help with types and composition
I would like to write a function that takes two lists of numbers and returns a number. For simplicity, let's assume an integer, i.e. myfunc:: [Integer]->[Integer]->Integer But I can't quite get things right when trying to define myfunc = ... and making the arguments implicit. My difficulty might be seen with the following two functions, let, f1 = (zipWith ($)) . (map (*)) f2 = sum if I set the types such that f1 returns [Integer] and sum accepts [Integer] it seems that somehow I should be able to compose them in to a single function that takes two lists and returns the number, but f1 . f2 and numerous variations don't work. I can curry some list l and f1 . (f2 l) works, but is there a way to get f1 and f2 combined into a function that accepts two lists? My problem is not really about writing the function but about composition. I can write the function with arguments or a local lambda that suits my practical purpose. But the fact that I think I should be able to compose f1 . f2 somehow reveals a conceptual misunderstanding that I hope someone will help me clear up. Thank you, Britt Anderson
f1 = (zipWith ($)) . (map (*))
f2 = sum
First, f1 would be clearer as zipWith (*). Second, look at the type of (.): (.) :: (b -> c) -> (a -> b) -> (a -> c) Notice that (b -> c) and (a -> b) each take one argument, but f1 takes two arguments. That's why using (.) with f1 doesn't work. You can do what you want by uncurrying f1 so it takes only one argument, which makes it easier to compose. You can then re-curry the result after you do the composition. f1 :: [Integer] -> [Integer] -> [Integer] uncurry f1 :: ([Integer], [Integer]) -> [Integer] f2 . uncurry f1 :: ([Integer], [Integer]) -> Integer curry (f2 . uncurry f1) :: [Integer] -> [Integer] -> Integer I'm sure there are shorter versions that use more than just (.), curry, and uncurry.
I usually go with
(f1 .) . f2
Which makes the solution for the particular example:
sumOfProducts = (sum .) . zipWith (*)
But if you want the operator that achieves this effect for arbitrary functions,
((.) (.) (.))
does the trick. Or, if SKI is your thing, you might also try
(ap (const ap) (ap (const const) (ap (const ap) const)))
but I don't usually do it that way unless I'm feeling particularly perverse.
On Thu, Jul 2, 2009 at 11:54 AM, Britt Anderson
I would like to write a function that takes two lists of numbers and returns a number. For simplicity, let's assume an integer, i.e. myfunc:: [Integer]->[Integer]->Integer But I can't quite get things right when trying to define myfunc = ... and making the arguments implicit.
My difficulty might be seen with the following two functions, let,
f1 = (zipWith ($)) . (map (*))
f2 = sum
if I set the types such that f1 returns [Integer] and sum accepts [Integer] it seems that somehow I should be able to compose them in to a single function that takes two lists and returns the number, but f1 . f2 and numerous variations don't work. I can curry some list l and f1 . (f2 l) works, but is there a way to get f1 and f2 combined into a function that accepts two lists?
My problem is not really about writing the function but about composition. I can write the function with arguments or a local lambda that suits my practical purpose. But the fact that I think I should be able to compose f1 . f2 somehow reveals a conceptual misunderstanding that I hope someone will help me clear up.
Thank you, Britt Anderson
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participants (3)
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Britt Anderson -
Geoffrey Marchant -
Sean Bartell