Ross Paterson wrote:
The Arrow class as originally defined by John Hughes had methods arr, >>> and first. (>>> has since been moved by #1773 to the Category class.) When writing the "Fun of Programming" paper, I added pure as a synonym for arr, because Richard Bird preferred it. However this name hasn't caught on, and now it clashes with a method in the Applicative class, so I propose to remove it.
I agree with deleting 'pure' from there. Now assuming that, I'm wondering... It looks like all Arrows are Applicative; is that a useful observation? (and then even further off topic, but it's still important); As follows: <*> :: (Applicative f) => f (a -> b) -> f a -> f b so <*> :: (Arrow arr) => arr x (a -> b) -> arr x a -> arr x b fmap :: (Arrow arr) => (a -> b) -> arr x a -> arr x b pure :: (Applicative f) => a -> f a pure :: (Arrow arr) => a -> arr x a Interesting, it looks a bit similar to 'Reader x', is that okay? instance (Arrow arr) => Applicative (arr x) where pure a = arr (const a) fmap f a = a >>> arr f f <*> a = fmap (uncurry ($)) (f &&& a) But I seem to recall arrConst indeed being of significance, for example. And the above definition of <*> preserves the ordering of f and a; for example, the effect-order-reversing Applicative-transformer could accurately be applied here. So I think it's nontrivially useful. Not all Applicatives are Arrows though! ArrowPlus, of course, corresponds with Alternative; the full types of the appending operation's arguments must be identical in all cases. instance (Arrow arr) => Alternative (arr x) where empty = zeroArrow; (<|>) = (<+>) and thenceforth with Monoid instance (Arrow arr) => Alternative (arr a b) where mempty = zeroArrow; mappend = (<+>) . It makes me wonder what is the point of ArrowPlus, MonadPlus, Alternative... when we have Monoid. But are they usable in all the same situations? It seems some places that use f :: (MonadPlus f) => ... would indeed need to require the polymorphic (invented syntax) f :: (forall a. Monoid (f a)) => ... not just for some particular 'a' f :: (Monoid (f a)) => ... Why does that make sense? Should it? Did I get confused somehow? -Isaac