Dependent type theory of stateful higher-order functions

We present a dependent Hoare Type Theory (HTT) which provides support for reasoning about programs with higherorder functions and effects, including non-termination, state with aliasing and pointer arithmetic. The type structure encapsulates effectful commands using a monad indexed by preand post-conditions in the style of Hoare logic. The theory carefully distinguishes between an appropriate notion of definitional equality and propositional equality, in order to maintain the relative decidability of

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