Type invariants for Haskell

Multi-parameter type classes, functional dependencies, and recently GADTs and open type families open up opportunities to use complex type-level programming to let GHC's type checker verify various properties of your programs. But type-level code is special in that its correctness is crucial to the safety of the program; so except in those cases simple enough for the type checker to see trivially that the code is correct (or harmless), type-level programs need to come with a specification of their properties together with their proof. In this article, we propose an extension to Haskell that allows the specification of invariants for type classes and open type families, together with accompanying evidence that those invariants hold. To accommodate the open nature of type classes and type families, the evidence itself needs to be open and every subcase of the proof can be provided independently from the others.