Transitive comparisons

infixl 4 ==., <., <=., >., >=., /=.
infixl 4 .==., .<., .<=., .>., .>=., ./=.
infixl 4 .==, .<, .<=, .>, .>=, ./=

data ACompResult a = TrueCond a | FalseCond

(==.) :: Eq a => a -> a -> ACompResult a
(<.) :: Ord a => a -> a -> ACompResult a
(<=.) :: Ord a => a -> a -> ACompResult a
(>.) :: Ord a => a -> a -> ACompResult a
(>=.) :: Ord a => a -> a -> ACompResult a
(/=.) :: Eq a => a -> a -> ACompResult a
makeFirstComparison :: (a -> a -> Bool) -> a -> a -> ACompResult a

makeFirstComparison f x y =
    if f x y
        then TrueCond y  -- Comparison successful, carry the right argument on
        else FalseCond   -- Comparison failed
(==.) = makeFirstComparison (==)
(<.) = makeFirstComparison (<)
(<=.) = makeFirstComparison (<=)
(>.) = makeFirstComparison (>)
(>=.) = makeFirstComparison (>=)
(/=.) = makeFirstComparison (/=)

(.==.) :: Eq a => ACompResult a -> a -> ACompResult a
(.<.) :: Ord a => ACompResult a -> a -> ACompResult a
(.<=.) :: Ord a => ACompResult a -> a -> ACompResult a
(.>.) :: Ord a => ACompResult a -> a -> ACompResult a
(.>=.) :: Ord a => ACompResult a -> a -> ACompResult a
(./=.) :: Eq a => ACompResult a -> a -> ACompResult a
makeMiddleComparison :: (a -> a -> Bool) -> ACompResult a -> a -> ACompResult a

makeMiddleComparison _ FalseCond _ = FalseCond  -- Previous failure
makeMiddleComparison f (TrueCond x) y =
    if f x y
        then TrueCond y  -- Comparison successful, carry the right argument on
        else FalseCond   -- Comparison failed
(.==.) = makeMiddleComparison (==)
(.<.) = makeMiddleComparison (<)
(.<=.) = makeMiddleComparison (<=)
(.>.) = makeMiddleComparison (>)
(.>=.) = makeMiddleComparison (>=)
(./=.) = makeMiddleComparison (/=)

(.==) :: Eq a => ACompResult a -> a -> Bool
(.<) :: Ord a => ACompResult a -> a -> Bool
(.<=) :: Ord a => ACompResult a -> a -> Bool
(.>) :: Ord a => ACompResult a -> a -> Bool
(.>=) :: Ord a => ACompResult a -> a -> Bool
(./=) :: Eq a => ACompResult a -> a -> Bool
makeLastComparison :: (a -> a -> Bool) -> ACompResult a -> a -> Bool

makeLastComparison _ FalseCond _ = False  -- Previous failure
makeLastComparison f (TrueCond x) y = f x y
(.==) = makeLastComparison (==)
(.<) = makeLastComparison (<)
(.<=) = makeLastComparison (<=)
(.>) = makeLastComparison (>)
(.>=) = makeLastComparison (>=)
(./=) = makeLastComparison (/=)

-- Example:
-- Haskell> 1 <. 3 .==. 3 .< 6
-- True