Normalization by Evaluation for Martin-Löf Type Theory with Equality Judgements
Journal article, 2007

The decidability of equality is proved for Martin-Löf type theory with a universe a la Russell and typed beta-eta-equality judgements. A corollary of this result is that the constructor for dependent function types is injective, a property which is crucial for establishing the correctness of the type-checking algorithm. The decision procedure uses normalization by evaluation, an algorithm which first interprets terms in a domain with untyped semantic elements and then extracts normal forms. The correctness of this algorithm is established using a PER-model and a logical relation between syntax and semantics.

Author

Andreas Abel

Ludwig-Maximilians-Universität München

Thierry Coquand

University of Gothenburg

Peter Dybjer

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Proceedings of 22nd IEEE Annual Symposium on Logic in ComputerScience, Wroclaw, Poland, July 2007.

1043-6871 (ISSN)

3-12

Subject Categories

Computer Science

DOI

10.1109/lics.2007.33

ISBN

0769529089