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A generalization of the Takeuti–Gandy interpretation

Published online by Cambridge University Press:  20 February 2015

BRUNO BARRAS,
THIERRY COQUAND and
SIMON HUBER
BRUNO BARRAS
Affiliation:
INRIA Saclay - Île de France, 4, rue Jacques Monod, 91893 ORSAY Cedex, France Email: bruno.barras@inria.fr
THIERRY COQUAND
Affiliation:
Department of Computer Science and Engineering, University of Gothenburg, SE-412 96 Göteborg, Sweden Email: thierry.coquand@cse.gu.se, simon.huber@cse.gu.se
SIMON HUBER
Affiliation:
Department of Computer Science and Engineering, University of Gothenburg, SE-412 96 Göteborg, Sweden Email: thierry.coquand@cse.gu.se, simon.huber@cse.gu.se
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Abstract

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We present an interpretation of a version of dependent type theory where a type is interpreted by a Kan semisimplicial set. This interprets only a weak notion of conversion similar to the one used in the first published version of Martin-Löf type theory. Each truncated version of this model can be carried out internally in dependent type theory, and we have formalized the first truncated level, which is enough to represent isomorphisms of algebraic structure as equality.

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