Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
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A theory of combinators in the setting of concurrent processes is formulated. The new combinators are derived from an analysis of the operation called asynchronous name passing, just as an analysis of logical substitution gave rise to the sequential combinators. A system with seven atoms and fixed interaction rules, but with no notion of prefixing, is introduced, and is shown to be capable of representing input and output prefixes over arbitrary terms in a behaviourally correct way, just as SK-combinators are closed under functional abstraction without having it as a proper syntactic construct. The basic equational correspondence between concurrent combinators and a system of asynchronous mobile processes, as well as the embedding of the finite part of &pgr;-calculus in concurrent combinators, is proved. These results will hopefully serve as a cornerstone for further investigation of the theoretical as well as pragmatic possibilities of the presented construction.