semigroupoids-5.1: Semigroupoids: Category sans id

Copyright(C) 2011-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityprovisional
Portabilityportable
Safe HaskellSafe
LanguageHaskell98

Data.Functor.Extend

Contents

Description

 

Synopsis

Extendable Functors

There are two ways to define an Extend instance:

I. Provide definitions for extended satisfying this law:

extended f . extended g = extended (f . extended g)

II. Alternately, you may choose to provide definitions for duplicated satisfying this law:

duplicated . duplicated = fmap duplicated . duplicated

You may of course, choose to define both duplicated and extended. In that case you must also satisfy these laws:

extended f = fmap f . duplicated
duplicated = extended id

These are the default definitions of extended and duplicated.

class Functor w => Extend w where #

Minimal complete definition

duplicated | extended

Methods

duplicated :: w a -> w (w a) #

duplicated = extended id
fmap (fmap f) . duplicated = duplicated . fmap f

extended :: (w a -> b) -> w a -> w b #

extended f  = fmap f . duplicated

Instances

Extend [] # 

Methods

duplicated :: [a] -> [[a]] #

extended :: ([a] -> b) -> [a] -> [b] #

Extend Maybe # 

Methods

duplicated :: Maybe a -> Maybe (Maybe a) #

extended :: (Maybe a -> b) -> Maybe a -> Maybe b #

Extend Identity # 

Methods

duplicated :: Identity a -> Identity (Identity a) #

extended :: (Identity a -> b) -> Identity a -> Identity b #

Extend NonEmpty # 

Methods

duplicated :: NonEmpty a -> NonEmpty (NonEmpty a) #

extended :: (NonEmpty a -> b) -> NonEmpty a -> NonEmpty b #

Extend Tree # 

Methods

duplicated :: Tree a -> Tree (Tree a) #

extended :: (Tree a -> b) -> Tree a -> Tree b #

Extend Seq # 

Methods

duplicated :: Seq a -> Seq (Seq a) #

extended :: (Seq a -> b) -> Seq a -> Seq b #

Semigroup m => Extend ((->) m) # 

Methods

duplicated :: (m -> a) -> m -> m -> a #

extended :: ((m -> a) -> b) -> (m -> a) -> m -> b #

Extend (Either a) # 

Methods

duplicated :: Either a a -> Either a (Either a a) #

extended :: (Either a a -> b) -> Either a a -> Either a b #

Extend ((,) e) # 

Methods

duplicated :: (e, a) -> (e, (e, a)) #

extended :: ((e, a) -> b) -> (e, a) -> (e, b) #

Extend f => Extend (MaybeApply f) # 

Methods

duplicated :: MaybeApply f a -> MaybeApply f (MaybeApply f a) #

extended :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b #

(Extend w, Semigroup m) => Extend (TracedT m w) # 

Methods

duplicated :: TracedT m w a -> TracedT m w (TracedT m w a) #

extended :: (TracedT m w a -> b) -> TracedT m w a -> TracedT m w b #

Extend w => Extend (StoreT s w) # 

Methods

duplicated :: StoreT s w a -> StoreT s w (StoreT s w a) #

extended :: (StoreT s w a -> b) -> StoreT s w a -> StoreT s w b #

Extend w => Extend (EnvT e w) # 

Methods

duplicated :: EnvT e w a -> EnvT e w (EnvT e w a) #

extended :: (EnvT e w a -> b) -> EnvT e w a -> EnvT e w b #

Extend w => Extend (IdentityT * w) # 

Methods

duplicated :: IdentityT * w a -> IdentityT * w (IdentityT * w a) #

extended :: (IdentityT * w a -> b) -> IdentityT * w a -> IdentityT * w b #

(Extend f, Semigroup a) => Extend (Static f a) # 

Methods

duplicated :: Static f a a -> Static f a (Static f a a) #

extended :: (Static f a a -> b) -> Static f a a -> Static f a b #

(Extend f, Extend g) => Extend (Sum * f g) # 

Methods

duplicated :: Sum * f g a -> Sum * f g (Sum * f g a) #

extended :: (Sum * f g a -> b) -> Sum * f g a -> Sum * f g b #