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Combining Proofs And Programs In A Dependently Typed Language, Stephanie Weirich, Vilhelm Sjoberg, Chris Casinghino
Combining Proofs And Programs In A Dependently Typed Language, Stephanie Weirich, Vilhelm Sjoberg, Chris Casinghino
Stephanie Weirich
Most dependently-typed programming languages either require that all expressions terminate (e.g. Coq, Agda, and Epigram), or allow infinite loops but are inconsistent when viewed as logics (e.g. Haskell, ATS, mega). Here, we combine these two approaches into a single dependently-typed core language. The language is composed of two fragments that share a common syntax and overlapping semantics: a logic that guarantees total correctness, and a call-by-value programming language that guarantees type safety but not termination. The two fragments may interact: logical expressions may be used as programs; the logic may soundly reason about potentially nonterminating programs; programs can require logical …