Hal Daume answers a question on how to define nice, infix ops acting on vectors:
What you want to do is make your Vector an instance of the Num(eric) type class. For instance:
instance Num Vector where (+) v1 v2 = zipWith (+) v1 v2 (-) v1 v2 = zipWith (-) v1 v2 negate v1 = map negate v1 abs v1 = map abs v1 (*) v1 v2 = ... fromInteger i = ... signum v1 = ...
I've left the last three blank because it's unclear what should go there. Since (*) has type Vector->Vector->Vector (in this instance), you can't use dot product or something like that.
signum :: Vector->Vector could be written and just return [-1], [0] or [1], I suppose.
fromInteger :: Integer->Vector is a little harder. Perhaps just 'fromInteger i = [fromInteger i]' would be acceptable. Or you could leave these undefined.
-- Hal Daume III | [EMAIL PROTECTED] "Arrest this man, he talks in maths." | www.isi.edu/~hdaume
While this is a possible solution, I would shout loudly: "Arrest this man, he is disrespectful wrt math!". Actually, this shows once more that the Num class and its relatives is a horror...
Signum in this context has no sense. The multiplication might be the cross product, but its anti-commutativity shows plainly that this is not a 'standard' multiplication. 'fromInteger' has even less sense than signum... I am particularly horrified by "abs v = map abs v", and I am sure all of you see why.
I think that a more sane solution would be the definition of a particular class with operations porting names like <+>, or ^+^, or whatever similar to standard ones, but different.
Jerzy Karczmarczuk
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