Safe Haskell	None
Language	Haskell2010

Optic.Lens

Contents

Lens
HasAny
Subtype
At
Contains

Synopsis

type Lens s t a b = forall (f :: * -> *). Functor f => (a -> f b) -> s -> f t
type Lens' s a = Lens s s a a
lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
class HasAny (sel :: k) s t a b | s sel k -> a where
class Subtype sup sub where
class Ixed m => At m where
sans :: At m => Index m -> m -> m
type family Index s :: *
type family IxValue m :: *
class Contains m where

Lens

type Lens s t a b = forall (f :: * -> *). Functor f => (a -> f b) -> s -> f t #

A Lens is actually a lens family as described in http://comonad.com/reader/2012/mirrored-lenses/.

With great power comes great responsibility and a Lens is subject to the three common sense Lens laws:

1) You get back what you put in:

view l (set l v s)  ≡ v

2) Putting back what you got doesn't change anything:

set l (view l s) s  ≡ s

3) Setting twice is the same as setting once:

set l v' (set l v s) ≡ set l v' s

These laws are strong enough that the 4 type parameters of a Lens cannot vary fully independently. For more on how they interact, read the "Why is it a Lens Family?" section of http://comonad.com/reader/2012/mirrored-lenses/.

There are some emergent properties of these laws:

1) set l s must be injective for every s This is a consequence of law #1

2) set l must be surjective, because of law #2, which indicates that it is possible to obtain any v from some s such that set s v = s

3) Given just the first two laws you can prove a weaker form of law #3 where the values v that you are setting match:

set l v (set l v s) ≡ set l v s

Every Lens can be used directly as a Setter or Traversal.

You can also use a Lens for Getting as if it were a Fold or Getter.

Since every Lens is a valid Traversal, the Traversal laws are required of any Lens you create:

l pure ≡ pure
fmap (l f) . l g ≡ getCompose . l (Compose . fmap f . g)

type Lens s t a b = forall f. Functor f => LensLike f s t a b

type Lens' s a = Lens s s a a #

type Lens' = Simple Lens

lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b #

Build a Lens from a getter and a setter.

lens :: Functor f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t

>>> s ^. lens getter setter
getter s

>>> s & lens getter setter .~ b
setter s b

>>> s & lens getter setter %~ f
setter s (f (getter s))

lens :: (s -> a) -> (s -> a -> s) -> Lens' s a

HasAny

class HasAny (sel :: k) s t a b | s sel k -> a where #

Minimal complete definition

the

Methods

the :: Lens s t a b #

A lens that focuses on a part of a product as identified by some selector. Currently supported selectors are field names, positions and unique types. Compatible with the lens package's Lens type.

>>> human ^. the @Int
50

>>> human ^. the @"name"
"Tunyasz"

>>> human ^. the @3
"London"

Instances

HasPosition i s t a b => HasAny (i :: Nat) s t a b
Instance details Defined in Data.Generics.Product.Any Methods the :: Lens s t a b #
HasField field s t a b => HasAny (field :: Symbol) s t a b
Instance details Defined in Data.Generics.Product.Any Methods the :: Lens s t a b #
(HasType a s, t ~ s, a ~ b) => HasAny (a :: *) s t a b
Instance details Defined in Data.Generics.Product.Any Methods the :: Lens s t a b #

Subtype

class Subtype sup sub where #

Structural subtype relationship

sub is a (structural) subtype of sup, if its fields are a subset of those of sup.

Minimal complete definition

super | smash, upcast

Methods

super :: Lens sub sub sup sup #

Structural subtype lens. Given a subtype relationship sub :< sup, we can focus on the sub structure of sup.

>>> human ^. super @Animal
Animal {name = "Tunyasz", age = 50}

>>> set (super @Animal) (Animal "dog" 10) human
Human {name = "dog", age = 10, address = "London"}

upcast :: sub -> sup #

Cast the more specific subtype to the more general supertype

>>> upcast human :: Animal
Animal {name = "Tunyasz", age = 50}

>>> upcast (upcast human :: Animal) :: Human
...
... The type 'Animal' is not a subtype of 'Human'.
... The following fields are missing from 'Animal':
... address
...

smash :: sup -> sub -> sub #

Plug a smaller structure into a larger one

>>> smash (Animal "dog" 10) human
Human {name = "dog", age = 10, address = "London"}

Instances

(Generic a, Generic b, GSmash (Rep a) (Rep b), GUpcast (Rep a) (Rep b), ErrorUnless b a (CollectFieldsOrdered (Rep b) \\ CollectFieldsOrdered (Rep a))) => Subtype b a
Instance details Defined in Data.Generics.Product.Subtype Methods super :: Lens a a b b # upcast :: a -> b # smash :: b -> a -> a #
Subtype a Void
Instance details Defined in Data.Generics.Product.Subtype Methods super :: Lens Void Void a a # upcast :: Void -> a # smash :: a -> Void -> Void #
Subtype Void a
Instance details Defined in Data.Generics.Product.Subtype Methods super :: Lens a a Void Void # upcast :: a -> Void # smash :: Void -> a -> a #

At

class Ixed m => At m where #

At provides a Lens that can be used to read, write or delete the value associated with a key in a Map-like container on an ad hoc basis.

