A Rewriting Semantics for Maude Strategies

Abstract

Intuitively, a strategy language is a way of taming the nondeterminism of a rewrite theory. We can think of a strategy language S as a rewrite theory transformation R → S(R) such that S(R) provides a way of executing R in a controlled way. One such theory transformation for the Maude strategy language is presented in detail in this paper. Progress in the semantic foundations of Maude's strategy language has led us to study some general requirements for strategy languages. Some of these requirements, like soundness and completeness with respect to the rewrites in R, are absolute requirements that every strategy language should fulfill. Other more optional requirements, that we call monotonicity and persistence, represent the fact that no solution is ever lost. We show that the Maude strategy language satisfies all these four requirements.

Twenty years of rewriting logic

“…from its, possibly quite complex, heuristics. Following this point of view, a strategy language SL is understood in [303] as a theory transformation of the form:…”

“…In concurrent system applications the relevant strategies may have other purposes, such as, for example, having a winning strategy in a game-theoretic interaction between agents. Given all these useful purposes, different rule-based languages such as, for example, ELAN [70,71], Maude [113,114,303], and Stratego [468], provide strategy languages to guide and control rule executions. The ELAN researchers deserve much credit as pioneers in this area for having made key contributions to rewriting strategy ideas from the beginning of the ELAN language.…”

Strategic port graph rewriting: an interactive modelling framework

“…As presented in [Martí-Oliet et al, 2008], it is expected from a strategy language to satisfy the properties of correctness and completeness with respect to rewriting derivations (in our case, port graph rewriting, see Def. 7).…”

A Strategy Language for Graph Rewriting

“…1 are defined by semantic rules given below. Thus, the semantics of the strategy language is also defined by rewriting, as done for example in [30]. Our semantic rules are applied to configurations containing graph programs, defining a small step operational semantics in the style of [34].…”