[Haskell-beginners] lambda notation vs function-argument notation in GHCi

[Morel Pisum]

Let's define a function in GHCi:

> Prelude> let f s n = and (map (==s) n)
> Prelude> :t f
> f :: Eq a => a -> [a] -> Bool

This is fine. But when I define this function using lambda notation, I
get this

> Prelude> let f = \s n -> and (map (==s) n)
> Prelude> :t f
> f :: () -> [()] -> Bool

which is really weird.

Why does this happen?