An instance of At should satisfy:

ix k ≡ at k . traverse

Minimal complete definition

at

Methods

at :: Index m -> Lens' m (Maybe (IxValue m)) #

>>> Map.fromList [(1,"world")] ^.at 1
Just "world"

>>> at 1 ?~ "hello" $ Map.empty
fromList [(1,"hello")]

Note: Map-like containers form a reasonable instance, but not Array-like ones, where you cannot satisfy the Lens laws.

Instances

At IntSet
Instance details Defined in Control.Lens.At Methods at :: Index IntSet -> Lens' IntSet (Maybe (IxValue IntSet)) #
At (Maybe a)
Instance details Defined in Control.Lens.At Methods at :: Index (Maybe a) -> Lens' (Maybe a) (Maybe (IxValue (Maybe a))) #
At (IntMap a)
Instance details Defined in Control.Lens.At Methods at :: Index (IntMap a) -> Lens' (IntMap a) (Maybe (IxValue (IntMap a))) #
Ord k => At (Set k)
Instance details Defined in Control.Lens.At Methods at :: Index (Set k) -> Lens' (Set k) (Maybe (IxValue (Set k))) #
(Eq k, Hashable k) => At (HashSet k)
Instance details Defined in Control.Lens.At Methods at :: Index (HashSet k) -> Lens' (HashSet k) (Maybe (IxValue (HashSet k))) #
(Eq k, Hashable k) => At (HashMap k a)
Instance details Defined in Control.Lens.At Methods at :: Index (HashMap k a) -> Lens' (HashMap k a) (Maybe (IxValue (HashMap k a))) #
Ord k => At (Map k a)
Instance details Defined in Control.Lens.At Methods at :: Index (Map k a) -> Lens' (Map k a) (Maybe (IxValue (Map k a))) #
(Eq k, Hashable k) => At (InsOrdHashMap k a)
Instance details Defined in Data.HashMap.Strict.InsOrd Methods at :: Index (InsOrdHashMap k a) -> Lens' (InsOrdHashMap k a) (Maybe (IxValue (InsOrdHashMap k a))) #

sans :: At m => Index m -> m -> m #

Delete the value associated with a key in a Map-like container

sans k = at k .~ Nothing

type family Index s :: * #

Instances

type Index ByteString
Instance details Defined in Control.Lens.At type Index ByteString = Int
type Index ByteString
Instance details Defined in Control.Lens.At type Index ByteString = Int64
type Index Text
Instance details Defined in Control.Lens.At type Index Text = Int
type Index Value
Instance details Defined in Data.Aeson.Lens type Index Value = Text
type Index Text
Instance details Defined in Control.Lens.At type Index Text = Int64
type Index IntSet
Instance details Defined in Control.Lens.At type Index IntSet = Int
type Index [a]
Instance details Defined in Control.Lens.At type Index [a] = Int
type Index (Maybe a)
Instance details Defined in Control.Lens.At type Index (Maybe a) = ()
type Index (Complex a)
Instance details Defined in Control.Lens.At type Index (Complex a) = Int
type Index (Identity a)
Instance details Defined in Control.Lens.At type Index (Identity a) = ()
type Index (NonEmpty a)
Instance details Defined in Control.Lens.At type Index (NonEmpty a) = Int
type Index (IntMap a)
Instance details Defined in Control.Lens.At type Index (IntMap a) = Int
type Index (Tree a)
Instance details Defined in Control.Lens.At type Index (Tree a) = [Int]
type Index (Seq a)
Instance details Defined in Control.Lens.At type Index (Seq a) = Int
type Index (Set a)
Instance details Defined in Control.Lens.At type Index (Set a) = a
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (HashSet a)
Instance details Defined in Control.Lens.At type Index (HashSet a) = a
type Index (Vector a)
Instance details Defined in Control.Lens.At type Index (Vector a) = Int
type Index (e -> a)
Instance details Defined in Control.Lens.At type Index (e -> a) = e
type Index (a, b)
Instance details Defined in Control.Lens.At type Index (a, b) = Int
type Index (HashMap k a)
Instance details Defined in Control.Lens.At type Index (HashMap k a) = k
type Index (Map k a)
Instance details Defined in Control.Lens.At type Index (Map k a) = k
type Index (UArray i e)
Instance details Defined in Control.Lens.At type Index (UArray i e) = i
type Index (Array i e)
Instance details Defined in Control.Lens.At type Index (Array i e) = i
type Index (InsOrdHashMap k v)
Instance details Defined in Data.HashMap.Strict.InsOrd type Index (InsOrdHashMap k v) = k
type Index (a, b, c)
Instance details Defined in Control.Lens.At type Index (a, b, c) = Int
type Index (a, b, c, d)
Instance details Defined in Control.Lens.At type Index (a, b, c, d) = Int
type Index (a, b, c, d, e)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e) = Int
type Index (a, b, c, d, e, f)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f) = Int
type Index (a, b, c, d, e, f, g)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g) = Int
type Index (a, b, c, d, e, f, g, h)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g, h) = Int
type Index (a, b, c, d, e, f, g, h, i)
Instance details Defined in Control.Lens.At type Index (a, b, c, d, e, f, g, h, i) = Int

