Is it possible to emulate a function using your own data type?

Is it possible to emulate a function with your own data type with some GHC extension? What I want to do is e.g.

(imaginary syntax)

data MyFunc = MyFunc String (Int->Int)

instance (Int->Int) MyFunc where
    ($) (MyFunc _ f) i = f i

inc = MyFunc "increment" (1+)

test = inc 1

I.e. data that carries some meta-information with it and can be pattern matched, but which can still be called like a regular function. Now, I know that I could define my own infix operator like $$ and call inc $$ 1, but being able to use the regular function call syntax would be very useful in embedded DSLs.