Proceedings 6th Workshop on Mathematically Structured Functional Programming vol:207 pages:23-56
Electronic Proceedings in Theoretical Computer Science
Workshop on Mathematically Structured Functional Programming edition:6 location:Eindhoven, Netherlands date:8 April 2016
We develop an algebraic underpinning of backtracking monad transformers in the general setting of monoidal categories. As our main technical device, we introduce Eilenberg–Moore monoids, which combine monoids with algebras for strong monads. We show that Eilenberg–Moore monoids coincide with algebras for the list monad transformer ('done right') known from Haskell libraries. From this, we obtain a number of results, including the facts that the list monad transformer is indeed a monad, a transformer, and an instance of the MonadPlus class. Finally, we construct an Eilenberg–Moore monoid of endomorphisms, which, via the codensity monad construction, yields a continuation-based implementation a la Hinze.