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Barendregt Convenes with Knaster and Tarski: Strong Rule Induction for Syntax with Bindings

Authors:

Jan van Brügge,

Andrei Popescu,

Dmitriy TraytelAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 9, Issue POPL

Article No.: 57, Pages 1687 - 1718

https://doi.org/10.1145/3704893

Published: 09 January 2025 Publication History

Abstract

This paper is a contribution to the meta-theory of systems featuring syntax with bindings, such as 𝜆-calculi and logics. It provides a general criterion that targets inductively defined rule-based systems, enabling for them inductive proofs that leverage Barendregt's variable convention of keeping the bound and free variables disjoint. It improves on the state of the art by (1) achieving high generality in the style of Knaster–Tarski fixed point definitions (as opposed to imposing syntactic formats), (2) capturing systems of interest without modifications, and (3) accommodating infinitary syntax and non-equivariant predicates.

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Cited By

From AStark KTimany ABlazy STabareau N(2025)An Isabelle/HOL Framework for Synthetic Completeness ProofsProceedings of the 14th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3703595.3705882(171-186)Online publication date: 10-Jan-2025
https://dl.acm.org/doi/10.1145/3703595.3705882

Index Terms

Barendregt Convenes with Knaster and Tarski: Strong Rule Induction for Syntax with Bindings
1. Theory of computation
  1. Logic
    1. Logic and verification

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 9, Issue POPL

January 2025

2363 pages

EISSN:2475-1421

DOI:10.1145/3554321

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Amazon, USA

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From AStark KTimany ABlazy STabareau N(2025)An Isabelle/HOL Framework for Synthetic Completeness ProofsProceedings of the 14th ACM SIGPLAN International Conference on Certified Programs and Proofs10.1145/3703595.3705882(171-186)Online publication date: 10-Jan-2025
https://dl.acm.org/doi/10.1145/3703595.3705882

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