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A Modular Type-checking algorithm for Type Theory with Singleton Types and Proof Irrelevance

We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluation algorithm. We prove completeness and soundness of the algorithm; and get as a corollary the injectivity of type constructors. Then we give the definition of a correct and complete type-checking algorithm for terms in normal form. We extend the results to proof-irrelevant propositions.

preprint2011arXivOpen access
Andreas AbelThierry CoquandMiguel Pagano
Logic in Computer Science
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Andreas AbelThierry CoquandMiguel Pagano

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