Abstract semantics for functional constraint programming

A denotational semantics is given for a lazy functional language with monotonic side-effects arising from the unification of singly-bound logical variables. The semantics is based on a Scott-style information system, which elegantly captures the notion of "constraint additin" inherent in unification. A novel feature of our approach is exploitation of the representational duality of denotations defined by information systems: (i) as domain elements in the traditional sense, and (ii) as sets of propositions or constraints. Spread care is taken to express accurately the interactions of lazy evaluation (e.g. evaluation by need), and read-only accesses of logical variables defer function applications. The purpose of our semantic description is to establish language properties such as determinacy under parallel evaluation, to validate implementation strategies, and to support the design of program analysis techniques such as those based on abstract interpretation.