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Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality (1911.08174v4)
Published 19 Nov 2019 in cs.LO, cs.PL, and math.LO
Abstract: 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].
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