Copyright	(C) 2011-2016 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Distributive

Description

Synopsis

class Functor g => Distributive g where
- distribute :: Functor f => f (g a) -> g (f a)
- collect :: Functor f => (a -> g b) -> f a -> g (f b)
- distributeM :: Monad m => m (g a) -> g (m a)
- collectM :: Monad m => (a -> g b) -> m a -> g (m b)
cotraverse :: (Distributive g, Functor f) => (f a -> b) -> f (g a) -> g b
comapM :: (Distributive g, Monad m) => (m a -> b) -> m (g a) -> g b

Documentation

class Functor g => Distributive g where #

This is the categorical dual of Traversable.

Due to the lack of non-trivial comonoids in Haskell, we can restrict ourselves to requiring a Functor rather than some Coapplicative class. Categorically every Distributive functor is actually a right adjoint, and so it must be Representable endofunctor and preserve all limits. This is a fancy way of saying it is isomorphic to (->) x for some x.

To be distributable a container will need to have a way to consistently zip a potentially infinite number of copies of itself. This effectively means that the holes in all values of that type, must have the same cardinality, fixed sized vectors, infinite streams, functions, etc. and no extra information to try to merge together.

Minimal complete definition

distribute | collect

Methods

distribute :: Functor f => f (g a) -> g (f a) #

The dual of sequenceA

>>> distribute [(+1),(+2)] 1
[2,3]

distribute = collect id
distribute . distribute = id

collect :: Functor f => (a -> g b) -> f a -> g (f b) #

collect f = distribute . fmap f
fmap f = runIdentity . collect (Identity . f)
fmap distribute . collect f = getCompose . collect (Compose . f)

