invertible-0.2.0.5: bidirectional arrows, bijective functions, and invariant functors

Safe Haskell	Safe
Language	Haskell2010

Data.Invertible.Monoid

Description

Bidirectional transforms for Data.Monoid.

Synopsis

newtype BiEndo a = BiEndo {
- appBiEndo :: a <-> a
}
dual :: a <-> Dual a
endo :: (a -> a) <-> Endo a
biEndo :: (a <-> a) <-> BiEndo a
all :: Bool <-> All
any :: Bool <-> Any
sum :: a <-> Sum a
product :: a <-> Product a
first :: Maybe a <-> First a
last :: Maybe a <-> Last a
alt :: f a <-> Alt f a

Documentation

newtype BiEndo a #

The monoid of endomorphisms under composition.

Constructors

BiEndo
Fields appBiEndo :: a <-> a

Instances

Functor BiEndo #
Instance details Defined in Control.Invertible.Functor Methods fmap :: (a <-> b) -> BiEndo a -> BiEndo b #
Semigroup (BiEndo a) #
Instance details Defined in Data.Invertible.Monoid Methods (<>) :: BiEndo a -> BiEndo a -> BiEndo a # sconcat :: NonEmpty (BiEndo a) -> BiEndo a # stimes :: Integral b => b -> BiEndo a -> BiEndo a #
Monoid (BiEndo a) #
Instance details Defined in Data.Invertible.Monoid Methods mempty :: BiEndo a # mappend :: BiEndo a -> BiEndo a -> BiEndo a # mconcat :: [BiEndo a] -> BiEndo a #

dual :: a <-> Dual a #

(Un)wrap the Dual monoid.

endo :: (a -> a) <-> Endo a #

(Un)wrap the Endo monoid.

biEndo :: (a <-> a) <-> BiEndo a #

(Un)wrap the BiEndo monoid.

all :: Bool <-> All #

(Un)wrap the All monoid.

any :: Bool <-> Any #

(Un)wrap the Any monoid.

sum :: a <-> Sum a #

(Un)wrap the Sum monoid.

product :: a <-> Product a #

(Un)wrap the Product monoid.

first :: Maybe a <-> First a #

(Un)wrap the First monoid.

last :: Maybe a <-> Last a #

(Un)wrap the Last monoid.

alt :: f a <-> Alt f a #

(Un)wrap the Last monoid.