Data.Distributive

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

Distributive Par1

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

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

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

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

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

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

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

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

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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