distributeM :: Monad m => m (g a) -> g (m a) #

The dual of sequence

distributeM = fmap unwrapMonad . distribute . WrapMonad

collectM :: Monad m => (a -> g b) -> m a -> g (m b) #

collectM = distributeM . liftM f

Instances

Instances details

Distributive Par1 #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Par1 a) -> Par1 (f a) # collect :: Functor f => (a -> Par1 b) -> f a -> Par1 (f b) # distributeM :: Monad m => m (Par1 a) -> Par1 (m a) # collectM :: Monad m => (a -> Par1 b) -> m a -> Par1 (m b) #
Distributive Complex #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Complex a) -> Complex (f a) # collect :: Functor f => (a -> Complex b) -> f a -> Complex (f b) # distributeM :: Monad m => m (Complex a) -> Complex (m a) # collectM :: Monad m => (a -> Complex b) -> m a -> Complex (m b) #
Distributive Min #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Min a) -> Min (f a) # collect :: Functor f => (a -> Min b) -> f a -> Min (f b) # distributeM :: Monad m => m (Min a) -> Min (m a) # collectM :: Monad m => (a -> Min b) -> m a -> Min (m b) #
Distributive Max #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Max a) -> Max (f a) # collect :: Functor f => (a -> Max b) -> f a -> Max (f b) # distributeM :: Monad m => m (Max a) -> Max (m a) # collectM :: Monad m => (a -> Max b) -> m a -> Max (m b) #
Distributive First #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (First a) -> First (f a) # collect :: Functor f => (a -> First b) -> f a -> First (f b) # distributeM :: Monad m => m (First a) -> First (m a) # collectM :: Monad m => (a -> First b) -> m a -> First (m b) #
Distributive Last #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Last a) -> Last (f a) # collect :: Functor f => (a -> Last b) -> f a -> Last (f b) # distributeM :: Monad m => m (Last a) -> Last (m a) # collectM :: Monad m => (a -> Last b) -> m a -> Last (m b) #
Distributive Identity #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Identity a) -> Identity (f a) # collect :: Functor f => (a -> Identity b) -> f a -> Identity (f b) # distributeM :: Monad m => m (Identity a) -> Identity (m a) # collectM :: Monad m => (a -> Identity b) -> m a -> Identity (m b) #
Distributive Dual #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Dual a) -> Dual (f a) # collect :: Functor f => (a -> Dual b) -> f a -> Dual (f b) # distributeM :: Monad m => m (Dual a) -> Dual (m a) # collectM :: Monad m => (a -> Dual b) -> m a -> Dual (m b) #
Distributive Sum #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Sum a) -> Sum (f a) # collect :: Functor f => (a -> Sum b) -> f a -> Sum (f b) # distributeM :: Monad m => m (Sum a) -> Sum (m a) # collectM :: Monad m => (a -> Sum b) -> m a -> Sum (m b) #
Distributive Product #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Product a) -> Product (f a) # collect :: Functor f => (a -> Product b) -> f a -> Product (f b) # distributeM :: Monad m => m (Product a) -> Product (m a) # collectM :: Monad m => (a -> Product b) -> m a -> Product (m b) #
Distributive (U1 :: Type -> Type) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (U1 a) -> U1 (f a) # collect :: Functor f => (a -> U1 b) -> f a -> U1 (f b) # distributeM :: Monad m => m (U1 a) -> U1 (m a) # collectM :: Monad m => (a -> U1 b) -> m a -> U1 (m b) #
(Distributive m, Monad m) => Distributive (WrappedMonad m) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (WrappedMonad m a) -> WrappedMonad m (f a) # collect :: Functor f => (a -> WrappedMonad m b) -> f a -> WrappedMonad m (f b) # distributeM :: Monad m0 => m0 (WrappedMonad m a) -> WrappedMonad m (m0 a) # collectM :: Monad m0 => (a -> WrappedMonad m b) -> m0 a -> WrappedMonad m (m0 b) #
Distributive (Proxy :: Type -> Type) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Proxy a) -> Proxy (f a) # collect :: Functor f => (a -> Proxy b) -> f a -> Proxy (f b) # distributeM :: Monad m => m (Proxy a) -> Proxy (m a) # collectM :: Monad m => (a -> Proxy b) -> m a -> Proxy (m b) #
Distributive f => Distributive (Rec1 f) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f0 => f0 (Rec1 f a) -> Rec1 f (f0 a) # collect :: Functor f0 => (a -> Rec1 f b) -> f0 a -> Rec1 f (f0 b) # distributeM :: Monad m => m (Rec1 f a) -> Rec1 f (m a) # collectM :: Monad m => (a -> Rec1 f b) -> m a -> Rec1 f (m b) #
Distributive (Tagged t) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (Tagged t a) -> Tagged t (f a) # collect :: Functor f => (a -> Tagged t b) -> f a -> Tagged t (f b) # distributeM :: Monad m => m (Tagged t a) -> Tagged t (m a) # collectM :: Monad m => (a -> Tagged t b) -> m a -> Tagged t (m b) #
Distributive f => Distributive (Reverse f) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f0 => f0 (Reverse f a) -> Reverse f (f0 a) # collect :: Functor f0 => (a -> Reverse f b) -> f0 a -> Reverse f (f0 b) # distributeM :: Monad m => m (Reverse f a) -> Reverse f (m a) # collectM :: Monad m => (a -> Reverse f b) -> m a -> Reverse f (m b) #
Distributive g => Distributive (ReaderT e g) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (ReaderT e g a) -> ReaderT e g (f a) # collect :: Functor f => (a -> ReaderT e g b) -> f a -> ReaderT e g (f b) # distributeM :: Monad m => m (ReaderT e g a) -> ReaderT e g (m a) # collectM :: Monad m => (a -> ReaderT e g b) -> m a -> ReaderT e g (m b) #
Distributive g => Distributive (IdentityT g) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (IdentityT g a) -> IdentityT g (f a) # collect :: Functor f => (a -> IdentityT g b) -> f a -> IdentityT g (f b) # distributeM :: Monad m => m (IdentityT g a) -> IdentityT g (m a) # collectM :: Monad m => (a -> IdentityT g b) -> m a -> IdentityT g (m b) #
Distributive f => Distributive (Backwards f) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f0 => f0 (Backwards f a) -> Backwards f (f0 a) # collect :: Functor f0 => (a -> Backwards f b) -> f0 a -> Backwards f (f0 b) # distributeM :: Monad m => m (Backwards f a) -> Backwards f (m a) # collectM :: Monad m => (a -> Backwards f b) -> m a -> Backwards f (m b) #
Distributive ((->) e :: Type -> Type) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f (e -> a) -> e -> f a # collect :: Functor f => (a -> e -> b) -> f a -> e -> f b # distributeM :: Monad m => m (e -> a) -> e -> m a # collectM :: Monad m => (a -> e -> b) -> m a -> e -> m b #
(Distributive a, Distributive b) => Distributive (a :*: b) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f ((a :: b) a0) -> (a :: b) (f a0) # collect :: Functor f => (a0 -> (a :: b) b0) -> f a0 -> (a :: b) (f b0) # distributeM :: Monad m => m ((a :: b) a0) -> (a :: b) (m a0) # collectM :: Monad m => (a0 -> (a :: b) b0) -> m a0 -> (a :: b) (m b0) #
(Distributive f, Distributive g) => Distributive (Product f g) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f0 => f0 (Product f g a) -> Product f g (f0 a) # collect :: Functor f0 => (a -> Product f g b) -> f0 a -> Product f g (f0 b) # distributeM :: Monad m => m (Product f g a) -> Product f g (m a) # collectM :: Monad m => (a -> Product f g b) -> m a -> Product f g (m b) #
Distributive f => Distributive (M1 i c f) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f0 => f0 (M1 i c f a) -> M1 i c f (f0 a) # collect :: Functor f0 => (a -> M1 i c f b) -> f0 a -> M1 i c f (f0 b) # distributeM :: Monad m => m (M1 i c f a) -> M1 i c f (m a) # collectM :: Monad m => (a -> M1 i c f b) -> m a -> M1 i c f (m b) #
(Distributive a, Distributive b) => Distributive (a :.: b) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f => f ((a :.: b) a0) -> (a :.: b) (f a0) # collect :: Functor f => (a0 -> (a :.: b) b0) -> f a0 -> (a :.: b) (f b0) # distributeM :: Monad m => m ((a :.: b) a0) -> (a :.: b) (m a0) # collectM :: Monad m => (a0 -> (a :.: b) b0) -> m a0 -> (a :.: b) (m b0) #
(Distributive f, Distributive g) => Distributive (Compose f g) #
Instance details Defined in Data.Distributive Methods distribute :: Functor f0 => f0 (Compose f g a) -> Compose f g (f0 a) # collect :: Functor f0 => (a -> Compose f g b) -> f0 a -> Compose f g (f0 b) # distributeM :: Monad m => m (Compose f g a) -> Compose f g (m a) # collectM :: Monad m => (a -> Compose f g b) -> m a -> Compose f g (m b) #

cotraverse :: (Distributive g, Functor f) => (f a -> b) -> f (g a) -> g b #

The dual of traverse

cotraverse f = fmap f . distribute

comapM :: (Distributive g, Monad m) => (m a -> b) -> m (g a) -> g b #

The dual of mapM

comapM f = fmap f . distributeM