-- The game of 24
-- Mon Apr 15 7:57:46 CST 2019

-- https://en.wikipedia.org/wiki/24_Game
-- https://www.coolmathgames.com/0-make-24
-- https://www.4nums.com/

data Op = Add | Mul | Sub | Div
data Exp = Num Int | Bin Op Exp Exp

dispatch Add = (+)
dispatch Mul = (*)
dispatch Sub = (-)
dispatch Div = \x y -> if y == 0 || x `mod` y /= 0 then failed else x `div` y

permute [] = []
permute (y++[x]++z) = x : permute (y++z)

test (Num y) [y] = y
test (Bin op x y) (u@(_:_)++v@(_:_)) = (dispatch op) (test x u) (test y v)

main | test X (permute problem) == 24 = X where X free

problem = [2,3,8,6]