Am Mittwoch 19 August 2009 16:32:57 schrieb Eugene Kirpichov: > 2009/8/19 Dan Doel <dan.d...@gmail.com>: > > On Wednesday 19 August 2009 12:14:24 am Jason McCarty wrote: > >> Interestingly, foldM can also be written as a left fold. To see this, > >> note that it is a theorem that foldr f z xs = foldl f z xs as long as f > >> is associative and z is a unit for f. > > This is not true: f has to be commutative, not associative. > > Consider matrix multiplication. >
It is true: foldr: A1*(A2*(... *AN*E)) foldl: (...((E*A1)*A2)*...*AN) Commutativity doesn't help, consider data Foo = Z | A | B (~) :: Foo -> Foo -> Foo Z ~ x = x x ~ Z = x B ~ B = A _ ~ _ = B (~) is commutative, but not associative, Z is a unit for (~). foldr (~) Z [A,A,B] = B foldl (~) Z [A,A,B] = A _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
