We present the -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 -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 -calculus can elegantly express one-to-many and many-to-one communication.
There is an interesting relationship between the -calculus and the -calculus: The -calculus is subsumed by a calculus obtained by extending the asynchronous and polyadic -calculus with logic variables.
The -calculus can be extended with primitives providing for constraint-based problem solving in the style of logic programming. A such extended -calculus has the remarkable property that it combines first-order constraints with higher-order programming.
1st International Conference on Constraints in Computational Logics, 7–9 Sep 1994, Springer-Verlag