Twenty years of rewriting logic

Abstract

Rewriting 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.

Constrained narrowing for conditional equational theories modulo axioms

“…In general, the rewrite rules of a conditional rewrite theory R have a nonequational meaning as transition rules in a concurrent system [56,58]. However, in this work we will focus for the most part on rewrite theories with an equational interpretation.…”

“…As pointed out in the Introduction, a rewrite theory has often a non-equational meaning in which rules are viewed as transition rules in a concurrent system [56,58]. We have developed, with K. Bae, a narrowing-based model checking method and implementation for such concurrent systems in [31,9], called logical model checking, which allows rules to describe a concurrent system while the equational theory describes both system properties and state predicates.…”

“…Various kinds of symbolic techniques such as: (i) automata and grammars, e.g., [1,15,13,14,38,66,5,4,3,33]; (ii) SMT and other forms of constraint solving, e.g., [6,20,35,36,64,73,75,39,11]; and (iii) narrowing [72,30,31,9,10], have been employed for this purpose. All are useful in their own way and can complement each other; and there is great interest in combining the power of these different symbolic approaches to handle a wider range of applications [59,60] (see, e.g., [70] and the survey [58] for combinations of this kind).…”

“…Instead of concrete system states, we can represent a possibly infinite set of such states by a term t with logical variables. We can then use narrowing modulo E to "symbolically execute" state transitions as narrowing steps t ; R,E t , thus obtaining a useful form of symbolic reachability analysis and model checking with many applications [72,30,31,9,10] (see [58] for a survey of this work).…”

Lem

“…For some examples in current use (this is by no means exhaustive) we mention ASF+SDF [35], K [29], and Maude [23] (all of which support some form of term rewriting), Ott [33] (for inductive relations over inductive syntax), and PLT Redex [16] (for reduction semantics); other tools target SMT and first-order problems. These all have advantages in their particular domains, but they are tackling rather different problems to Lem (with its focus on specification portable across multiple provers), and they lack the definitional expressiveness of higher-order logic and inductively defined relations.…”