منابع مشابه
Idempotents in intensional type theory
We study idempotents in intensional Martin-Löf type theory, and in particular the question of when and whether they split. We show that in the presence of propositional truncation and Voevodsky’s univalence axiom, there exist idempotents that do not split; thus in plain MLTT not all idempotents can be proven to split. On the other hand, assuming only function extensionality, an idempotent can b...
متن کاملInternalizing Intensional Type Theory
Homotopical interpretations of Martin-Löf type theory lead toward an interpretation of equality as a richer, more extensional notion. Extensional or axiomatic presentations of the theory with principles based on such models do not yet fully benefit from the power of dependent type theory, that is its computational character. Reconciling intensional type theory with this richer notion of equalit...
متن کاملCongruence Closure in Intensional Type Theory
Congruence closure procedures are used extensively in automated reasoning and are a core component of most satisfiability modulo theories solvers. However, no known congruence closure algorithms can support any of the expressive logics based on intensional type theory (ITT), which form the basis of many interactive theorem provers. The main source of expressiveness in these logics is dependent ...
متن کاملInterpreting descriptions in intensional type theory
Calculi of indefinite and definite descriptions are presented, and interpreted in Martin-Löf’s intensional type theory. The interpretations are formalizations of the implicit ideas found in the literature of constructive mathematics: if we have proved that an element with a certain property exists, we speak of ’the element such that the property holds’ and refer by that phrase to the element co...
متن کاملExtensional Equality in Intensional Type Theory
We present a new approach to introducing an extensional propositional equality in Intensional Type Theory. Our construction is based on the observation that there is a sound, intensional setoid model in Intensional Type theory with a proof-irrelevant universe of propositions and -rules for and -types. The Type Theory corresponding to this model is decidable, has no irreducible constants and per...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2017
ISSN: 1860-5974
DOI: 10.2168/lmcs-12(3:9)2016