Eq3Expr.hs

-- http://math.stackexchange.com/questions/307201/how-to-verify-if-three-numbers-are-equal-using-logical-operators-with-a-restric?rq=1

module Eq3Expr where

data Bit = Zero | One deriving (Eq, Show)

type Operator = Bit -> Bit -> Bit

notB :: Bit -> Bit
notB Zero = One
notB One  = Zero

andB :: Operator
andB One One = One
andB _   _   = Zero

orB :: Operator
orB Zero Zero = Zero
orB _    _    = One

xorB :: Operator
xorB Zero One  = One
xorB One  Zero = One
xorB _    _    = Zero

operators :: [Operator]
operators = ops ++ map (\o a b -> notB (o a b)) ops
  where ops = [andB, orB, xorB]

test :: Operator -> Operator -> Bool
test op1 op2 = all id $ do
  a <- [Zero, One]
  b <- [Zero, One]
  c <- [Zero, One]
  let allEqual = a == b && b == c
  let expected = if allEqual then One else Zero
  return $ (a `op1` b) `op2` c == expected

main :: IO ()
main = print $ do
  op1 <- operators
  op2 <- operators
  return $ test op1 op2