module XOR where

-- Both + and * are associative operators with identity elements for Integer, so
-- which one should we use to make Integer an instance of Semigroup and
-- Monoid?
--
-- Both && and || are associative operators with identity elements for Bool, so
-- which one should we use to make Bool an instance of Semigroup and Monoid?
--
-- The Haskell community decided to do none of the above, but instead use
-- wrapper types.  You will do something similar in this lab.
--
-- Logical-xor is also an associative operator for Bool.  We won't make Bool an
-- instance of Semigroup and Monoid directly.  We define this type wrapping
-- Bool:

data BoolX = MkBoolX Bool deriving (Eq, Show)

-- Make BoolX an instance of Semigroup and Monoid.  The <> operator should do
-- logical xor.  mempty should be the corresponding identity element.

instance Semigroup BoolX where
    -- Reminder: (<>) :: BoolX -> BoolX -> BoolX


instance Monoid BoolX where
    -- Reminder: mempty :: BoolX



-- In Data.Semigroup, you can find similar wrapper types:
-- All wraps Bool and makes <> do logical-and
-- Any wraps Bool and makes <> do logical-or
-- Sum wraps a Num instance and makes <> do addition
-- Product wraps a Num instance and makes <> do multiplication