We consider the extension of Curry's basic functionality theory presented by Barendregt et al. (to appear), and we define, for any term X, a principal type scheme (p.t.s.).Expand

A calculus is a language equipped with some reduction rules. All the calculi we consider in this book share the same language, which is the language of λ-calculus, while they differ each other in… Expand

We show that a term satisfying a given property has a principal type scheme in an extended meaning, i.e., there is a type scheme deducible for it from which all and only the type schemes deducibles for it are reachable, by means of suitable operations.Expand

Abstract It is well known that a reflexive object in the Cartesian closed category of complete partial orders and Scott-continuous functions is a model of λ-calculus (briefly a topological model). A… Expand

The notion of solvability in the call-by-value λ -calculus is defined and completely characterized, both from an operational and a logical point of view.Expand

This paper is about a categorical approach for modelling the pure (i.e., without constants) call-by-value λ-calculus, defined by Plotkin as a restriction of the call-by-name λ-calculus. In… Expand

The filter λ-model is a model of the ,λ-calculus, based on a system of type assignment which extends the basic functionality theory of Curry, invented in order to give a completeness proof for Scott's semantics of Curry's type assignment.Expand