-- Task: compute all arithmetic expressions containing exactly -- the numbers 2,3,6,8 having the value 24 perm :: [Int] -> [Int] perm [] = [] perm (x:xs) | perm xs == us ++ vs = us ++ [x] ++ vs where us,vs free -- Representation of arithmetic expressions: data Exp = Num Int -- a number | Add Exp Exp | Sub Exp Exp | Mul Exp Exp | Div Exp Exp deriving Show -- Evaluate some arithmetic expression to a value if -- this arithmetic expression contains a given list of numbers test :: Exp -> [Int] -> Int --test (Num y) [z] | y == z = y test (Num x) [x] = x test (Add e1 e2) zs | split u v zs = test e1 u + test e2 v where u,v free test (Sub e1 e2) zs | split u v zs = test e1 u - test e2 v where u,v free test (Mul e1 e2) zs | split u v zs = test e1 u * test e2 v where u,v free test (Div e1 e2) zs | split u v zs = opdiv (test e1 u) (test e2 v) where u,v free opdiv a b = if b == 0 || a `mod` b /= 0 then failed else a `div` b -- Split is satisfied if the two first non-empty(!) lists concatenates -- to the third list. split :: [Int] -> [Int] -> [Int] -> Bool split (u:us) (v:vs) xs | (u:us) ++ (v:vs) == xs = True -- The main expression to compute all solutions to the puzzle: -- > solve \$ test e (perm [2,3,6,8]) == 24 where e free