Why does Text.Show.Functions only return <function>?

Question

The standard package to show functions only returns a constant string:

λ> :m +Text.Show.Functions 
λ> show (+1)
"<function>"

GHCi's :type command is much more useful:

λ> :t (+1)
(+1) :: Num a => a -> a

Is it impossible to get such a level of detail at runtime? Does the compilation process leave any kind of information at all about functions, except for them being functions?

Answer 1

Not exactly the same level of details, but you can use typeOf from Data.Typeable:

Prelude> import Data.Typeable
Prelude Data.Typeable> typeOf (+1)
Integer -> Integer