Data.Functor.Invariant

Invariant

class Invariant f where

A functor is Invariant if it is parametric in its type parameter a.

Laws

invmap id id ≡ id
invmap f2 f2' . invmap f1 f1' ≡ invmap (f2 . f1) (f1' . f2')

Minimal complete definition

Nothing

Methods

invmap :: (a -> a') -> (a' -> a) -> f a -> f a'

Given two isomorphic functions f and g, map over the invariant parameter a.

Examples

>>> :t invmap @Identity (read @Bool) show
invmap @Identity (read @Bool) show :: Identity String -> Identity Bool

>>> invmap @Identity (read @Bool) show (Identity "True")
Identity True

default invmap :: Functor f => (a -> a') -> (a' -> a) -> f a -> f a'

Instances

Invariant ZipList

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> ZipList a -> ZipList a'

Invariant Identity

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> Identity a -> Identity a'

Invariant IO

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> IO a -> IO a'

Invariant NonEmpty

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> NonEmpty a -> NonEmpty a'

Invariant Maybe

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> Maybe a -> Maybe a'

Invariant []

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> [a] -> [a']

Invariant (Either e)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> Either e a -> Either e a'

Invariant ((,) x1)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> (x1, a) -> (x1, a')

Invariant ((,,) x1 x2)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> (x1, x2, a) -> (x1, x2, a')

(Functor f, Functor g) => Invariant (Product f g)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> Product f g a -> Product f g a'

(Functor f, Functor g) => Invariant (Sum f g)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> Sum f g a -> Sum f g a'

Invariant ((,,,) x1 x2 x3)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> (x1, x2, x3, a) -> (x1, x2, x3, a')

(Functor f, Functor g) => Invariant (Compose f g)

Defined in Data.Functor.Invariant

Methods

invmap :: (a -> a') -> (a' -> a) -> Compose f g a -> Compose f g a'

invIso :: Invariant f => Iso (->) a a' -> Iso (->) (f a) (f a')