Generalized rewrite theories, coherence completion, and symbolic methods

• Published in: Journal of logical and algebraic methods in programming Vol. 110; p. 100483
• Main Author: Meseguer, José
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2020
• Subjects: Coherence; Constrained narrowing; Generalized rewrite theories; Pattern predicates; Symbolic invariant verification; Symbolic invariant verification; Constrained narrowing; Generalized rewrite theories; Coherence; Pattern predicates
• ISSN: 2352-2208
• DOI: 10.1016/j.jlamp.2019.100483

A new notion of generalized rewrite theory suitable for symbolic reasoning and generalizing the standard notion in [19] is motivated and defined. Also, new requirements for symbolic executability of generalized rewrite theories that extend those in [33] for standard rewrite theories, including a generalized notion of coherence, are given. Symbolic executability, including coherence, is both ensured and made available for a wide class of such theories by automatable theory transformations. Using these foundations, several symbolic reasoning methods using generalized rewrite theories are studied, including: (i) symbolic description of sets of terms by pattern predicates; (ii) reasoning about universal reachability properties by generalized rewriting; (iii) reasoning about existential reachability properties by constrained narrowing; and (iv) symbolic verification of safety properties such as invariants and stability properties.