Why is GHCi typing this statement oddly?

Question

In answering a question on stackoverflow, I noticed that GHCi (interactive) is assigning a too-restrictive type in a let statement. Namely, given the code,

import Control.Arrow
f = maximum &&& id >>> fst &&& (\(m,l) -> length $ filter (==m) l)

(as on my answer to https://stackoverflow.com/questions/6281813/maximum-of-list-and-count-of-repeat-maximum-number/6283594#6283594), if one inserts a "let" before f and enters this in ghci, it gives the following type information

Prelude Control.Arrow> :t f
f :: [()] -> ((), Int)

whereas just asking for the type of the expression gives the correct result, namely Ord a => [a] -> (a, Int). I'm using ghc 7.0.3.

Answer 1

See the extended defaulting rules used in GHCi for an explanation of where the () is coming from.

As for why the defaulting occurs in this case, compare the following:

> let f x = maximum &&& id >>> fst &&& (\(m,l) -> length $ filter (==m) l) $ x
> :t f
f :: (Ord a) => [a] -> (a, Int)

I assume this has something to do with bindings being monomorphic, but I'm not certain of the details.