op2str :: Op -> String
op2str Plus = " + "
op2str Minus = " - "
op2str Mul = " * "
op2str Div = " / "
op2str Pow = " ^ "

prettyShow :: (Show a, Num a) => SymbolicManip a -> String
prettyShow = fst . prettyShow'

prettyShow' :: (Show a, Num a) => SymbolicManip a -> (String, Maybe Op)
prettyShow' (Number x) = (show x, Nothing)
prettyShow' (Symbol x) = (x, Nothing)
prettyShow' (UnaryArith op2str a) = (op2str ++ "(" ++ show a ++ ")", Nothing)
prettyShow' (BinaryArith op a b) =
  let (ra, mopa) = prettyShow' a
      (rb, mopb) = prettyShow' b
      opa = maybe op id mopa
      opb = maybe op id mopb
      pop = op2str op
  in  if opa == op && opb == op then (ra ++ pop ++ rb, Just op)
      else if opa == op && opb /= op then (ra ++ pop ++ "(" ++ rb ++ ")", Just op)
      else if opa /= op && opb == op then ("(" ++ ra ++ ")" ++ pop ++ rb, Just op)
      else ("(" ++ ra ++ ")" ++ pop ++ "(" ++ rb ++ ")", Just op)