research-article

Order-sorted equality enrichments modulo axioms

Authors:

Raúl Gutiérrez,

José Meseguer,

Camilo RochaAuthors Info & Claims

Science of Computer Programming, Volume 99, Issue C

Pages 235 - 261

https://doi.org/10.1016/j.scico.2014.07.003

Published: 01 March 2015 Publication History

Abstract

We make the addition of equationally defined equality predicates effective and automatic by means of a transformation.The transformation is constructive and valid for a wide class of equational specifications.All the expected good properties of the input theory are preserved by the transformation.The transformation is implemented in Maude and integrated into Maude formal tools. Built-in equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications with initial algebra semantics beyond the pale of theorem proving tools based, for example, on explicit or inductionless induction techniques, and of other formal tools for checking key properties such as confluence, termination, and sufficient completeness. Such specifications would instead be amenable to formal analysis if an equationally-defined equality predicate enriching the algebraic data types were to be added to them. Furthermore, having an equationally-defined equality predicate is very useful in its own right, particularly in inductive theorem proving. Is it possible to effectively define a theory transformation E E ~ that extends an algebraic specification E to a specification E ~ having an equationally-defined equality predicate__ __ This paper answers this question in the affirmative for a broad class of order-sorted conditional specifications E that are sort-decreasing, ground confluent, and operationally terminating modulo axioms B and have a subsignature of constructors. The axioms B can consist of associativity, or commutativity, or associativity-commutativity axioms, so that the constructors are free modulo B. We prove that the transformation E E ~ preserves all the just-mentioned properties of E . The transformation has been automated in Maude using reflection and is used as a component in many Maude formal tools.

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Cited By

Durán FEscobar SMeseguer JSapiña J(2024)NuITP: An Inductive Theorem Prover for Equational Program VerificationProceedings of the 26th International Symposium on Principles and Practice of Declarative Programming10.1145/3678232.3678236(1-11)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1145/3678232.3678236
Meseguer J(2022)Building Correct-by-Construction Systems with Formal PatternsRecent Trends in Algebraic Development Techniques10.1007/978-3-031-43345-0_1(3-24)Online publication date: 28-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-43345-0_1
Meseguer JSkeirik S(2022)On Ground Convergence and Completeness of Conditional Equational Program HierarchiesRewriting Logic and Its Applications10.1007/978-3-031-12441-9_10(191-211)Online publication date: 2-Apr-2022
https://dl.acm.org/doi/10.1007/978-3-031-12441-9_10
Show More Cited By

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Order-sorted equality enrichments modulo axioms
1. Theory of computation

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cover image Science of Computer Programming

Science of Computer Programming Volume 99, Issue C

March 2015

262 pages

ISSN:0167-6423

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Copyright © Elsevier B.V.

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Elsevier North-Holland, Inc.

United States

Publication History

Published: 01 March 2015

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Cited By

Durán FEscobar SMeseguer JSapiña J(2024)NuITP: An Inductive Theorem Prover for Equational Program VerificationProceedings of the 26th International Symposium on Principles and Practice of Declarative Programming10.1145/3678232.3678236(1-11)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1145/3678232.3678236
Meseguer J(2022)Building Correct-by-Construction Systems with Formal PatternsRecent Trends in Algebraic Development Techniques10.1007/978-3-031-43345-0_1(3-24)Online publication date: 28-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-43345-0_1
Meseguer JSkeirik S(2022)On Ground Convergence and Completeness of Conditional Equational Program HierarchiesRewriting Logic and Its Applications10.1007/978-3-031-12441-9_10(191-211)Online publication date: 2-Apr-2022
https://dl.acm.org/doi/10.1007/978-3-031-12441-9_10
Meseguer JSkeirik S(2020)Inductive Reasoning with Equality Predicates, Contextual Rewriting and Variant-Based SimplificationRewriting Logic and Its Applications10.1007/978-3-030-63595-4_7(114-135)Online publication date: 25-Apr-2020
https://dl.acm.org/doi/10.1007/978-3-030-63595-4_7

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