On Dec 16, 2011, at 3:59 AM, Carl Howells wrote:
Monoid and Alternative are not the same. There is a very important difference between them:
class Alternative f where (<|>) :: f a -> f a -> f a ...
class Monoid a where mappend :: a -> a -> a ...
The equivalent to Alternative is MonadPlus, not Monoid. The kinds matter. In Alternative, you are guaranteed that the type that f is applied to cannot affect the semantics of (<|>).
I understand that one needs to worry about kinds in general, but in this particular case such a subtlety is non-issue because you would always be defining Monad for a particular type. That is to say, given an alternative f, the instance of Monoid would be instance Monoid (f a) where { ... } where in the above a is an arbitrary type variable. To give you a more concrete example, the following code compiles and runs, producing the output [1,2,3,4,5,6] ================================================ import Data.Monoid newtype L a = L [a] deriving (Show,Eq) instance Monoid (L a) where mempty = L [] mappend (L x) (L y) = L (x ++ y) main = putStrLn . show $ (L [1,2,3]) `mappend` (L [4,5,6]) ================================================ Cheers, Greg