Check whether a type is an instance of Show in Haskell?

Question

Suppose I have a simple data type in Haskell for storing a value:

data V a = V a

I want to make V an instance of Show, regardless of a\'s t

Answer 1

As I said in a comment, the runtime objects allocated in memory don't have type tags in a Haskell program. There is therefore no universal instanceof operation like in, say, Java.

It's also important to consider the implications of the following. In Haskell, to a first approximation (i.e., ignoring some fancy stuff that beginners shouldn't tackle too soon), all runtime function calls are monomorphic. I.e., the compiler knows, directly or indirectly, the monomorphic (non-generic) type of every function call in an executable program. Even though your V type's show function has a generic type:

-- Specialized to `V a`
show :: V a -> String  -- generic; has variable `a`

...you can't actually write a program that calls the function at runtime without, directly or indirectly, telling the compiler exactly what type a will be in every single call. So for example:

-- Here you tell it directly that `a := Int`
example1 = show (V (1 :: Int)) 

-- Here you're not saying which type `a` is, but this just "puts off" 
-- the decision—for `example2` to be called, *something* in the call
-- graph will have to pick a monomorphic type for `a`.
example2 :: a -> String
example2 x = show (V x) ++ example1

Seen in this light, hopefully you can spot the problem with what you're asking:

instance Show (V a) where
    show (V a) = if a instanceof Show
                   then show a
                   else "Some Error."

Basically, since the type for the a parameter will be known at compilation time for any actual call to your show function, there's no point to testing for this type at runtime—you can test for it at compilation time! Once you grasp this, you're led to Will Sewell's suggestion:

-- No call to `show (V x)` will compile unless `x` is of a `Show` type.
instance Show a => Show (V a) where ...

---

EDIT: A more constructive answer perhaps might be this: your V type needs to be a tagged union of multiple cases. This does require using the GADTs extension:

{-# LANGUAGE GADTs #-}

-- This definition requires `GADTs`.  It has two constructors:
data V a where
  -- The `Showable` constructor can only be used with `Show` types.
  Showable   :: Show a => a -> V a
  -- The `Unshowable` constructor can be used with any type.
  Unshowable :: a -> V a

instance Show (V a) where
  show (Showable a) = show a
  show (Unshowable a) = "Some Error."

But this isn't a runtime check of whether a type is a Show instance—your code is responsible for knowing at compilation time where the Showable constructor is to be used.