Control.ForFree

Contents

• Plus
• Yoneda
• CoYoneda
• Free monad
• Free comonad
• Codensity monad
• Density comonad
• Monads from comonads
• Codensity ask monad
• Density ask comonad
• Miscellaneous
• Instances of types from other modules

Synopsis

• class Plus f where
  • zero :: f x
  • plus :: f x -> f x -> f x
• newtype OpT f a b = OpT {
  • getOpT :: f b -> a
  }
• newtype Yoneda f x = Yoneda {
  • runYoneda :: forall z. (x -> z) -> f z
  }
• unreduceYoneda :: Functor w => (forall z. w z -> f z) -> w x -> Yoneda f x
• data CoYoneda f x = forall z . CoYoneda (z -> x) (f z)
• reduceCoYoneda :: Functor m => (forall z. f z -> m z) -> CoYoneda f x -> m x
• data Free f x
  • = Pure x
  • | Free (f (Free f x))
• reduceFree :: Monad m => (forall z. f z -> m z) -> Free f x -> m x
• affectFree :: Functor g => (forall z. (s, f z) -> g (s, z)) -> (s, Free f x) -> Free g (s, x)
• newtype FreeT f m r = FreeT {
  • runFreeT :: m (Either r (f (FreeT f m r)))
  }
• reduceFreeT :: Monad m => (forall z. f z -> m z) -> FreeT f m x -> m x
• data Cofree f x = x :< (f (Cofree f x))
• unreduceCofree :: Comonad w => (forall z. w z -> f z) -> w x -> Cofree f x
• affectCofree :: Functor g => (forall z. (s, f z) -> g (s, z)) -> (s, Cofree f x) -> Cofree g (s, x)
• data CofreeT f w x = CofreeT (w x) (f (CofreeT f w x))
• unreduceCofreeT :: Comonad w => (forall z. w z -> f z) -> w x -> CofreeT f w x
• newtype Codensity f x = Codensity {
  • runCodensity :: forall z. (x -> f z) -> f z
  }
• lowerCodensity :: Applicative f => Codensity f x -> f x
• data Density f x = forall z . Density (f z -> x) (f z)
• liftDensity :: Comonad w => w a -> Density w a
• newtype CoT w m a = CoT {
  • runCoT :: forall r. w (a -> m r) -> m r
  }
• type Co w = CoT w Identity
• runCo :: Functor w => Co w a -> w (a -> r) -> r
• liftCoT0 :: Comonad w => (forall a. w a -> s) -> CoT w m s
• lowerCoT0 :: (Functor w, Applicative m) => CoT w m s -> w a -> m s
• lowerCo0 :: Functor w => Co w s -> w a -> s
• liftCoT1 :: (forall a. w a -> a) -> CoT w m ()
• lowerCoT1 :: (Functor w, Applicative m) => CoT w m z -> w a -> m a
• lowerCo1 :: Functor w => Co w z -> w a -> a
• newtype CodensityAsk w x = CodensityAsk {
  • runCodensityAsk :: forall z. w z -> (x -> z) -> z
  }
• peekCodensityAsk :: w x -> CodensityAsk w x -> x
• newtype CodensityAskT w m x = CodensityAskT {
  • runCodensityAskT :: forall z. w (m z) -> (x -> m z) -> m z
  }
• peekCodensityAskT :: Applicative m => w (m x) -> CodensityAskT w m x -> m x
• lowerCodensityAskT :: (Plus w, Applicative m) => CodensityAskT w m x -> m x
• catchCodensityAsk :: w (CodensityAsk w x) -> CodensityAsk w x -> CodensityAsk w x
• catchCodensityAskT :: (Functor w, Monad m) => w (CodensityAskT w m x) -> CodensityAskT w m x -> CodensityAskT w m x
• data DensityAskT p f x = forall z . DensityAskT (p z -> f z -> x) (f z)
• type DensityAsk p = DensityAskT p Identity
• liftDensityAsk :: Comonad w => w x -> DensityAskT p w x
• data Finalize x = Finalize
• data Initialize x
• data Decompose where
  • Decompose :: y z -> Decompose x y (x z)
• data Recompose where
  • Recompose :: forall w x y z. w x y (x z) -> Recompose w y z
• newtype Op a b = Op {
  • getOp :: b -> a
  }
• newtype Endo a = Endo {
  • appEndo :: a -> a
  }
• newtype Const a b = Const {
  • getConst :: a
  }

Plus

Yoneda

CoYoneda

Free monad

Free comonad

Codensity monad

Density comonad

Monads from comonads

Codensity ask monad

Density ask comonad

Miscellaneous

Instances of types from other modules