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

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17

Advanced Properties and Applications

This chapter proves some properties of intersection types in relation to terms and models.

Section 17.1 defines a realizability interpretation of types (Barendregt et al. (1983)). Types are interpreted as subsets of a domain of discourse D. Assuming a (partial) application image, and a type environment ξ, i.e. a mapping from type atoms to subsets of D, we can define an interpretation image for each type A in image by giving ...

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