Generic and flexible defaults for verified, law-abiding type-class instances

Abstract

Dependently typed languages allow programmers to state and prove type class laws by simply encoding the laws as class methods. But writing implementations of these methods frequently give way to large amounts of routine, boilerplate code, and depending on the law involved, the size of these proofs can grow superlinearly with the size of the datatypes involved. We present a technique for automating away large swaths of this boilerplate by leveraging datatype-generic programming. We observe that any algebraic data type has an equivalent representation type that is composed of simpler, smaller types that are simpler to prove theorems over. By constructing an isomorphism between a datatype and its representation type, we derive proofs for the original datatype by reusing the corresponding proof over the representation type. Our work is designed to be general-purpose and does not require advanced automation techniques such as tactic systems. As evidence for this claim, we implement these ideas in a Haskell library that defines generic, canonical implementations of the methods and proof obligations for classes in the standard base library.