The distinction between the conjunctive nature of non-determinism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λ-calculus is extended with both a non-deterministic choice and a parallel operator; a notion of reduction is introduced, extending fi-reduction of the classical calculus. We study type assignment systems for this calculus, together with a denotational semantics which is initially defined constructing a set semimodel via simple types. We enrich the type system with intersection and union types, dually reflecting the disjunctive and conjunctive behaviour of the operators, and we build a filter model. The theory of this model is compared both with a Morris-style operational semantics and with a semantics based on a notion of capabilities.

Type free lazy -calculus is enriched with angelic parallelism and demonic nondeterminism. Call-by-name and call-by-value abstractions are considered and the operational semantics is stated in terms of a must convergence predicate. We introduce a type assignment system with intersection and union types and we prove that the induced logical semantics is fully abstract.

Parallelism and non-determinism are fundamental concepts in the process algebra theory. Combining them with -calculus can enlighten the theory of higher-order process algebras. In recent papers an analysis of a -calculus containing parallel and non-deterministic operators was carried on by means of a type assignment system with intersection and union types. The present paper answers the problem of determining principal types for this system. For correspondence contact Franco Barbanera Dipartimento di Informatica, Universit'a di Torino Corso Svizzera 185, 10149 Torino Italy e-mail: barba@di.unito.it tel: +39 11 7429111 Fax: +39 11 751603 1 Principal Typing for Parallel and non-Deterministic -calculus Abstract Parallelism and non-determinism are fundamental concepts in the process algebra theory. Combining them with -calculus can enlighten the theory of higher-order process algebras. In recent papers an analysis of a -calculus containing parallel and non-deterministic operators ...