Re: [Haskell-cafe] Another monad question...

On Sun, Jul 15, 2007 at 12:03:06AM -0400, David LaPalomento wrote:

On 7/14/07, Stefan O'Rear wrote:

...

Your base case is subtly wrong - it should be return [], not mzero. Mzero always fails - mzero `mplus` x = x, by one of the MonadPlus laws.

Ah! So here's another quick question: if mzero is the identity element, why isn't it part of the Monad class? Correct me if I'm wrong but aren't Monads (in the mathematical sense) required an identity element by definition?

You're probably confusing Monads with Monoids. Monoid: * Concept from abstract algebra * A set Ty, a distinguished element mempty :: Ty, and a binary operator mappend :: Ty -> Ty -> Ty * mempty `mappend` x = x * x `mappend` mempty = x * a `mappend` (b `mappend` c) = (a `mappend` b) `mappend` c Monad: * Concept from category theory * A category C (assumed to be Haskell objects in the type class) * A functor F :: C -> C * Two natural transformations η :: F^0 -> F^1, μ :: F^2 -> F^1 * the monad laws MonadPlus: * Monads that are also monoids * mappend, mempty named mplus, mzero to avoid conflicts * (OK it was the other way around, monadplus came first) I've heard that Monads are in some way like Monoids, hence the name. But I don't understand the explanation yet myself :( Stefan