Set Theory and Logic


Refutation of Shallow Embedding in Martin-Löf Type Theory

Authors: Colin James III

In Martin-Löf type theory (MLTT), we evaluate shallow embedding as the following conjecture: “if we add the rewrite rule ∀x. f x (not x) = true, the expression f true false will not be rewritten to true, since it does not rigidly match the not x on the left hand side”. The conjecture is not tautologous, hence refuting shallow embedding in MLTT and forming a non tautologous fragment of the universal logic VŁ4.

Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at

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[v1] 2019-07-18 07:16:12

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