[Haskell-cafe] lists with mixed types

If I define something like this: data Bar = Bi Int | Bf String deriving Show data Foo = Fi Int | Fs Float deriving Show func::Foo -> Bar func (Fi xx) = Bi xx func (Fs ff) = Bf (show ff) I can do:

map func [(Fi 1), (Fs 2.0)] [Bi 1,Bf "2.0"]

but what i really want to do is just do map func [1, 2.0] [1, "2.0"] I understand that this is impossible in haskell, but why cant the compiler generate the Foo and Bar data types for me and just require that i have a func defined for Int -> Int and Float -> String?