Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Formal Aspects of Computing
Type theory and functional programming
Type theory and functional programming
Information and Computation
Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
A non-type-theoretic semantics for type-theoretic language
A non-type-theoretic semantics for type-theoretic language
The metaprl logical programming environment
The metaprl logical programming environment
Quotient Types: A Modular Approach
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Extracting computer algebra programs from statements
EUROCAST'05 Proceedings of the 10th international conference on Computer Aided Systems Theory
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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.