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 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 U1

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 Par1

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 Identity

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 Min

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

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

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

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 Complex

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 Dual

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

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

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 ((->) e)

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 f => Distributive (Rec1 f)

Methods

distribute :: Functor f => f (Rec1 f a) -> Rec1 f (f a)

collect :: Functor f => (a -> Rec1 f b) -> f a -> Rec1 f (f 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 (Proxy *)

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 a, Distributive b) => Distributive ((:*:) a b)

Methods

distribute :: Functor f => f ((a :*: b) a) -> (a :*: b) (f a)

collect :: Functor f => (a -> (a :*: b) b) -> f a -> (a :*: b) (f b)

distributeM :: Monad m => m ((a :*: b) a) -> (a :*: b) (m a)

collectM :: Monad m => (a -> (a :*: b) b) -> m a -> (a :*: b) (m b)

(Distributive a, Distributive b) => Distributive ((:.:) a b)

Methods

distribute :: Functor f => f ((a :.: b) a) -> (a :.: b) (f a)

collect :: Functor f => (a -> (a :.: b) b) -> f a -> (a :.: b) (f b)

distributeM :: Monad m => m ((a :.: b) a) -> (a :.: b) (m a)

collectM :: Monad m => (a -> (a :.: b) b) -> m a -> (a :.: b) (m b)

Distributive (Tagged * t)

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)

Methods

distribute :: Functor f => f (Reverse * f a) -> Reverse * f (f a)

collect :: Functor f => (a -> Reverse * f b) -> f a -> Reverse * f (f 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 f => Distributive (Backwards * f)

Methods

distribute :: Functor f => f (Backwards * f a) -> Backwards * f (f a)

collect :: Functor f => (a -> Backwards * f b) -> f a -> Backwards * f (f 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 g => Distributive (IdentityT * g)

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 (M1 i c f)

Methods

distribute :: Functor f => f (M1 i c f a) -> M1 i c f (f a)

collect :: Functor f => (a -> M1 i c f b) -> f a -> M1 i c f (f 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 f, Distributive g) => Distributive (Product * f g)

Methods

distribute :: Functor f => f (Product * f g a) -> Product * f g (f a)

collect :: Functor f => (a -> Product * f g b) -> f a -> Product * f g (f 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 g => Distributive (ReaderT * e g)

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 f, Distributive g) => Distributive (Compose * * f g)

Methods

distribute :: Functor f => f (Compose * * f g a) -> Compose * * f g (f a)

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

fmapCollect :: forall f a b. Distributive f => (a -> b) -> f a -> f b

fmapCollect is a viable default definition for fmap given a Distributive instance defined in terms of collect.