A Fully Abstract Semantics for Constructor Systems

Abstract

Constructor-based term rewriting systems are a useful subclass of TRS, in particular for programming purposes. In this kind of systems constructors determine a universe of values, which are the expected output of the computations. Then it would be natural to think of a semantics associating each expression to the set of its reachable values. Somehow surprisingly, the resulting semantics has poor properties, for it is not compositional nor fully abstract when non-confluent systems are considered. In this paper we propose a novel semantics for expressions in constructor systems, which is compositional and fully abstract (with respect to sensible observation functions, in particular the set of reachable values for an expression), and therefore can serve as appropriate basis for semantic based analysis or manipulation of such kind of rewrite systems.