Monads as adjunctions

Question

I\'ve been reading about monads in category theory. One definition of monads uses a pair of adjoint functors. A monad is defined by a round-trip using those functors. Appare

Answer 1

Derek Elkins was showing me recently over dinner how the Cont Monad arises from composing the (_ -> k) contravariant functor with itself, since it happens to be self-adjoint. That's how you get (a -> k) -> k out of it. Its counit, however, leads to double negation elimination, which can't be written in Haskell.

For some Agda code that illustrates and proves this, please see http://hpaste.org/68257.