New Types of Lambda-Transitive and Weakly Lambda-Mixing Sets

Lambda Calculus with Types

This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author’s classic The Lambda Calculus (1984). The formalism has since been extended with types...

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-...

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...

Lambda-calculus, types and models

Intersection types and lambda models

Invariance of interpretation by β-conversion is one of the minimal requirements for any standard model for the λ-calculus. With the intersection type systems being a general framework for the study of semantic domains for the λ-calculus, the present paper provides a (syntactic) characterisation of the above mentioned requirement in terms of characterisation results for intersection type assignm...