Extensional Martin-Loef Type Theory

In this episode, I discuss the basic distinguishing rule of Extensional Martin-Loef Type Theory, namely equality reflection. This rule says that propositional equality implies definitional equality. Algorithmically, it would imply that the type checker should do arbitrary proof search during type checking, to see if two expressions are definitionally equal. This immediately gives us undecidability of type checking for the theory, at least as usually realized.