Question

For learning purposes I am trying to write my own implementation of the zipWith function. However, I am hitting an issue with pattern matching on edge cases with _. First I will describe the good case, then the bad case. Hopefully someone will be able to explain why they behave differently. Thanks

If I write the zipWith function as follows, it works (Note the order of the edge cases matching empty list on lines 2 & 3):-

zipWith' :: (a -> b -> c) -> [a] -> [b] -> [c]
zipwith' _ [] _ = []
zipWith' _ _ [] = []
zipWith' f (x:xs) (y:ys) = f x y : zipWith' f xs ys

Compiling in GHCI:-

ghci> :l ZipWith.hs 
[1 of 1] Compiling Main             ( ZipWith.hs, interpreted )

Ok, the above is fine, yet if I swap the pattern matching for the edge cases around GHCI throws ‘Multiple declarations of’ error for lines 2 and 4.

zipWith' :: (a -> b -> c) -> [a] -> [b] -> [c]
zipWith' _ _ [] = []
zipwith' _ [] _ = []
zipWith' f (x:xs) (y:ys) = f x y : zipWith' f xs ys

Compiling in GHCI:-

ZipWith.hs:4:0:
    Multiple declarations of `Main.zipWith''
    Declared at: ZipWith.hs:2:0
                 ZipWith.hs:4:0
Failed, modules loaded: none.

I’m stumped…

1. Looking at the patterns on lines 2 and 4 they seem mutually exclusive but i’m obviously missing something fundamental here
2. Why would switching the patterns on lines 2 and 3 cause the compilation error to go away.

Answer 1

The error message isn’t complaining about overlapping patterns (your patterns do overlap in the case of two empty lists, but that’s neither the problem, nor a problem), but multiple definitions of the zipWith function.

The reason for that is that in your second case you have one definition of zipWith followed by an unrelated definition of zipwith (note the lower case w), followed by a new, conflicting definition of zipWith. In other words it’s a simple typo. (Did take me a while to see though – quite a sneaky typo)