Raúl Gutiérrez ; Salvador Lucas ; Miguel Vítores - Proving Confluence in the Confluence Framework with CONFident

fi:11515 - Fundamenta Informaticae, November 10, 2024, Volume 192, Issue 2: LOPSTR 2022
Proving Confluence in the Confluence Framework with CONFidentArticle

Authors: Raúl Gutiérrez ; Salvador Lucas ; Miguel Vítores

    This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically prove and disprove confluence of *Generalized Term Rewriting Systems*, where (i) only selected arguments of function symbols can be rewritten and (ii) a rather general class of conditional rules can be used. This includes, as particular cases, several variants of rewrite systems such as (context-sensitive) *term rewriting systems*, *string rewriting systems*, and (context-sensitive) *conditional term rewriting systems*. The divide-and-conquer modular strategy allows us to combine in a proof tree different techniques for proving confluence, including modular decompositions, checking joinability of (conditional) critical and variable pairs, transformations, etc., and auxiliary tasks required by them, e.g., joinability of terms, joinability of conditional pairs, etc.


    Volume: Volume 192, Issue 2: LOPSTR 2022
    Published on: November 10, 2024
    Accepted on: May 6, 2024
    Submitted on: June 29, 2023
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages

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