lens-4.16.1: Lenses, Folds and Traversals

Copyright (C) 2012-16 Edward Kmett BSD-style (see the file LICENSE) Edward Kmett provisional Rank2Types Safe Haskell98

Control.Lens.Lens

Description

A Lens s t a b is a purely functional reference.

While a Traversal could be used for Getting like a valid Fold, it wasn't a valid Getter as a Getter can't require an Applicative constraint.

Functor, however, is a constraint on both.

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


Every Lens is a valid Setter.

Every Lens can be used for Getting like a Fold that doesn't use the Applicative or Contravariant.

Every Lens is a valid Traversal that only uses the Functor part of the Applicative it is supplied.

Every Lens can be used for Getting like a valid Getter.

Since every Lens can be used for Getting like a valid Getter it follows that it must view exactly one element in the structure.

The Lens laws follow from this property and the desire for it to act like a Traversable when used as a Traversal.

In the examples below, getter and setter are supplied as example getters and setters, and are not actual functions supplied by this package.

Synopsis

# Lenses

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

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 Source #

type Lens' = Simple Lens


type IndexedLens i s t a b = forall f p. (Indexable i p, Functor f) => p a (f b) -> s -> f t Source #

Every IndexedLens is a valid Lens and a valid IndexedTraversal.

type IndexedLens' i s a = IndexedLens i s s a a Source #

type IndexedLens' i = Simple (IndexedLens i)


## Concrete Lenses

type ALens s t a b = LensLike (Pretext (->) a b) s t a b Source #

When you see this as an argument to a function, it expects a Lens.

This type can also be used when you need to store a Lens in a container, since it is rank-1. You can turn them back into a Lens with cloneLens, or use it directly with combinators like storing and (^#).

type ALens' s a = ALens s s a a Source #

type ALens' = Simple ALens


type AnIndexedLens i s t a b = Optical (Indexed i) (->) (Pretext (Indexed i) a b) s t a b Source #

When you see this as an argument to a function, it expects an IndexedLens

type AnIndexedLens' i s a = AnIndexedLens i s s a a Source #

type AnIndexedLens' = Simple (AnIndexedLens i)


# Combinators

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

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


ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b Source #

Build an IndexedLens from a Getter and a Setter.

iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b Source #

Build an index-preserving Lens from a Getter and a Setter.

(%%~) :: LensLike f s t a b -> (a -> f b) -> s -> f t infixr 4 Source #

(%%~) can be used in one of two scenarios:

When applied to a Lens, it can edit the target of the Lens in a structure, extracting a functorial result.

When applied to a Traversal, it can edit the targets of the traversals, extracting an applicative summary of its actions.

>>> [66,97,116,109,97,110] & each %%~ \a -> ("na", chr a)
("nananananana","Batman")


For all that the definition of this combinator is just:

(%%~) ≡ id


It may be beneficial to think about it as if it had these even more restricted types, however:

(%%~) :: Functor f =>     Iso s t a b       -> (a -> f b) -> s -> f t
(%%~) :: Functor f =>     Lens s t a b      -> (a -> f b) -> s -> f t
(%%~) :: Applicative f => Traversal s t a b -> (a -> f b) -> s -> f t


When applied to a Traversal, it can edit the targets of the traversals, extracting a supplemental monoidal summary of its actions, by choosing f = ((,) m)

(%%~) ::             Iso s t a b       -> (a -> (r, b)) -> s -> (r, t)
(%%~) ::             Lens s t a b      -> (a -> (r, b)) -> s -> (r, t)
(%%~) :: Monoid m => Traversal s t a b -> (a -> (m, b)) -> s -> (m, t)


(%%=) :: MonadState s m => Over p ((,) r) s s a b -> p a (r, b) -> m r infix 4 Source #

Modify the target of a Lens in the current state returning some extra information of type r or modify all targets of a Traversal in the current state, extracting extra information of type r and return a monoidal summary of the changes.

>>> runState (_1 %%= \x -> (f x, g x)) (a,b)
(f a,(g a,b))

(%%=) ≡ (state .)


