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Formalization of metatheory of the Lambda Calculus in constructive type theory using the Barendregt variable convention
Published online by Cambridge University Press: 26 November 2021
Abstarct
We formalize in Constructive Type Theory the Lambda Calculus in its classical first-order syntax, employing only one sort of names for both bound and free variables, and with α-conversion based upon name swapping. As a fundamental part of the formalization, we introduce principles of induction and recursion on terms which provide a framework for reproducing the use of the Barendregt Variable Convention as in pen-and-paper proofs within the rigorous formal setting of a proof assistant. The principles in question are all formally derivable from the simple principle of structural induction/recursion on concrete terms. We work out applications to some fundamental meta-theoretical results, such as the Church–Rosser Theorem and Weak Normalization for the Simply Typed Lambda Calculus. The whole development has been machine checked using the system Agda.
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- Information
- Mathematical Structures in Computer Science , Volume 31 , Special Issue 3: Logical and Semantic Frameworks with Applications , March 2021 , pp. 341 - 360
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
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