Lunchtime experiment with booleans

bools.purs

-- booleans as a partition on a set
type Bool a = a -> Either a a

true' :: forall a. Bool a
true' = Right

false' :: forall a. Bool a
false' = Left

not' :: forall a. Bool a -> Bool a
not' b = \a -> case b a of
  Left a  -> Right a 
  Right a -> Left a

(||) :: forall a b. Bool a -> Bool b -> Bool (Tuple a b)
(||) l r = \(Tuple a b) -> case (Tuple (l a) (r b)) of
  Tuple (Right a) (Right b) -> Right (Tuple a b)
  Tuple (Left a)  (Right b) -> Right (Tuple a b)
  Tuple (Right a) (Left b)  -> Right (Tuple a b)
  Tuple (Left a)  (Left b)  -> Left (Tuple a b)

(&&) :: forall a b. Bool a -> Bool b -> Bool (Tuple a b)
(&&) l r = \(Tuple a b) -> case (Tuple (l a) (r b)) of
  Tuple (Right a) (Right b) -> Right (Tuple a b)
  Tuple (Left a)  (Right b) -> Left (Tuple a b)
  Tuple (Right a) (Left b)  -> Left (Tuple a b)
  Tuple (Left a)  (Left b)  -> Left (Tuple a b)

if' :: forall a b. Bool a -> b -> b -> a -> b
if' p t f a = case p a of
  Left a -> f
  Right a -> t

Lol. That's me, perpetually reinventing ancient findings in computer science... since 1990 or so.