lens-1.5: Lenses, Folds and Traversals

Portability Rank2Types provisional Edward Kmett Safe-Infered

Control.Lens.Iso

Contents

Description

Synopsis

# Isomorphisms

class Category k => Isomorphic k whereSource

This is a `Category` with a canonical mapping to it from the category of isomorphisms over Haskell types.

Methods

isomorphic :: (a -> b) -> (b -> a) -> k a bSource

Build this morphism out of an isomorphism

The intention is that by using `isomorphic`, you can supply both halves of an isomorphism, but k can be instantiated to (->), so you can freely use the resulting isomorphism as a function.

isomap :: ((a -> b) -> c -> d) -> ((b -> a) -> d -> c) -> k a b -> k c dSource

Map a morphism in the target category using an isomorphism between morphisms in Hask.

Instances

 Isomorphic (->) Isomorphic Isomorphism

data Isomorphism a b Source

A concrete data type for isomorphisms.

This lets you place an isomorphism inside a container without using `ImpredicativeTypes`.

Constructors

 Isomorphism (a -> b) (b -> a)

iso :: (Isomorphic k, Functor f) => (a -> b) -> (b -> a) -> k (b -> f b) (a -> f a)Source

Build a simple isomorphism from a pair of inverse functions

``` iso :: (a -> b) -> (b -> a) -> Simple Iso a b
```

isos :: (Isomorphic k, Functor f) => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> k (c -> f d) (a -> f b)Source

Build an isomorphism family from two pairs of inverse functions

``` isos :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Iso a b c d
```

from :: Isomorphic k => Isomorphism a b -> k b aSource

Invert an isomorphism.

Note to compose an isomorphism and receive an isomorphism in turn you'll need to use `Category`

``` from (from l) = l
```

If you imported 'Control.Category.(.)', then:

``` from l . from r = from (r . l)
```
``` from :: (a :~> b) -> (b :~> a)
```

via :: Isomorphic k => Isomorphism a b -> k a bSource

``` via :: Isomorphism a b -> (a :~> b)
```

type Iso a b c d = forall k f. (Isomorphic k, Functor f) => k (c -> f d) (a -> f b)Source

Isomorphim families can be composed with other lenses using either' (.)' and `id` from the Prelude or from Control.Category. However, if you compose them with each other using '(.)' from the Prelude, they will be dumbed down to a mere `Lens`.

``` import Control.Category
import Prelude hiding ((.),id)
```
``` type Iso a b c d = forall k f. (Isomorphic k, Functor f) => Overloaded k f a b c d
```

type SimpleIso a b = Iso a a b bSource

``` type SimpleIso a b = Simple Iso a b
```

_const :: Iso a b (Const a c) (Const b d)Source

This isomorphism can be used to wrap or unwrap a value in `Const`

``` x^._const = Const x
Const x^.from _const = x
```

identity :: Iso a b (Identity a) (Identity b)Source

This isomorphism can be used to wrap or unwrap a value in `Identity`.

``` x^.identity = Identity x
Identity x^.from identity = x
```