Non-determinism in a functional setting

Abstract

The pure untyped lambda calculus augmented with an (erratic) choice operator is considered as an idealised nondeterministic functional language. Both the 'may' and the 'must' modalities of convergence are of interest. Following Abramsky's (1991) work on domain theory in logical form, we identify the denotational type that captures the computational situation delta =P(( delta to delta ) perpendicular to ), where P(-) is the Plotkin power-domain functor. We then carry out a systematic programme that hinges on three distinct interpretations of delta , namely process-theoretic, denotational, and logical. The main theme of the programme is the complementarity of the various interpretations of delta . This work may be seen as a step towards a rapprochement between the algebraic theory of processes in concurrency on the one hand, and the lazy lambda calculus as a foundation for functional programming on the other.<>