem for the Lambda Calculus using Multiple Substitution

Authors:Martín Copes, Nora Szasz (Universidad ORT Uruguay), Álvaro Tasistro (Universidad ORT Uruguay)
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Abstract:We present a full formalization in Martin-Löf's Constructive Type Theory of the Standardization Theorem for the Lambda Calculus using first-order syntax with one sort of names for both free and bound variables and Stoughton's multiple substitution. Our formalization is based on a proof by Ryo Kashima, in which a notion of beta-reducibility with a standard sequence is captured by an inductive relation. The proof uses only structural induction over the syntax and the relations defined, which is possible due to the specific formulation of substitution that we employ. The whole development has been machine-checked using the system Agda.
Comments: In Proceedings LFMTP 2018, arXiv:1807.01352
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:1807.01871 [cs.LO]
  (or arXiv:1807.01871v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.1807.01871
Journal reference: EPTCS 274, 2018, pp. 27-41
Related DOI: https://doi.org/10.4204/EPTCS.274.3

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Thu, 5 Jul 2018 07:09:24 UTC (27 KB)
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