[Haskell-cafe] Re: what is inverse of mzero and return?
k.schupke at imperial.ac.uk
Tue Jan 25 05:32:41 EST 2005
I think I see, but if the objects are types, arn't the morphisms functions
on types not values?
Ashley Yakeley wrote:
>In article <41F61A0B.90005 at imperial.ac.uk>,
> Keean Schupke <k.schupke at imperial.ac.uk> wrote:
>>I am sure monads in Haskell (and other functional languages like ML) are
>>defined on types not values.
>The objects of the category are types. The morphisms on the category are
>functions. Two functions are the same if they match each value to the
>same value. For the Functor laws and the Monad laws, the values
>certainly do matter: if they didn't, they wouldn't correspond to the
>category theory notions of functor and monad because the morphisms would
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