How to hide helper functions when implementing `instance`

Question

I have data RegEx and I want to implement instance Show a => Show RegEx a. Here's my code:

showAtom :: Show a => RegEx a -> String
showAtom (Lit x) = show x
showAtom r       = "(" ++ (show r) ++ ")"

instance Show a => Show (RegEx a) where
    show (Lit x)   = show [x]
    show (Opt r)   = (showAtom r) ++ "?"
    show (Alt p q) = (showAtom p) ++ "|" ++ (showAtom q)
    show (Seq p q) = (show p) ++ (show q)
    show (Rep r)   = (showAtom r) ++ "*"

The showAtom function is just an implementation detail. Is there any way for me to hide it, such that it is visible only withing the instance definition? Or better yet, make it visible only within show.

Answer 1

Something like this should work:

instance Show a => Show (RegEx a) where
    show x = show' x
      where
        showAtom :: Show a => RegEx a -> String
        showAtom (Lit x) = show x
        showAtom r       = "(" ++ (show r) ++ ")"

        show' (Lit x)   = show [x]
        show' (Opt r)   = (showAtom r) ++ "?"
        show' (Alt p q) = (showAtom p) ++ "|" ++ (showAtom q)
        show' (Seq p q) = (show p) ++ (show q)
        show' (Rep r)   = (showAtom r) ++ "*"

Alternatively, you can just exclude showAtom from the module's export list.