Summary: Verifying a Semantic ##­Conversion Test for
Martin­L˜of Type Theory
Andreas Abel, 1 Thierry Coquand, 2 and Peter Dybjer 2#
1 Department of Computer Science, Ludwig­Maximilians­University, Munich
abel@tcs.ifi.lmu.de
2 Department of Computer Science, Chalmers University of Technology
coquand,peterd@cs.chalmers.se
Abstract. Type­checking 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.
The algorithm is part of a bi­directional type checking algorithm which
checks whether a normal term has a certain semantic type, a technique
used in the proof assistants Agda and Epigram. We work with an abstract
notion of semantic domain in order to accommodate a variety of possible

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München

Collections: Computer Technologies and Information Sciences