Typeclass representing functions

Question

Forgive me if this is a dumb question, but is there a typeclass that represents all functions? Like, lets say I have a type like this

data Foo a = Thing a 

instance (Show a) => Show (Foo a) where
    show (Thing a) = show a

And I want to display Thing (\x -> 1). Maybe do some sort o reflection on the method to pretty print some metadata about this?

Trying it I get the following error

> Thing (\x -> 1)

<interactive>:113:1:
    No instance for (Show (t0 -> a0)) arising from a use of `print'
    Possible fix: add an instance declaration for (Show (t0 -> a0))
    In a stmt of an interactive GHCi command: print it

<interactive>:113:14:
    No instance for (Num a0) arising from the literal `1'
    The type variable `a0' is ambiguous
    Possible fix: add a type signature that fixes these type variable(s)
    Note: there are several potential instances:
      instance Num Double -- Defined in `GHC.Float'
      instance Num Float -- Defined in `GHC.Float'
      instance Integral a => Num (GHC.Real.Ratio a)
        -- Defined in `GHC.Real'
      ...plus 11 others
    In the expression: 1
    In the first argument of `Thing', namely `(\ x -> 1)'
    In the expression: Thing (\ x -> 1)

Which makes sense, since there is no instance of show for t0 -> a0 but I am not sure how to describe an instance of this typeclass?

This isn't for anything production, I am just messing around with Haskell and curious what I can and can't do.

Answer 1

Since your goal is just to have fun, you might like Data.Universe.Instances.Show. For a more serious goal, though, you may want to wait until there's been some progress on the Cloud Haskell project, which aims in part to have a way to serialize and deserialize functions so that they can be migrated across machines.