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arXiv · 1102.2405

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

Andreas Abel·Thierry Coquand·Miguel Pagano
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Abstract

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.

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Andreas Abel, Thierry Coquand, Miguel Pagano. 2011-05-04. A Modular Type-checking algorithm for Type Theory with Singleton Types and Proof Irrelevance. https://doi.org/10.2168/lmcs-7(2%3A4)2011

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