It may be useful to think of (%%=), instead, as having either of the following more restricted type signatures:

(%%=) :: MonadState s m             => Iso s s a b       -> (a -> (r, b)) -> m r
(%%=) :: MonadState s m             => Lens s s a b      -> (a -> (r, b)) -> m r
(%%=) :: (MonadState s m, Monoid r) => Traversal s s a b -> (a -> (r, b)) -> m r


(%%@~) :: IndexedLensLike i f s t a b -> (i -> a -> f b) -> s -> f t infixr 4 Source #

Adjust the target of an IndexedLens returning a supplementary result, or adjust all of the targets of an IndexedTraversal and return a monoidal summary of the supplementary results and the answer.

(%%@~) ≡ withIndex

(%%@~) :: Functor f => IndexedLens i s t a b      -> (i -> a -> f b) -> s -> f t
(%%@~) :: Applicative f => IndexedTraversal i s t a b -> (i -> a -> f b) -> s -> f t


In particular, it is often useful to think of this function as having one of these even more restricted type signatures:

(%%@~) ::             IndexedLens i s t a b      -> (i -> a -> (r, b)) -> s -> (r, t)
(%%@~) :: Monoid r => IndexedTraversal i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)


(%%@=) :: MonadState s m => IndexedLensLike i ((,) r) s s a b -> (i -> a -> (r, b)) -> m r infix 4 Source #

Adjust the target of an IndexedLens returning a supplementary result, or adjust all of the targets of an IndexedTraversal within the current state, and return a monoidal summary of the supplementary results.

l %%@= f ≡ state (l %%@~ f)

(%%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> (r, b)) -> s -> m r
(%%@=) :: (MonadState s m, Monoid r) => IndexedTraversal i s s a b -> (i -> a -> (r, b)) -> s -> m r


(<%@~) :: Over (Indexed i) ((,) b) s t a b -> (i -> a -> b) -> s -> (b, t) infixr 4 Source #

Adjust the target of an IndexedLens returning the intermediate result, or adjust all of the targets of an IndexedTraversal and return a monoidal summary along with the answer.

l <%~ f ≡ l <%@~ const f


When you do not need access to the index then (<%~) is more liberal in what it can accept.

If you do not need the intermediate result, you can use (%@~) or even (%~).

(<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (b, t)
(<%@~) :: Monoid b => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (b, t)


(<%@=) :: MonadState s m => IndexedLensLike i ((,) b) s s a b -> (i -> a -> b) -> m b infix 4 Source #

Adjust the target of an IndexedLens returning the intermediate result, or adjust all of the targets of an IndexedTraversal within the current state, and return a monoidal summary of the intermediate results.

(<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m b
(<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m b


(<<%@~) :: Over (Indexed i) ((,) a) s t a b -> (i -> a -> b) -> s -> (a, t) infixr 4 Source #

Adjust the target of an IndexedLens returning the old value, or adjust all of the targets of an IndexedTraversal and return a monoidal summary of the old values along with the answer.

(<<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (a, t)
(<<%@~) :: Monoid a => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (a, t)


(<<%@=) :: MonadState s m => IndexedLensLike i ((,) a) s s a b -> (i -> a -> b) -> m a infix 4 Source #

Adjust the target of an IndexedLens returning the old value, or adjust all of the targets of an IndexedTraversal within the current state, and return a monoidal summary of the old values.

(<<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m a
(<<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m a


## General Purpose Combinators

(&) :: a -> (a -> b) -> b infixl 1 #

& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

Since: 4.8.0.0

(<&>) :: Functor f => f a -> (a -> b) -> f b infixl 1 Source #

Infix flipped fmap.

