Portability | Rank2Types |
---|---|
Stability | provisional |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Safe Haskell | None |
- type Iso a b c d = forall k f. (Isomorphic k, Functor f) => k (c -> f d) (a -> f b)
- iso :: (Isomorphic k, Functor f) => (a -> b) -> (b -> a) -> k (b -> f b) (a -> f a)
- isos :: (Isomorphic k, Functor f) => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> k (c -> f d) (a -> f b)
- ala :: Simple Iso a b -> ((a -> b) -> c -> b) -> c -> a
- auf :: Simple Iso a b -> ((d -> b) -> c -> b) -> (d -> a) -> c -> a
- under :: Isomorphism (c -> Mutator d) (a -> Mutator b) -> (a -> b) -> c -> d
- from :: Isomorphic k => Isomorphism a b -> k b a
- via :: Isomorphic k => Isomorphism a b -> k a b
- data Isomorphism a b = Isomorphism (a -> b) (b -> a)
- class Category k => Isomorphic k where
- isomorphic :: (a -> b) -> (b -> a) -> k a b
- isomap :: ((a -> b) -> c -> d) -> ((b -> a) -> d -> c) -> k a b -> k c d
- _const :: Iso a b (Const a c) (Const b d)
- identity :: Iso a b (Identity a) (Identity b)
- newtype ReifiedIso a b c d = ReifyIso {
- reflectIso :: Iso a b c d
- type SimpleIso a b = Iso a a b b
- type SimpleReifiedIso a b = ReifiedIso a a b b
Isomorphism Lenses
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
)
typeIso
a b c d = forall k f. (Isomorphic
k,Functor
f) =>Overloaded
k f a b c d
iso :: (Isomorphic k, Functor f) => (a -> b) -> (b -> a) -> k (b -> f b) (a -> f a)Source
isos :: (Isomorphic k, Functor f) => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> k (c -> f d) (a -> f b)Source
ala :: Simple Iso a b -> ((a -> b) -> c -> b) -> c -> aSource
Based on ala
from Conor McBride's work on Epigram.
>>>
:m + Data.Monoid.Lens Data.Foldable
>>>
ala _sum foldMap [1,2,3,4]
10
auf :: Simple Iso a b -> ((d -> b) -> c -> b) -> (d -> a) -> c -> aSource
Based on ala'
from Conor McBride's work on Epigram.
Mnemonically, the German auf plays a similar role to à la, and the combinator
is ala
with an extra function argument.
under :: Isomorphism (c -> Mutator d) (a -> Mutator b) -> (a -> b) -> c -> dSource
Primitive isomorphisms
from :: Isomorphic k => Isomorphism a b -> k b aSource
via :: Isomorphic k => Isomorphism a b -> k a bSource
Convert from an Isomorphism
back to any Isomorphic
value.
This is useful when you need to store an isomoprhism as a data type inside a container and later reconstitute it as an overloaded function.
data Isomorphism a b Source
A concrete data type for isomorphisms.
This lets you place an isomorphism inside a container without using ImpredicativeTypes
.
Isomorphism (a -> b) (b -> a) |
class Category k => Isomorphic k whereSource
Used to provide overloading of isomorphism application
This is a Category
with a canonical mapping to it from the
category of isomorphisms over Haskell types.
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.
Common Isomorphisms
Storing Isomorphisms
newtype ReifiedIso a b c d Source
Useful for storing isomorphisms in containers.
ReifyIso | |
|
Simplicity
type SimpleReifiedIso a b = ReifiedIso a a b bSource
typeSimpleReifiedIso
=Simple
ReifiedIso