[Haskell-cafe] Before

[Andrew Coppin]

Dan Piponi wrote:
> 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.

Right. So it's a pretty close correspondence.

> http://en.wikipedia.org/wiki/Monad_%28category_theory%29

"Monads are important in the theory of pairs of adjoint functors. They 
can be viewed as monoid objects in a category of endofunctors (hence the 
name) and they generalize closure operators on posets to arbitrary 
categories."

*cried softly in the corner*

I knew asking questions about theoretical mathematics probably wasn't a 
good idea...

> 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 
>

Heh. *I* would have just told my past self next week's lottery numbers...