Summary: Verifying a Semantic -Conversion Test for
Martin-L®of Type Theory
and Peter Dybjer2
Department of Computer Science, Ludwig-Maximilians-University, Munich
Department of Computer Science, Chalmers University of Technology
Abstract. Type-checking algorithms for dependent type theories often
rely on the interpretation of terms in some semantic domain of values
when checking equalities. Here we analyze a version of Coquand's algo-
rithm for checking the -equality of such semantic values in a theory
with a predicative universe hierarchy and large elimination rules. Al-
though this algorithm does not rely on normalization by evaluation ex-
plicitly, we show that similar ideas can be employed for its verification.
In particular, our proof uses the new notions of contextual reification and
strong semantic equality.