You're right. My bad, indeed. 2009/8/19 Daniel Fischer <daniel.is.fisc...@web.de>: > 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 >
-- Eugene Kirpichov Web IR developer, market.yandex.ru _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
