-- # Software Tools for Discrete Mathematics
module Stdm06LogicOperators where

-- ∨ Disjunction / or defined for symbolic convenience.
infix 3 \/

(\/) :: Bool -> Bool -> Bool
(\/) = (||)

-- ∧ Conjunction / and defined for symbolic convenience.
infix 4 /\

(/\) :: Bool -> Bool -> Bool
(/\) = (&&)

-- ↔ Equivalence / If and only if
infix 1 <=>

-- |
-- >>> True <=> True
-- True

-- |
-- >>> True <=> False
-- False

-- |
-- >>> False <=> False
-- True

-- |
-- >>> False <=> True
-- False
(<=>) :: Bool -> Bool -> Bool
(<=>) a b = a == b

-- → Implication / Therefore / if
infix 2 ==>

-- |
-- >>> False ==> False
-- True

-- |
-- >>> False ==> True
-- True

-- |
-- >>> True ==> False
-- False

-- |
-- >>> True ==> True
-- True
(==>) :: Bool -> Bool -> Bool
(==>) True False = False
(==>) _ _ = True

-- Exclusive or
infixr 2 <+>

-- |
-- >>> False <+> False
-- False

-- |
-- >>> False <+> True
-- True

-- |
-- >>> True <+> False
-- True

-- |
-- >>> True <+> True
-- False
(<+>) :: Bool -> Bool -> Bool
x <+> y = x /= y