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Preprints, Working Papers, ... Year : 2021

Confluence in UnTyped Higher-Order Theories by means of Critical Pairs

Abstract

User-defined higher-order rewrite rules are becoming a standard in proof assistants based on intuitionistic type theory. This raises the question of proving that they preserve the properties of beta-reductions for the corresponding type systems. We develop here techniques that reduce confluence proofs to the checking of various forms of critical pairs for higher-order rewrite rules extending beta-reduction on pure lambda-terms. The present paper concentrates on the case where rewrite rules are left-linear and critical pairs can be joined without using beta-rewrite steps. The other two cases will be addressed in forthcoming papers.
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Dates and versions

hal-03126102 , version 1 (01-02-2021)
hal-03126102 , version 2 (12-05-2021)
hal-03126102 , version 3 (14-09-2021)

Identifiers

  • HAL Id : hal-03126102 , version 3

Cite

Gaspard Férey, Jean-Pierre Jouannaud. Confluence in UnTyped Higher-Order Theories by means of Critical Pairs. 2021. ⟨hal-03126102v3⟩
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