(<&>) = flip fmap


(??) :: Functor f => f (a -> b) -> a -> f b infixl 1 Source #

This is convenient to flip argument order of composite functions defined as:

fab ?? a = fmap ($a) fab  For the Functor instance f = ((->) r) you can reason about this function as if the definition was (??) ≡ flip: >>> (h ?? x) a h a x  >>> execState ?? []$ modify (1:)
[1]

>>> over _2 ?? ("hello","world") $length ("hello",5)  >>> over ?? length ?? ("hello","world")$ _2
("hello",5)


(&~) :: s -> State s a -> s infixl 1 Source #

This can be used to chain lens operations using op= syntax rather than op~ syntax for simple non-type-changing cases.

>>> (10,20) & _1 .~ 30 & _2 .~ 40
(30,40)

>>> (10,20) &~ do _1 .= 30; _2 .= 40
(30,40)


This does not support type-changing assignment, e.g.

>>> (10,20) & _1 .~ "hello"
("hello",20)


# Lateral Composition

choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (Either s s') (Either t t') a b Source #

Merge two lenses, getters, setters, folds or traversals.

chosen ≡ choosing id id

choosing :: Getter s a     -> Getter s' a     -> Getter (Either s s') a
choosing :: Fold s a       -> Fold s' a       -> Fold (Either s s') a
choosing :: Lens' s a      -> Lens' s' a      -> Lens' (Either s s') a
choosing :: Traversal' s a -> Traversal' s' a -> Traversal' (Either s s') a
choosing :: Setter' s a    -> Setter' s' a    -> Setter' (Either s s') a


chosen :: IndexPreservingLens (Either a a) (Either b b) a b Source #

This is a Lens that updates either side of an Either, where both sides have the same type.

chosen ≡ choosing id id

>>> Left a^.chosen
a

>>> Right a^.chosen
a

>>> Right "hello"^.chosen
"hello"

>>> Right a & chosen *~ b
Right (a * b)

chosen :: Lens (Either a a) (Either b b) a b
chosen f (Left a)  = Left <$> f a chosen f (Right a) = Right <$> f a


alongside :: LensLike (AlongsideLeft f b') s t a b -> LensLike (AlongsideRight f t) s' t' a' b' -> LensLike f (s, s') (t, t') (a, a') (b, b') Source #

alongside makes a Lens from two other lenses or a Getter from two other getters by executing them on their respective halves of a product.

>>> (Left a, Right b)^.alongside chosen chosen
(a,b)

>>> (Left a, Right b) & alongside chosen chosen .~ (c,d)
(Left c,Right d)

alongside :: Lens   s t a b -> Lens   s' t' a' b' -> Lens   (s,s') (t,t') (a,a') (b,b')
alongside :: Getter s t a b -> Getter s' t' a' b' -> Getter (s,s') (t,t') (a,a') (b,b')


inside :: Corepresentable p => ALens s t a b -> Lens (p e s) (p e t) (p e a) (p e b) Source #

Lift a Lens so it can run under a function (or other corepresentable profunctor).

inside :: Lens s t a b -> Lens (e -> s) (e -> t) (e -> a) (e -> b)

>>> (\x -> (x-1,x+1)) ^. inside _1 $5 4  >>> runState (modify (1:) >> modify (2:)) ^. (inside _2)$ []
[2,1]


# Setting Functionally with Passthrough

(<%~) :: LensLike ((,) b) s t a b -> (a -> b) -> s -> (b, t) infixr 4 Source #

Modify the target of a Lens and return the result.

When you do not need the result of the operation, (%~) is more flexible.

(<%~) ::             Lens s t a b      -> (a -> b) -> s -> (b, t)
(<%~) ::             Iso s t a b       -> (a -> b) -> s -> (b, t)
(<%~) :: Monoid b => Traversal s t a b -> (a -> b) -> s -> (b, t)


(<+~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 Source #

Increment the target of a numerically valued Lens and return the result.

When you do not need the result of the addition, (+~) is more flexible.

(<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<+~) :: Num a => Iso' s a  -> a -> s -> (a, s)


(<-~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 Source #

Decrement the target of a numerically valued Lens and return the result.

When you do not need the result of the subtraction, (-~) is more flexible.

(<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<-~) :: Num a => Iso' s a  -> a -> s -> (a, s)


(<*~) :: Num a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 Source #

Multiply the target of a numerically valued Lens and return the result.

