Safe Haskell	Safe
Language	Haskell2010

Distributive

Contents

Distributive

Synopsis

class Functor g => Distributive (g :: * -> *) where
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
fmapCollect :: Distributive f => (a -> b) -> f a -> f b

Distributive

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 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 Log
Instance details Defined in Numeric.Log Methods distribute :: Functor f => f (Log a) -> Log (f a) # collect :: Functor f => (a -> Log b) -> f a -> Log (f b) # distributeM :: Monad m => m (Log a) -> Log (m a) # collectM :: Monad m => (a -> Log b) -> m a -> Log (m b) #
Distributive (U1 :: * -> *)
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) #
Representable f => Distributive (Co f)
Instance details Defined in Data.Functor.Rep Methods distribute :: Functor f0 => f0 (Co f a) -> Co f (f0 a) # collect :: Functor f0 => (a -> Co f b) -> f0 a -> Co f (f0 b) # distributeM :: Monad m => m (Co f a) -> Co f (m a) # collectM :: Monad m => (a -> Co f b) -> m a -> Co f (m b) #
Distributive (Proxy :: * -> *)
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 (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods distribute :: Functor f0 => f0 (Cofree f a) -> Cofree f (f0 a) # collect :: Functor f0 => (a -> Cofree f b) -> f0 a -> Cofree f (f0 b) # distributeM :: Monad m => m (Cofree f a) -> Cofree f (m a) # collectM :: Monad m => (a -> Cofree f b) -> m a -> Cofree f (m b) #
Distributive f => Distributive (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods distribute :: Functor f0 => f0 (Yoneda f a) -> Yoneda f (f0 a) # collect :: Functor f0 => (a -> Yoneda f b) -> f0 a -> Yoneda f (f0 b) # distributeM :: Monad m => m (Yoneda f a) -> Yoneda f (m a) # collectM :: Monad m => (a -> Yoneda f b) -> m a -> Yoneda f (m b) #
Distributive (ReifiedGetter s)
Instance details Defined in Control.Lens.Reified Methods distribute :: Functor f => f (ReifiedGetter s a) -> ReifiedGetter s (f a) # collect :: Functor f => (a -> ReifiedGetter s b) -> f a -> ReifiedGetter s (f b) # distributeM :: Monad m => m (ReifiedGetter s a) -> ReifiedGetter s (m a) # collectM :: Monad m => (a -> ReifiedGetter s b) -> m a -> ReifiedGetter s (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 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) #
(Representable f, Representable g) => Distributive (Day f g)
Instance details Defined in Data.Functor.Day Methods distribute :: Functor f0 => f0 (Day f g a) -> Day f g (f0 a) # collect :: Functor f0 => (a -> Day f g b) -> f0 a -> Day f g (f0 b) # distributeM :: Monad m => m (Day f g a) -> Day f g (m a) # collectM :: Monad m => (a -> Day f g b) -> m a -> Day f 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 f => Distributive (Star f a)
Instance details Defined in Data.Profunctor.Types Methods distribute :: Functor f0 => f0 (Star f a a0) -> Star f a (f0 a0) # collect :: Functor f0 => (a0 -> Star f a b) -> f0 a0 -> Star f a (f0 b) # distributeM :: Monad m => m (Star f a a0) -> Star f a (m a0) # collectM :: Monad m => (a0 -> Star f a b) -> m a0 -> Star f a (m b) #
Distributive (Costar f d)
Instance details Defined in Data.Profunctor.Types Methods distribute :: Functor f0 => f0 (Costar f d a) -> Costar f d (f0 a) # collect :: Functor f0 => (a -> Costar f d b) -> f0 a -> Costar f d (f0 b) # distributeM :: Monad m => m (Costar f d a) -> Costar f d (m a) # collectM :: Monad m => (a -> Costar f d b) -> m a -> Costar f d (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 ((->) e :: * -> *)
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 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 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

fmapCollect :: 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.