In denotational semantics and functional programming, the terms monad morphism, monad layering, monad constructor, and monad transformer have by now accumulated 20 years of twisted history. The exchange between Eric Kidd and sigfpe about the probability monad prompted me to investigate this history
Suppose someone stole all the monads but one, which monad would you want it to be? If you're a Haskell programmer you wouldn't be too bothered, you could just roll your own monads using nothing more than functions. But suppose someone stole do-notation leaving you with a version that only supported one type of monad. Which one would you choose? Rolling your own Haskell syntax is hard so you really want to choose wisely. Is there a universal monad that encompasses the functionality of all other monads? About a year ago I must have skimmed this post because the line "the continuation monad is in some sense the mother of all monads" became stuck in my head. So maybe Cont is the monad we should choose. This post is my investigation of why exactly it's the best choice. Along the way I'll also try to give some insight into how you can make practical use the continuation monad.
Comonads are an abstraction from category theory dualing many qualities of Monads. They are conceptually much simpler than arrows but seem to offer a solution to some problems not easily solved by monads. The ideas presented here are not novel except for the comonadic combinators for a nicer syntax. Typeclass Combinators Reader State Stream Writer Links