A fully abstract semantics for a first-order functional language with logic variables
ACM Transactions on Programming Languages and Systems (TOPLAS)
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We present a novel denotational semantics for a functional language with logic variables intended for parallel execution. The intuition behind this semantics is that equations represent equational constraints on data. Thus, a system of equations can be viewed as defining a set of possibly inconsistent constraints. The semantics is couched in terms of closure operators on a Scott domain. This allows one to abstract away from all the complexities associated with operational reasoning expressed in terms of concurrent threads of execution. We define a structural operational semantics for the language that expresses precisely the concurrent execution model that we have in mind. We show that the abstract denotational semantics is fully abstract with respect to the operational semantics. This is surprising, given how very different the two semantic descriptions are. It also shows that thinking in terms of constraints is an accurate substitute for thinking in terms of explicit parallel execution. The proof of full abstraction is complicated by the fact that there are potentially infinite objects in the domain.