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A Foundation for Higher-order Concurrent Constraint Programming

Gert Smolka
DFKI, DFKI Research Reports (RR), Vol. 94-16, 1994.


We present the γ-calculus, a computational calculus for higher-order concurrent programming. The calculus can elegantly express higher-order functions (both eager and lazy) and concurrent objects with encapsulated state and multiple inheritance. The primitives of the γ-calculus are logic variables, names, procedural abstraction, and cells. Cells provide a notion of state that is fully compatible with concurrency and constraints. Although it does not have a dedicated communication primitive, the γ-calculus can elegantly express one-to-many and many-to-one communication. There is an interesting relationship between the γ-calculus and the π-calculus: The γ-calculus is subsumed by a calculus obtained by extending the asynchronous and polyadic π-calculus with logic variables. The γ-calculus can be extended with primitives providing for constraint-based problem solving in the style of logic programming. A such extended γ-calculus has the remarkable property that it combines first-order constraints with higher-order programming.