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Equational reasoning is one of the key features of pure functional languagessuch as Haskell. To date, however, such reasoning always took place externallyto Haskell, either manually on paper, or mechanised in a theorem prover. Thisarticle shows how equational reasoning can be performed directly and seamlesslywithin Haskell itself, and be checked using Liquid Haskell. In particular,language learners --- to whom external theorem provers are out of reach --- canbenefit from having their proofs mechanically checked. Concretely, we show howthe equational proofs and derivations from Graham's textbook can be recast asproofs in Haskell (spoiler: they look essentially the same).

Functional Pearl: Theorem Proving for All (Equational Reasoning in Liquid Haskell)