Question

when I type

:t map length . sum

into GHCi, it says that the type would be:

map length . sum :: Num [[a]] => [[[a]]] -> [Int]

However, if I create a file type-test.hs containing

x :: Num [[a]] => [[[a]]] -> [Int]
x = map length . sum

both ghc and ghci complain:

type-test.hs:1:1:
    Non type-variable argument in the constraint: Num [[a]]
    (Use -XFlexibleContexts to permit this)
    In the type signature for `x': x :: Num [[a]] => [[[a]]] -> [Int]

Why does ghci allow me to infer the type for this (using :t), when FlexibleContexts are not enabled?

Answer 1

(This doesn’t answer your original question, but solves the problem with the code instead)

These errors hint at that your code as written probably isn’t what you meant. This code:

map length . sum

means “Take my list of numbers, and sum it, then compute the length of each element(??) of the resulting number.” That makes no sense.

You probably meant:

sum . map length

which means “Take my list of lists, compute the length of every element, and sum the lengths.”

What the error message itself means is that since sum returns a number, aka the type of sum is Num n => [n] -> n, and you then try to use map length on that, which has type Num m => [[a]] -> [m], the compiler tries to say that n == [[a]] to make the types match, and everything goes downhill from there.