How can I have Show display the name of a function?

Question

As a simple exercise to get me acquainted with Haskell, after idling around on Youtube and stumbling into the American Countdown game show, I wanted to make a solver for the Numbers game.

You get 6 numbers and need to combine them with (+) (-) (*) (/) in order to get a given result.

What I've got so far is the very brain-dead,

let operands = [75, 2, 6, 3, 8, 7] :: [Double]
let goal = 623 :: Double
let operations = [(+), (-), (*), (/)]

show (head [(a, x, b, y, c, z, d, t, e) |
      a <- operands,
      b <- filter (\ q -> q /= a) operands,
      c <- filter (\ q -> q /= a && q /= b) operands,
      d <- filter (\ q -> q /= a && q /= b && q /= c) operands,
      e <- filter (\ q -> q /= a && q /= b && q /= c && q /= d) operands,
      x <- operations,
      y <- operations,
      z <- operations,
      t <- operations,
      t (z (y (x a b) c) d) e == goal])

...but obviously Show doesn't know what to do with functions.

No instance for (Show (Double -> Double -> Double))
  arising from a use of `show'
Possible fix:
  add an instance declaration for (Show (Double -> Double -> Double))

How can I work around this? Do I need to mess with type and data constructors to make my own functions that can print or is there some easier way around it?

Answer 1

Another option:

data Operation = Add | Subtract | Multiply | Divide deriving (Show)

apply :: Operation -> Double -> Double -> Double
apply Add      = (+)
apply Subtract = (-)
apply Multiply = (*)
apply Divide   = (/)