Semantic foundations of concurrent constraint programming
Vijay A. Saraswat, et al.
Concurrent constraint programming [Sar89,SR90] is a sim-ple and powerful model of concurrent computation based on the notions of store-as-constraint and process as information transducer. The store-as-valuation conception of von Neu-mann computing is replaced by the notion that the store is a constraint (a finite representation of a possibly infinite set of valuations) which provides partial information about the possible values that variables can take. Instead of “reading” and “writing ” the values of variables, processes may now ask (check if a constraint is entailed by the store) and tell (augment the store with a new constraint). This is a very general paradigm which subsumes (among others) nonde-terminate data-flow and the (concurrent) (constraint) logic programming languages. This paper develops the basic ideas involved in giving a coherent semantic account of these languages. Our first con-tribution is to give a simple and general formulation of the notion that a constraint system is a system of partial infor-mation (a la the information systems of Scott). Parameter passing and hiding is handled by borrowing ideas from the cylindric algebras of Henkin, Monk and Tarski to introduce diagonal elements and “cylindrification ” operations (which mimic the projection of information induced by existential quantifiers). The se;ond contribution is to introduce the notion of determinate concurrent constraint programming languages. The combinators treated are ask, tell, parallel composition, hiding and recursion. We present a simple model for this language based on the specification-oriented methodology of [OH86]. The crucial insight is to focus on observing the resting points of a process—those stores in which the pro-cess quiesces without producing more information. It turns out that for the determinate language, the set of resting points of a process completely characterizes its behavior on all inputs, since each process can be identified with a closure operator over the underlying constraint system. Very nat-ural definitions of parallel composition, communication and hiding are given. For example, the parallel composition of two agents can be characterized by just the intersection of the sets of constraints associated with them. We also give a complete axiomatization of equality in this model, present