Data.Profunctor

Profunctor.hs

-- Source: https://hackage.haskell.org/package/profunctors-5.4/docs/Data-Profunctor.html

class Profunctor p where
  -- dimap | lmap, rmap
  dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
  lmap :: (a -> b) -> p b c -> p a c
  rmap :: (b -> c) -> p a b -> p a c
  
class Profunctor p => Strong p where
  -- first' | second'
  first'  :: p a b -> p (a, c) (b, c)
  second' :: p a b -> p (c, a) (c, b)
  
class Profunctor p => Choice p where
  -- left' | right'
  left' :: p a b -> p (Either a c) (Either b c)
  righ' :: p a b -> p (Either c a) (Either c b) 
  
class Profunctor p => Closed p where
  closed :: p a b -> p (x -> a) (x -> b)
  
class (Traversing p, Closed p) => Mapping p where
  map' :: Functor f => p a b -> p (f a) (f b)
  roam :: (forall f. (Distributive f, Applicative f) => (a -> f b) -> s -> f t) -> p a b -> p s t 
  
class Profunctor p => Costrong p where
  -- unfirst | unsecond
  unfirst :: p (a, d) (b, d) -> p a b 
  unsecond :: p (d, a) (d, b) -> p a b 
  
class Profunctor p => Cochoice p where 
  -- unleft | unright
  unleft :: p (Either a d) (Either b d) -> p a b 
  unright :: p (Either d a) (Either d b) -> p a b 
  
-- ### Common Profunctors

-- Lift a Functor into a Profunctor (forwards)
newtype Start f d c = Start { runStart :: d -> f c }

-- Lift a Functor into a Profunctor (backwards)
newtype Costart f d c = Costart { runStart :: f d -> c }

-- Wrap an arrow for use as a Profunctor
newtype WrappedArrow p a b = WrapArrow { unwrapArrow :: p a b }

-- Const for arrows
newtype Forget r a b = Forget { runForget :: a -> r }