A Specification for Dependently-Typed Haskell (Extended version)

We propose a semantics for Dependent Haskell, an extension of Haskell with full-spectrum dependent types. Our semantics consists of two strongly related languages. The rst is a Curry-style dependently-typed language with nontermination, irrelevant arguments, and equality abstraction. The second, strongly inspired by GHC’s core language FC, is its explicitly-typed analogue, suitable for implementation. In contrast to prior work, our design demonstrates that homogeneous equality is compatible with explicit equality proofs. All of our results—chie y, type safety, along with theorems that relate our two semantics—have been formalized using the Coq proof assistant.