Re: [Haskell-cafe] Observations about foldM

Am Mittwoch 19 August 2009 16:32:57 schrieb Eugene Kirpichov:

2009/8/19 Dan Doel :

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On Wednesday 19 August 2009 12:14:24 am Jason McCarty wrote:

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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