Control.Comonad

Contents

• Comonads
• Cokleisli Arrows
  • Cokleisli composition

Description

Synopsis

• class Functor w => Comonad w where
  • extract :: w a -> a
  • duplicate :: w a -> w (w a)
  • extend :: (w a -> b) -> w a -> w b
• (=>>) :: Comonad w => w a -> (w a -> b) -> w b
• (<<=) :: Comonad w => (w a -> b) -> w a -> w b
• liftW :: Comonad w => (a -> b) -> w a -> w b
• wfix :: Comonad w => w (w a -> a) -> a
• newtype Cokleisli w a b = Cokleisli {
  • runCokleisli :: w a -> b
  }
• (=>=) :: Comonad w => (w a -> b) -> (w b -> c) -> w a -> c
• (=<=) :: Comonad w => (w b -> c) -> (w a -> b) -> w a -> c

Comonads

 extract . fmap f = f . extract

 duplicate = extend id
 fmap (fmap f) . duplicate = duplicate . fmap f

 extend f  = fmap f . duplicate

 fmap f    = extend (f . extract)

Cokleisli Arrows

Cokleisli composition