A New Model Construction for Various Type Systems
نویسنده
چکیده
A construction of nondomain models for various type systems such as Martin-Löf’s type theory with intensional identity types, the polymorphic lambda calculus and other extensions of the simply typed lambda calculus is presented. These extensions include nearly all calculi in Barendregt’s lambda cube enriched by strong sums. The models can be arranged in such a way that the universal type Πα. α representing absurdity is interpreted by the empty set, which means they are also models of the consistent higher order logic defined by the type structure.
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