A Compositional Semantics for Conditional Term Rewriting Systems

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.