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

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8

Properties of Recursive Types

In this chapter we study the properties of recursive types independently of their use in typing λ-terms. Most of these properties will however be useful in the study of the properties of typed terms in the next chapter.

We will discuss properties of µ-types and of systems of type equations in two separate sections, even if most of them are indeed similar. In Section 8.1 we build a solution of a simultaneous recursion using μ-types, and show the essential equivalence of the two notations for recursive types. There are, nevertheless, aspects which are treated more naturally in one approach than in the other. For instance, in Chapter 9, the notion of principal type scheme is formulated and studied in a more natural ...

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