Kripke Semantics for Martin-Löf's Extensional Type Theory
نویسندگان
چکیده
منابع مشابه
Kripke Semantics for Martin-Löf's Extensional Type Theory
It is well-known that simple type theory is complete with respect to nonstandard set-valued models. Completeness for standard models only holds with respect to certain extended classes of models, e.g., the class of cartesian closed categories. Similarly, dependent type theory is complete for locally cartesian closed categories. However, it is usually difficult to establish the coherence of inte...
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We present a new game semantics for Martin-Löf type theory (MLTT); our aim is to give a mathematical and intensional explanation of MLTT. Specifically, we propose a category with families (a categorical model of MLTT) of a novel variant of games, which induces an injective (when Id-types are excluded) and surjective interpretation of the intensional variant of MLTT equipped with unit-, empty-, ...
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Constructive reasoning has played an increasingly important role in the development of provably correct software. Both typed and type-free frameworks stemming from ideas of Heyting, Kleene, and Curry have been developed for extracting computations from constructive specifications. These include Realizability, and Theories based on the Curry-Howard isomorphism. Realizability – in its various typ...
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Martin-Löf’s type theory is the basis of a variety of formal systems underlying many proof assistants. There are a lot of variants of type theory, among which two classes can be identified: intensional and extensional type theory. The difference between the two lies in the manner in which the equality is dealt with, but this results in huge differences. Intensional type theory requires the user...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2011
ISSN: 1860-5974
DOI: 10.2168/lmcs-7(3:18)2011