When you do not need the result of the multiplication, (*~) is more flexible.

(<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<*~) :: Num a => Iso'  s a -> a -> s -> (a, s)


(<//~) :: Fractional a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 Source #

Divide the target of a fractionally valued Lens and return the result.

When you do not need the result of the division, (//~) is more flexible.

(<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
(<//~) :: Fractional a => Iso'  s a -> a -> s -> (a, s)


(<^~) :: (Num a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t) infixr 4 Source #

Raise the target of a numerically valued Lens to a non-negative Integral power and return the result.

When you do not need the result of the operation, (^~) is more flexible.

(<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)


(<^^~) :: (Fractional a, Integral e) => LensLike ((,) a) s t a a -> e -> s -> (a, t) infixr 4 Source #

Raise the target of a fractionally valued Lens to an Integral power and return the result.

When you do not need the result of the operation, (^^~) is more flexible.

(<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s)
(<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> s -> (a, s)


(<**~) :: Floating a => LensLike ((,) a) s t a a -> a -> s -> (a, t) infixr 4 Source #

Raise the target of a floating-point valued Lens to an arbitrary power and return the result.

When you do not need the result of the operation, (**~) is more flexible.

(<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
(<**~) :: Floating a => Iso' s a  -> a -> s -> (a, s)


(<||~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t) infixr 4 Source #

Logically || a Boolean valued Lens and return the result.

When you do not need the result of the operation, (||~) is more flexible.

(<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<||~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)


(<&&~) :: LensLike ((,) Bool) s t Bool Bool -> Bool -> s -> (Bool, t) infixr 4 Source #

Logically && a Boolean valued Lens and return the result.

When you do not need the result of the operation, (&&~) is more flexible.

(<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<&&~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)


(<<>~) :: Monoid m => LensLike ((,) m) s t m m -> m -> s -> (m, t) infixr 4 Source #

mappend a monoidal value onto the end of the target of a Lens and return the result.

When you do not need the result of the operation, (<>~) is more flexible.

(<<%~) :: LensLike ((,) a) s t a b -> (a -> b) -> s -> (a, t) infixr 4 Source #

Modify the target of a Lens, but return the old value.

When you do not need the old value, (%~) is more flexible.

(<<%~) ::             Lens s t a b      -> (a -> b) -> s -> (a, t)
(<<%~) ::             Iso s t a b       -> (a -> b) -> s -> (a, t)
(<<%~) :: Monoid a => Traversal s t a b -> (a -> b) -> s -> (a, t)


(<<.~) :: LensLike ((,) a) s t a b -> b -> s -> (a, t) infixr 4 Source #

Replace the target of a Lens, but return the old value.

When you do not need the old value, (.~) is more flexible.

(<<.~) ::             Lens s t a b      -> b -> s -> (a, t)
(<<.~) ::             Iso s t a b       -> b -> s -> (a, t)
(<<.~) :: Monoid a => Traversal s t a b -> b -> s -> (a, t)


(<<?~) :: LensLike ((,) a) s t a (Maybe b) -> b -> s -> (a, t) infixr 4 Source #

Replace the target of a Lens with a Just value, but return the old value.

If you do not need the old value (?~) is more flexible.

