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Markov's Principle For Propositional Type Theory

by Alexei Kopylov, Aleksey Nogin

Proceedings of the 10 th Annual Conference of the EACSL

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Abstract. In this paper we show how to extend a constructive type theory with a principle that captures the spirit of Markov’s principle from constructive recursive mathematics. Markov’s principle is especially useful for proving termination of specific computations. Allowing a limited form of classical reasoning we get more powerful resulting system which remains constructive and valid in the standard constructive semantics of a type theory. We also show that this principle can be formulated and used in a propositional fragment of a type theory.

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