Abel, Andreas and Coquand, Thierry - Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality

lmcs:6068 - Logical Methods in Computer Science, June 30, 2020, Volume 16, Issue 2 - https://doi.org/10.23638/LMCS-16(2:14)2020
Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality

Authors: Abel, Andreas and Coquand, Thierry

Normalization fails in type theory with an impredicative universe of propositions and a proof-irrelevant propositional equality. The counterexample to normalization is adapted from Girard's counterexample against normalization of System F equipped with a decider for type equality. It refutes Werner's normalization conjecture [LMCS 2008].


Volume: Volume 16, Issue 2
Published on: June 30, 2020
Submitted on: February 3, 2020
Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages,Mathematics - Logic


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