Twenty years of rewriting logic

AbstractRewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification and verification, security, real-time and cyber-physical systems, probabilistic systems, bioinformatics and chemical systems

A Constructor-Based Reachability Logic for Rewrite Theories

Reachability logic has been applied to K rewrite-rule-based language definitions as a language-generic logic of programs. It has been proved successful in verifying a wide range of sophisticated programs in conventional languages. Here we study how reachability logic can be made not just language-generic, but rewrite-theory-generic to make it available not just for conventional program verification, but also to verify rewriting-logic-based programs and distributed system designs. A theory-generic reachability logic is presented and proved sound for a wide class of rewrite theories. Particular attention is given to increasing the logic's automation by means of constructor-based semantic unification, matching, and satisfiability procedures. The relationships to Hoare logic and LTL are discussed, new methods for proving invariants of possibly never terminating distributed systems are developed, and experiments with a prototype implementation illustrating the new methods are presented.Partially supported by NSF Grants CNS 13-19109 and CNS 14-09416, and AFOSR Contract FA8750-11-2-0084.Ope

Generalized Rewrite Theories and Coherence Completion

A new notion of generalized rewrite theory suitable for symbolic reasoning and generalizing the standard notion is motivated and defined. Also, new requirements for symbolic executability of generalized rewrite theories that extend those for standard rewrite theories, including a generalized notion of coherence, are given. Finally, symbolic executability, including coherence, is both ensured and made available for a wide class of such theories by automatable theory transformations.Partially supported by by NRL under contract number N00173-17-1-G002.Ope

Generalized Rewrite Theories, Coherence Completion and Symbolic Methods

A new notion of generalized rewrite theory suitable for symbolic reasoning and generalizing the standard notion is motivated and defined. Also, new requirements for symbolic executability of generalized rewrite theories that extend those 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.This work has been partially supported by NRL under contract number N00173-17-1-G002.Ope