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

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14

Basic Properties of Intersection Type Assignment

This chapter studies meta-theoretical properties of the type assignment systems. They will be crucial in Chapter 16 for the development of filter lambda models induced by these systems. The most important question here is whether the type assignment system satisfies β-, η-reduction or β-, η-expansion. Due to the intrinsic syntactic nature of the filter models, any property on the type assignment system is transferred into the filter structure. This is revealed by the Type Semantics Theorem (Theorem 16.2.7) which says that the interpretation of a term is the set of its types. The consequence of this is that the filter structure preserves the meaning of -terms under β- or η- reduction or expansion, ...

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