type family IxValue m :: * #

This provides a common notion of a value at an index that is shared by both Ixed and At.

Instances

type IxValue ByteString
Instance details Defined in Control.Lens.At type IxValue ByteString = Word8
type IxValue ByteString
Instance details Defined in Control.Lens.At type IxValue ByteString = Word8
type IxValue Text
Instance details Defined in Control.Lens.At type IxValue Text = Char
type IxValue Value
Instance details Defined in Data.Aeson.Lens type IxValue Value = Value
type IxValue Text
Instance details Defined in Control.Lens.At type IxValue Text = Char
type IxValue IntSet
Instance details Defined in Control.Lens.At type IxValue IntSet = ()
type IxValue [a]
Instance details Defined in Control.Lens.At type IxValue [a] = a
type IxValue (Maybe a)
Instance details Defined in Control.Lens.At type IxValue (Maybe a) = a
type IxValue (Identity a)
Instance details Defined in Control.Lens.At type IxValue (Identity a) = a
type IxValue (NonEmpty a)
Instance details Defined in Control.Lens.At type IxValue (NonEmpty a) = a
type IxValue (IntMap a)
Instance details Defined in Control.Lens.At type IxValue (IntMap a) = a
type IxValue (Tree a)
Instance details Defined in Control.Lens.At type IxValue (Tree a) = a
type IxValue (Seq a)
Instance details Defined in Control.Lens.At type IxValue (Seq a) = a
type IxValue (Set k)
Instance details Defined in Control.Lens.At type IxValue (Set k) = ()
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (HashSet k)
Instance details Defined in Control.Lens.At type IxValue (HashSet k) = ()
type IxValue (Vector a)
Instance details Defined in Control.Lens.At type IxValue (Vector a) = a
type IxValue (e -> a)
Instance details Defined in Control.Lens.At type IxValue (e -> a) = a
type IxValue (a, a2)
Instance details Defined in Control.Lens.At type IxValue (a, a2) = a
type IxValue (HashMap k a)
Instance details Defined in Control.Lens.At type IxValue (HashMap k a) = a
type IxValue (Map k a)
Instance details Defined in Control.Lens.At type IxValue (Map k a) = a
type IxValue (UArray i e)
Instance details Defined in Control.Lens.At type IxValue (UArray i e) = e
type IxValue (Array i e)
Instance details Defined in Control.Lens.At type IxValue (Array i e) = e
type IxValue (InsOrdHashMap k v)
Instance details Defined in Data.HashMap.Strict.InsOrd type IxValue (InsOrdHashMap k v) = v
type IxValue (a, a2, a3)
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3) = a
type IxValue (a, a2, a3, a4)
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4) = a
type IxValue (a, a2, a3, a4, a5)
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5) = a
type IxValue (a, a2, a3, a4, a5, a6)
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6) = a
type IxValue (a, a2, a3, a4, a5, a6, a7)
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7) = a
type IxValue (a, a2, a3, a4, a5, a6, a7, a8)
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7, a8) = a
type IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9)
Instance details Defined in Control.Lens.At type IxValue (a, a2, a3, a4, a5, a6, a7, a8, a9) = a

Contains

class Contains m where #

This class provides a simple Lens that lets you view (and modify) information about whether or not a container contains a given Index.

Minimal complete definition

contains

Methods

contains :: Index m -> Lens' m Bool #

>>> IntSet.fromList [1,2,3,4] ^. contains 3
True

>>> IntSet.fromList [1,2,3,4] ^. contains 5
False

>>> IntSet.fromList [1,2,3,4] & contains 3 .~ False
fromList [1,2,4]

Instances

Contains IntSet
Instance details Defined in Control.Lens.At Methods contains :: Index IntSet -> Lens' IntSet Bool #
Ord a => Contains (Set a)
Instance details Defined in Control.Lens.At Methods contains :: Index (Set a) -> Lens' (Set a) Bool #
(Eq a, Hashable a) => Contains (HashSet a)
Instance details Defined in Control.Lens.At Methods contains :: Index (HashSet a) -> Lens' (HashSet a) Bool #