Andreas Abel ; Gabriel Scherer - On Irrelevance and Algorithmic Equality in Predicative Type Theory

lmcs:1045 - Logical Methods in Computer Science, March 27, 2012, Volume 8, Issue 1 -
On Irrelevance and Algorithmic Equality in Predicative Type Theory

Authors: Andreas Abel ; Gabriel Scherer

Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irrelevant quantification which is compatible with a type-based notion of equality that respects eta-laws. We extend Pfenning's theory to universes and large eliminations and develop its meta-theory. Subject reduction, normalization and consistency are obtained by a Kripke model over the typed equality judgement. Finally, a type-directed equality algorithm is described whose completeness is proven by a second Kripke model.

Volume: Volume 8, Issue 1
Published on: March 27, 2012
Accepted on: June 25, 2015
Submitted on: May 23, 2011
Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages,F.4.1


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