Deriving Law-Abiding Instances

Liquid Haskell augments the Haskell language with theorem proving capabilities, allowing programmers to express and prove class laws. But many of these proofs require routine, boilerplate code and do not scale well, as the size of proof terms can grow superlinearlywith the size of the datatypes involved in the proofs. We present a technique to derive Haskell proof terms by leveraging datatype-generic programming.Our observation is thatwe can take any algebraic datatype, generate an equivalent representation type, and have Liquid Haskell automatically construct (and prove) an isomorphism between the original type and the representation type. This reducesmany proofs down to easy theorems over simple algebraic “building block” types, allowing programmers to write generic proofs cheaply and cheerfully. We applied our technique to derive verified instances of the Eq, Ord, Semigroup, Monoid and Functor Haskell classes for commonly used algebraic datatypes.