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

11

Applications

11.1 Subtyping

The model of recursive types discussed in the previous chapter justifies thinking of types as subsets of a model for the untyped λ-calculus (possibly extended with constants). This interpretation suggests a straightforward notion of subtyping: recursive types A, B are in the subtype relation, written image for all type environments η interpreting the free type variables occurring in them as complete and uniform subsets of D. We shall see later that a natural formal system for deriving type inequalities for recursive types is sound and complete for this interpretation. We start by introducing some basic systems of subtyping ...

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