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Confluence in Non-Left-Linear Untyped Higher-Order Rewrite Theories


We develop techniques based on van Oostrom's decreasing diagrams that reduce confluence proofs to the checking of critical pairs for higher-order rewrite rules extending betareduction on pure lambda-terms. We show that confluence is preserved for a large subset of terms that contains all pure lambda terms. Our results are applied to famous Klop's examples of non-confluent behaviours in lambda-calculi with convergent rewrite rules, on the one hand, and to fragments of an encoding in a dependent type theory augmented with rewrite rules of the Calculus of Constructions with polymorphic universes.
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Dates and versions

hal-03126115 , version 1 (01-02-2021)
hal-03126115 , version 2 (22-02-2021)
hal-03126115 , version 3 (03-03-2021)
hal-03126115 , version 4 (25-05-2021)
hal-03126115 , version 5 (21-07-2021)
hal-03126115 , version 6 (14-09-2021)



Gaspard Férey, Jean-Pierre Jouannaud. Confluence in Non-Left-Linear Untyped Higher-Order Rewrite Theories. PPDP 2021 - 23rd International Symposium on Principles and Practice of Declarative Programming, Sep 2021, Tallin, Estonia. ⟨10.1145/3479394.3479403⟩. ⟨hal-03126115v6⟩
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