Haskell function to check differences between two lists

Question

I want to write a function that checks if two lists are "almost" equal. The first parameter d is used for precision - the difference between the elements must not exceed d.

For example, nearlyEqual 0.5 [2,5] [2.5, 5.1] equals True, but nearlyEqual 0.1 [2,5] [2.5, 5.1] equals False.

I wrote this but it is not working:

nearlyEqual :: Int -> [Int] -> [Int] -> Bool
nearlyEqual d xs ys = foldr(&&) True $ zipWith (\x y -> abs(x-y)<=d)

What am I missing? Any help would be greatly appreciated!

Answer 1

Not sure if it's a typo, but you're not passing xs and ys to your function.

nearlyEqual d xs ys = foldr(&&) True $ zipWith (\x y -> abs(x-y)<=d)

should be

nearlyEqual d xs ys = foldr(&&) True $ zipWith (\x y -> abs(x-y)<=d) xs ys

at least for it to typecheck.

A clearer implementation would make use of all, which is of type Foldable t => (a -> Bool) -> t a -> Bool, and of the function composition operator (.):

nearlyEqual d xs ys = all ((<= d) . abs) $ zipWith (-) xs ys

where zipWith (-) xs ys is element-wise difference of the two lists, and all verifies that the predicate (<= d) . abs holds for all of the elements of that list; the predicate, given an argument, applies abs to it, and then (<= d) to the result.