Generative type abstractions -present in Haskell, OCaml, and other languages -are useful concepts to help prevent programmer errors. They serve to create new types that are distinct at compile time but share a run-time representation with some base type. We present a new mechanism that allows for zero-cost conversions between generative type abstractions and their representations, even when such types are deeply nested. We prove type safety in the presence of these conversions and have implemented our work in GHC.

We would like to use the Coq proof assistant to mechanically verify properties of Haskell programs. To that end, we present a tool, named hs-to-coq, that translates total Haskell programs into Coq programs via a shallow embedding. We apply our tool in three case studies -a lawful Monad instance, "Hutton's razor", and an existing data structure library -and prove their correctness. These examples show that this approach is viable: both that hs-to-coq applies to existing Haskell code, and that the output it produces is amenable to verification. CCS Concepts• Software and its engineering → Software verification;

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