Non-Determinism in a Functional Setting

The pure untyped Lambda Calculus augmented with an (erratic) choice operator is considered as an idealised non-deterministic functional language. Both the \may" and the \must" modalities of convergence are of interest to us. Following Abramsky's work on domain theory in logical form, we identify the deno-tational type that captures our computational situation: = P ! ] ? ] where P?] is the Plotkin pow-erdomain functor. We then carry out a systematic programme which hinges on three distinct interpretations of , namely, process-theoretic, denotational and logical. The main theme of our programme is the com-plementarity of the various interpretations of. This work may be seen as a step towards a reapprochement between the algebraic theory of processes in Concur-rency on the one hand, and the Lazy Lambda Calculus as a foundation for functional programming on the other.