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

Andreas Abel, Thierry Coquand, Miguel Pagano, Pierre-Louis Curien
2011 Logical Methods in Computer Science  
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.
doi:10.2168/lmcs-7(2:4)2011 fatcat:5mpxki77wza5teoyfvpvnpe6qe