In my talk I will show how to extend a computational 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. I will also show that this principle can be
formulated and used in a propositional fragment of a type theory.