Data.Functor.Foldable

Contents

• Base functors for fixed points
• Fixed points
• Folding
  • Combinators
  • Distributive laws
• Unfolding
  • Combinators
  • Distributive laws
• Refolding
  • Changing representation
• Common names
• Mendler-style
• Elgot (co)algebras
• Zygohistomorphic prepromorphisms

Description

Synopsis

• type family Base t :: * -> *
• newtype Fix f = Fix (f (Fix f))
• newtype Mu f = Mu (forall a. (f a -> a) -> a)
• data Nu f where
  • Nu :: (a -> f a) -> a -> Nu f
• data family Prim t :: * -> *
• class Functor (Base t) => Foldable t where
  • project :: t -> Base t t
  • cata :: (Base t a -> a) -> t -> a
  • para :: (Base t (t, a) -> a) -> t -> a
  • gpara :: (Unfoldable t, Comonad w) => (forall b. Base t (w b) -> w (Base t b)) -> (Base t (EnvT t w a) -> a) -> t -> a
  • prepro :: Unfoldable t => (forall b. Base t b -> Base t b) -> (Base t a -> a) -> t -> a
  • gprepro :: (Unfoldable t, Comonad w) => (forall b. Base t (w b) -> w (Base t b)) -> (forall c. Base t c -> Base t c) -> (Base t (w a) -> a) -> t -> a
• gapo :: Unfoldable t => (b -> Base t b) -> (a -> Base t (Either b a)) -> a -> t
• gcata :: (Foldable t, Comonad w) => (forall b. Base t (w b) -> w (Base t b)) -> (Base t (w a) -> a) -> t -> a
• zygo :: Foldable t => (Base t b -> b) -> (Base t (b, a) -> a) -> t -> a
• gzygo :: (Foldable t, Comonad w) => (Base t b -> b) -> (forall c. Base t (w c) -> w (Base t c)) -> (Base t (EnvT b w a) -> a) -> t -> a
• histo :: Foldable t => (Base t (Cofree (Base t) a) -> a) -> t -> a
• ghisto :: (Foldable t, Functor h) => (forall b. Base t (h b) -> h (Base t b)) -> (Base t (Cofree h a) -> a) -> t -> a
• futu :: Unfoldable t => (a -> Base t (Free (Base t) a)) -> a -> t
• distCata :: Functor f => f (Identity a) -> Identity (f a)
• distPara :: Unfoldable t => Base t (t, a) -> (t, Base t a)
• distParaT :: (Unfoldable t, Comonad w) => (forall b. Base t (w b) -> w (Base t b)) -> Base t (EnvT t w a) -> EnvT t w (Base t a)
• distZygo :: Functor f => (f b -> b) -> f (b, a) -> (b, f a)
• distZygoT :: (Functor f, Comonad w) => (f b -> b) -> (forall c. f (w c) -> w (f c)) -> f (EnvT b w a) -> EnvT b w (f a)
• distHisto :: Functor f => f (Cofree f a) -> Cofree f (f a)
• distGHisto :: (Functor f, Functor h) => (forall b. f (h b) -> h (f b)) -> f (Cofree h a) -> Cofree h (f a)
• distFutu :: Functor f => Free f (f a) -> f (Free f a)
• distGFutu :: (Functor f, Functor h) => (forall b. h (f b) -> f (h b)) -> Free h (f a) -> f (Free h a)
• class Functor (Base t) => Unfoldable t where
  • embed :: Base t t -> t
  • ana :: (a -> Base t a) -> a -> t
  • apo :: Foldable t => (a -> Base t (Either t a)) -> a -> t
  • postpro :: Foldable t => (forall b. Base t b -> Base t b) -> (a -> Base t a) -> a -> t
  • gpostpro :: (Foldable t, Monad m) => (forall b. m (Base t b) -> Base t (m b)) -> (forall c. Base t c -> Base t c) -> (a -> Base t (m a)) -> a -> t
• gana :: (Unfoldable t, Monad m) => (forall b. m (Base t b) -> Base t (m b)) -> (a -> Base t (m a)) -> a -> t
• distAna :: Functor f => Identity (f a) -> f (Identity a)
• distApo :: Foldable t => Either t (Base t a) -> Base t (Either t a)
• distGApo :: Functor f => (b -> f b) -> Either b (f a) -> f (Either b a)
• hylo :: Functor f => (f b -> b) -> (a -> f a) -> a -> b
• ghylo :: (Comonad w, Functor f, Monad m) => (forall c. f (w c) -> w (f c)) -> (forall d. m (f d) -> f (m d)) -> (f (w b) -> b) -> (a -> f (m a)) -> a -> b
• refix :: (Foldable s, Unfoldable t, Base s ~ Base t) => s -> t
• fold :: Foldable t => (Base t a -> a) -> t -> a
• gfold :: (Foldable t, Comonad w) => (forall b. Base t (w b) -> w (Base t b)) -> (Base t (w a) -> a) -> t -> a
• unfold :: Unfoldable t => (a -> Base t a) -> a -> t
• gunfold :: (Unfoldable t, Monad m) => (forall b. m (Base t b) -> Base t (m b)) -> (a -> Base t (m a)) -> a -> t
• refold :: Functor f => (f b -> b) -> (a -> f a) -> a -> b
• grefold :: (Comonad w, Functor f, Monad m) => (forall c. f (w c) -> w (f c)) -> (forall d. m (f d) -> f (m d)) -> (f (w b) -> b) -> (a -> f (m a)) -> a -> b
• mcata :: (forall y. (y -> c) -> f y -> c) -> Fix f -> c
• mhisto :: (forall y. (y -> c) -> (y -> f y) -> f y -> c) -> Fix f -> c
• elgot :: Functor f => (f a -> a) -> (b -> Either a (f b)) -> b -> a
• coelgot :: Functor f => ((a, f b) -> b) -> (a -> f a) -> a -> b
• zygoHistoPrepro :: (Unfoldable t, Foldable t) => (Base t b -> b) -> (forall c. Base t c -> Base t c) -> (Base t (EnvT b (Cofree (Base t)) a) -> a) -> t -> a

Base functors for fixed points

Fixed points

Folding

Combinators

Distributive laws

Unfolding

Combinators

Distributive laws

Refolding

Changing representation

Common names

Mendler-style

Elgot (co)algebras

Zygohistomorphic prepromorphisms