null created by marnix - https://repl.it/HQio/11

HQio-11.hs

-- first let's get the type signatures out of the way

band :: Integer -> Integer -> Integer
bor :: Integer -> Integer -> Integer
bnot :: Integer -> Integer


-- now a special case, to terminate the recursion for 'band';
-- this follows directly from the general definition below
a `band` b  | a == a `div` 2 && b == b `div` 2  = - ((a `mod` 2) * (b `mod` 2))


-- the definitions

a `band` b = ((a `div` 2) `band` (b `div` 2)) * 2 + ((a `mod` 2) * (b `mod` 2))

a `bor` b = a + b - (a `band` b)

-- An alternative definition of 'bor' using DeMorgan is the following:
-- @
--  a `bor` b = bnot (bnot a `band` bnot b)
-- @

bnot a = (-a) - 1