DeepControl.Commutative

This module is made of Traversable, distilling most function names polluted with action kind of concepts into crystalized(static) ones.

The Commutative class

class Applicative c => Commutative c where

[], Maybe, Either, Except and Writer are all commutative each other. So these monads can be deepened to Monad2, Monad3, Monad4 and Monad5.

Minimal complete definition

commute

Methods

commute :: Applicative f => c (f a) -> f (c a)

This method is equivalent for sequenceA except the name. The only difference is the name "commute", that is to say from which no action kind of concepts smell.

>>> commute $ Just [1]
[Just 1]
>>> commute $ [Just 1]
Just [1]

>>> commute $ Right (Just 1)
Just (Right 1)
>>> commute $ Just (Right 1)
Right (Just 1)

Instances

Commutative []

Methods

commute :: Applicative f => [f a] -> f [a]

Commutative Maybe

Methods

commute :: Applicative f => Maybe (f a) -> f (Maybe a)

Commutative (Either a)

Methods

commute :: Applicative f => Either a (f a) -> f (Either a a)

Commutative (Except e)

Methods

commute :: Applicative f => Except e (f a) -> f (Except e a)

Monoid w => Commutative (Writer w)

Methods

commute :: Applicative f => Writer w (f a) -> f (Writer w a)

(Commutative f1, Commutative f2) => Commutative (IdentityT2 f1 f2)

Methods

commute :: Applicative f => IdentityT2 f1 f2 (f a) -> f (IdentityT2 f1 f2 a)

(Commutative f1, Commutative f2, Commutative f3) => Commutative (IdentityT3 f1 f2 f3)

Methods

commute :: Applicative f => IdentityT3 f1 f2 f3 (f a) -> f (IdentityT3 f1 f2 f3 a)

(Commutative f1, Commutative f2, Commutative f3, Commutative f4) => Commutative (IdentityT4 f1 f2 f3 f4)

Methods

commute :: Applicative f => IdentityT4 f1 f2 f3 f4 (f a) -> f (IdentityT4 f1 f2 f3 f4 a)

(Commutative f1, Commutative f2, Commutative f3, Commutative f4, Commutative f5) => Commutative (IdentityT5 f1 f2 f3 f4 f5)

Methods

commute :: Applicative f => IdentityT5 f1 f2 f3 f4 f5 (f a) -> f (IdentityT5 f1 f2 f3 f4 f5 a)

Utility functions

cmap :: (Applicative f, Commutative c) => (a -> f b) -> c a -> f (c b)

Do fmap f then commute, equivalent for traverse.

cfor :: (Applicative f, Commutative c) => c a -> (a -> f b) -> f (c b)

The auguments-flipped function for cmap, equivalent for for.

General definitions for superclass methods

fmapDefault :: Commutative t => (a -> b) -> t a -> t b

This function may be used as a value for fmap in a Functor instance, provided that commute is defined. (Using fmapDefault with a Commutative instance will result in infinite recursion.)

foldMapDefault :: (Commutative t, Monoid m) => (a -> m) -> t a -> m

This function may be used as a value for foldMap in a Foldable instance.

Utility functions 2

Level-2

sink2 :: (Commutative m1, Commutative m2, Applicative m3) => m1 (m2 (m3 a)) -> m2 (m3 (m1 a))

sink2 = (commute|$>) . commute

>>> sink2 $ Right (Just [1])
Just [Right 1]

float2 :: (Applicative m1, Commutative m2, Commutative m3) => m2 (m3 (m1 a)) -> m1 (m2 (m3 a))

float2 = commute . (commute|$>)

>>> float2 $ Just [Right 1]
Right (Just [1])

Level-3

sink3 :: (Commutative m1, Commutative m2, Commutative m3, Applicative m4) => m1 (m2 (m3 (m4 a))) -> m2 (m3 (m4 (m1 a)))

sink3 = (sink2|$>) . commute

>>> sink3 $ Right [Just [1]]
[Just [Right 1]]

float3 :: (Applicative m1, Commutative m2, Commutative m3, Commutative m4) => m2 (m3 (m4 (m1 a))) -> m1 (m2 (m3 (m4 a)))

float3 = commute . (float2|$>)

>>> float3 $ [Just [Right 1]]
Right [Just [1]]

Level-4

sink4 :: (Commutative m1, Commutative m2, Commutative m3, Commutative m4, Applicative m5) => m1 (m2 (m3 (m4 (m5 a)))) -> m2 (m3 (m4 (m5 (m1 a))))

float4 :: (Applicative m1, Commutative m2, Commutative m3, Commutative m4, Commutative m5) => m2 (m3 (m4 (m5 (m1 a)))) -> m1 (m2 (m3 (m4 (m5 a))))

Level-5

sink5 :: (Commutative m1, Commutative m2, Commutative m3, Commutative m4, Commutative m5, Applicative m6) => m1 (m2 (m3 (m4 (m5 (m6 a))))) -> m2 (m3 (m4 (m5 (m6 (m1 a)))))

float5 :: (Applicative m1, Commutative m2, Commutative m3, Commutative m4, Commutative m5, Commutative m6) => m2 (m3 (m4 (m5 (m6 (m1 a))))) -> m1 (m2 (m3 (m4 (m5 (m6 a)))))