On 9/5/10 10:19 AM, Ivan Lazar Miljenovic wrote:
Hmmm.... is there any reason for Functor to be a superclass of Pointed? I understand Functor and Pointed being superclasses of Applicative (which in turn is a superclass of Monad), but can't see any relation between Pointed and Functor...
Because there's a law for pointed functors which ensures that return (point, unit, pure,...) only creates "trivial" structure: forall {A B : Type} (f : A -> B) (a : A) , fmap f (return a) = return (f a) If we require this law, then the five laws for Applicative can be reduced to only three; which is nice. (Though, if the extra two laws are satisfied, then we can prove this one.) We don't actually enforce that instances obey their class' laws anywhere else, so it's not like we'd need somewhere to store this proof. But the law is there nevertheless. What use would it be to have a return function that doesn't satisfy any laws (i.e., without fmap)? -- Live well, ~wren