## Paper: Normalization by Evaluation for Martin-Löf Type Theory with Typed Equality Judgements (at LICS 2007)

**Andreas Abel Thierry Coquand Peter Dybjer**

### Abstract

The decidability of equality is proved for Martin-Lof type theory with a universe Ža 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.

### BibTeX

@InProceedings{AbelCoquandDybjer-NormalizationbyEval, author = {Andreas Abel and Thierry Coquand and Peter Dybjer}, title = {Normalization by Evaluation for Martin-Löf Type Theory with Typed Equality Judgements}, booktitle = {Proceedings of the Twenty-Second Annual IEEE Symposium on Logic in Computer Science (LICS 2007)}, year = {2007}, month = {July}, pages = {3--12}, location = {Wroclaw, Poland}, publisher = {IEEE Computer Society Press} }