distributive-0.6.2.1: Distributive functors -- Dual to Traversable
Copyright(C) 2011-2016 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityprovisional
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Data.Distributive

Description

 
Synopsis

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) #

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

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

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