>>> import Data.Map as Map
>>> _2.at "hello" <<?~ "world" $(42,Map.fromList [("goodnight","gracie")]) (Nothing,(42,fromList [("goodnight","gracie"),("hello","world")]))  (<<?~) :: Iso s t a (Maybe b) -> b -> s -> (a, t) (<<?~) :: Lens s t a (Maybe b) -> b -> s -> (a, t) (<<?~) :: Traversal s t a (Maybe b) -> b -> s -> (a, t)  (<<+~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 Source # Increment the target of a numerically valued Lens and return the old value. When you do not need the old value, (+~) is more flexible. >>> (a,b) & _1 <<+~ c (a,(a + c,b))  >>> (a,b) & _2 <<+~ c (b,(a,b + c))  (<<+~) :: Num a => Lens' s a -> a -> s -> (a, s) (<<+~) :: Num a => Iso' s a -> a -> s -> (a, s)  (<<-~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 Source # Decrement the target of a numerically valued Lens and return the old value. When you do not need the old value, (-~) is more flexible. >>> (a,b) & _1 <<-~ c (a,(a - c,b))  >>> (a,b) & _2 <<-~ c (b,(a,b - c))  (<<-~) :: Num a => Lens' s a -> a -> s -> (a, s) (<<-~) :: Num a => Iso' s a -> a -> s -> (a, s)  (<<*~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 Source # Multiply the target of a numerically valued Lens and return the old value. When you do not need the old value, (-~) is more flexible. >>> (a,b) & _1 <<*~ c (a,(a * c,b))  >>> (a,b) & _2 <<*~ c (b,(a,b * c))  (<<*~) :: Num a => Lens' s a -> a -> s -> (a, s) (<<*~) :: Num a => Iso' s a -> a -> s -> (a, s)  (<<//~) :: Fractional a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 Source # Divide the target of a numerically valued Lens and return the old value. When you do not need the old value, (//~) is more flexible. >>> (a,b) & _1 <<//~ c (a,(a / c,b))  >>> ("Hawaii",10) & _2 <<//~ 2 (10.0,("Hawaii",5.0))  (<<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s) (<<//~) :: Fractional a => Iso' s a -> a -> s -> (a, s)  (<<^~) :: (Num a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s) infixr 4 Source # Raise the target of a numerically valued Lens to a non-negative power and return the old value. When you do not need the old value, (^~) is more flexible. (<<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s) (<<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)  (<<^^~) :: (Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s) infixr 4 Source # Raise the target of a fractionally valued Lens to an integral power and return the old value. When you do not need the old value, (^^~) is more flexible. (<<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s) (<<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> S -> (a, s)  (<<**~) :: Floating a => LensLike' ((,) a) s a -> a -> s -> (a, s) infixr 4 Source # Raise the target of a floating-point valued Lens to an arbitrary power and return the old value. When you do not need the old value, (**~) is more flexible. >>> (a,b) & _1 <<**~ c (a,(a**c,b))  >>> (a,b) & _2 <<**~ c (b,(a,b**c))  (<<**~) :: Floating a => Lens' s a -> a -> s -> (a, s) (<<**~) :: Floating a => Iso' s a -> a -> s -> (a, s)  (<<||~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s) infixr 4 Source # Logically || the target of a Bool-valued Lens and return the old value. When you do not need the old value, (||~) is more flexible. >>> (False,6) & _1 <<||~ True (False,(True,6))  >>> ("hello",True) & _2 <<||~ False (True,("hello",True))  (<<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s) (<<||~) :: Iso' s Bool -> Bool -> s -> (Bool, s)  (<<&&~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s) infixr 4 Source # Logically && the target of a Bool-valued Lens and return the old value. When you do not need the old value, (&&~) is more flexible. >>> (False,6) & _1 <<&&~ True (False,(False,6))  >>> ("hello",True) & _2 <<&&~ False (True,("hello",False))  (<<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s) (<<&&~) :: Iso' s Bool -> Bool -> s -> (Bool, s)  (<<<>~) :: Monoid r => LensLike' ((,) r) s r -> r -> s -> (r, s) infixr 4 Source # Modify the target of a monoidally valued Lens by mappending a new value and return the old value. When you do not need the old value, (<>~) is more flexible. >>> (Sum a,b) & _1 <<<>~ Sum c (Sum {getSum = a},(Sum {getSum = a + c},b))  >>> _2 <<<>~ ", 007"$ ("James", "Bond")
("Bond",("James","Bond, 007"))

(<<<>~) :: Monoid r => Lens' s r -> r -> s -> (r, s)
(<<<>~) :: Monoid r => Iso' s r -> r -> s -> (r, s)


# Setting State with Passthrough

(<%=) :: MonadState s m => LensLike ((,) b) s s a b -> (a -> b) -> m b infix 4 Source #

Modify the target of a Lens into your Monad's state by a user supplied function and return the result.

