module Main where

nand :: Bool -> Bool -> Bool
nand True True = False
nand _ _ = True

not :: Bool -> Bool
not x = Main.nand x x

and :: Bool -> Bool -> Bool
and x y = Main.not $ Main.nand x y

or :: Bool -> Bool -> Bool
or x y = Main.nand (Main.not x) (Main.not y)

nor :: Bool -> Bool -> Bool
nor x y = Main.not $ Main.or x y

xor :: Bool -> Bool -> Bool
xor x y = Main.or (Main.and x $ Main.not y) (Main.and y $ Main.not x)

add [Bool] -> [Bool] -> [Bool]
add [] x = x
add x [] = x
add x [False] = x
add [False] x = x
add [True] [True] = [True, False]

main = do
    print $ Main.nor True True
    print $ Main.nor False True
    print $ Main.nor True False
    print $ Main.nor False False