6 Jan
2011
6 Jan
'11
6:31 a.m.
On Wed, Jan 05, 2011 at 12:10:36PM -0500, Tyson Whitehead wrote:
I wonder if Patai hit upon the root of the issue when in his blog (which includes a nice hierarchy diagram) he suggested/proposed that "Arrow is strictly the intersection of Applicative and Category".
http://just-bottom.blogspot.com/2010/04/programming-with-effects-story-so-fa...
I don't think that's quite true. Category(~>) + forall a. Applicative(a~>) gives you the arrow constants, but not the arrow laws, without some additional conditions relating the two, like fmap f (g >>> h) = g >>> fmap f h liftA2 (,) id id = arr (\x -> (x,x)) liftA2 const f id = f arr f >>> g &&& h = (arr f >>> g) &&& (arr f >>> h) first f >>> first g = first (f >>> g)