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

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?