Virtual intersection theories

Intersection Types and Lambda Theories

We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of λ-theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation of an arbitrary simple easy term is any filter which can be described in an uniform way by a recursive predicate. This allows us to prove the consistency of a we...

Intersection Types and Lambda Theories

We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of λ-theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation of an arbitrary simple easy term is any filter which can be described in an uniform way by a predicate. This allows us to prove the consistency of a well-know λ-...

Virtual Intersection Numbers

Virtual Theories

Proof is a programming activity. Consequently programming environments which support proof in the large are required. We describe an environment which supports one area of proof-in-the-large: that of theory management. We present the notion of virtual theories. They give the illusion of multiple active theories allowing the user to switch between diierent theories at will, proving theorems and ...

A Complete Characterization of Complete Intersection-Type Theories

We characterize those intersection-type theories which yield complete intersection-type assignment systems for λ-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics, the simple semantics and the F-semantics.