A compositional semantics for conditional term rewriting systems

Abstract

This paper considers compositions of conditional term rewriting systems as a basis for a modular approach to the design and analysis of equational logic programs. In this context, an equational logic program is viewed as consisting of a set of modules, each module defining a part of the program's functions. We define a compositional semantics for conditional term rewriting systems which we show to be rich enough to capture computational properties related to the use of logical variables. We also study how such a semantics may be safely approximated, and how the results of such approximations may be composed to yield a bottom-up abstract semantics adequate for modular data-flow analysis. A compositional analysis for equational unsatisfiability illustrates our approach.General topics: Theory/semantics, functional/logic languages, abstract interpretation.

Modeling Self-* Systems Using Chemically-Inspired Composable Patterns

“…Eco-laws are reactions on LSA templates 1 . A template is any LSA, which may or may not have variables in the tuple.…”

“…Since a few years, approaches based on the original chemical abstract machine paradigm try to solve this problem by modeling systems using chemically-inspired formalisms, where "reactions" between system components are specified by rewriting rules. This is a step forward towards composition of simple behavioural patterns: if a behaviour is specified as a rewriting system, then it is possible to compose different behaviours via rewriting system composition [1] (modulo appropriate verification for keeping concurrency and convergence properties).…”

Safe folding/unfolding with conditional narrowing

“…Moreover, O ◭ (R) can be viewed as a (possibly infinite) set of 'unit' clauses, and the computed answer substitutions for g in R can be determined by 'executing' flat(g) in the program O ◭ (R) by syntactic unification, as if the equality symbol were an ordinary predicate. We note that in [2] a similar operational semantics was defined for basic conditional narrowing.…”

Compositional analysis for equational Horn programs

“…In the context of equational logic programming [15,19], consideration has been given to the problem of defining a compositional semantics for the direct union of complete theories which correctly models the computational properties related to the use of logical variables [4]. In this paper, we address the problem of solving equations in equationally defined theories but, unlike [4], we want to define compositionally the meaning of the union of E-unification problems. Let a theory E be fixed and consider two finite equation sets Γ 1 , Γ 2 .…”