O'Reilly logo

Lambda Calculus with Types by Richard Statman, Wil Dekkers, Henk Barendregt

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

10

Models

Our purpose in the present chapter is to build concrete type algebras for the interpretation of recursive types. In Section 10.1 we focus on systems à la Curry, where, in general, infinitely many types can be inferred for each (type-free) λ-term. Accordingly, it is natural to regard the interpretation of a type as a collection of elements of a model of the untyped λ-calculus. This idea is due to Scott (1975a).

We shall also describe, in Sections 10.2 and 10.3, how to build models for explicitly typed systems with recursive types. Classical categories of domains yield straightforward models for these formulations. Beside these, we shall also consider models based on different constructions (like continuous closures or partial equivalence ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required