[Haskell-cafe] Before

[Dan Piponi]

On 7/2/07, Andrew Coppin <andrewcoppin at btinternet.com> wrote:
> What were monads like before they became a Haskell language construct?
>
> Is Haskell's idea of a "monad" actually anywhere close to the original
> mathematical formalism?

It's as close to a mathematician's notion of a monad as Haskell's
types and functions are to the objects and arrows of category theory.
They are essentially the same thing. Using the notation here:
http://en.wikipedia.org/wiki/Monad_%28category_theory%29 'return' is
eta and join is mu. If you're more familiar with >>= than join, then
its definition is

> join x =  x >>= id

and I'll leave recovering >>= from join as a nice exercise.

Knowing that you were about to ask this question I told my past self
by tachyon express and wrote up on it this weekend:
http://sigfpe.blogspot.com/2007/06/monads-from-algebra-and-the-gray-code.html
--
Dan