When applied to a Traversal, it this will return a monoidal summary of all of the intermediate results.

When you do not need the result of the operation, (%=) is more flexible.

(<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
(<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
(<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a


(<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Add to the target of a numerically valued Lens into your Monad's state and return the result.

When you do not need the result of the addition, (+=) is more flexible.

(<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a


(<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Subtract from the target of a numerically valued Lens into your Monad's state and return the result.

When you do not need the result of the subtraction, (-=) is more flexible.

(<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a


(<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Multiply the target of a numerically valued Lens into your Monad's state and return the result.

When you do not need the result of the multiplication, (*=) is more flexible.

(<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a


(<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Divide the target of a fractionally valued Lens into your Monad's state and return the result.

When you do not need the result of the division, (//=) is more flexible.

(<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
(<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a


(<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 Source #

Raise the target of a numerically valued Lens into your Monad's state to a non-negative Integral power and return the result.

When you do not need the result of the operation, (^=) is more flexible.

(<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
(<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> e -> m a


(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 Source #

Raise the target of a fractionally valued Lens into your Monad's state to an Integral power and return the result.

When you do not need the result of the operation, (^^=) is more flexible.

(<^^=) :: (MonadState s m, Fractional b, Integral e) => Lens' s a -> e -> m a
(<^^=) :: (MonadState s m, Fractional b, Integral e) => Iso' s a  -> e -> m a


(<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Raise the target of a floating-point valued Lens into your Monad's state to an arbitrary power and return the result.

When you do not need the result of the operation, (**=) is more flexible.

(<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
(<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a


(<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 Source #

Logically || a Boolean valued Lens into your Monad's state and return the result.

When you do not need the result of the operation, (||=) is more flexible.

(<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<||=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool


(<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 Source #

Logically && a Boolean valued Lens into your Monad's state and return the result.

When you do not need the result of the operation, (&&=) is more flexible.

(<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<&&=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool


(<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r infix 4 Source #

mappend a monoidal value onto the end of the target of a Lens into your Monad's state and return the result.

When you do not need the result of the operation, (<>=) is more flexible.

(<<%=) :: (Strong p, MonadState s m) => Over p ((,) a) s s a b -> p a b -> m a infix 4 Source #

Modify the target of a Lens into your Monad's state by a user supplied function and return the old value that was replaced.

When applied to a Traversal, this will return a monoidal summary of all of the old values present.

When you do not need the result of the operation, (%=) is more flexible.

(<<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
(<<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
(<<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a

(<<%=) :: MonadState s m => LensLike ((,)a) s s a b -> (a -> b) -> m a

(<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a infix 4 Source #

Replace the target of a Lens into your Monad's state with a user supplied value and return the old value that was replaced.

When applied to a Traversal, this will return a monoidal summary of all of the old values present.

When you do not need the result of the operation, (.=) is more flexible.

(<<.=) :: MonadState s m             => Lens' s a      -> a -> m a
(<<.=) :: MonadState s m             => Iso' s a       -> a -> m a
(<<.=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m a


(<<?=) :: MonadState s m => LensLike ((,) a) s s a (Maybe b) -> b -> m a infix 4 Source #

Replace the target of a Lens into your Monad's state with Just a user supplied value and return the old value that was replaced.

When applied to a Traversal, this will return a monoidal summary of all of the old values present.

When you do not need the result of the operation, (?=) is more flexible.

(<<?=) :: MonadState s m             => Lens s t a (Maybe b)      -> b -> m a
(<<?=) :: MonadState s m             => Iso s t a (Maybe b)       -> b -> m a
(<<?=) :: (MonadState s m, Monoid a) => Traversal s t a (Maybe b) -> b -> m a


(<<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Modify the target of a Lens into your Monad's state by adding a value and return the old value that was replaced.

When you do not need the result of the operation, (+=) is more flexible.

(<<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a


(<<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Modify the target of a Lens into your Monad's state by subtracting a value and return the old value that was replaced.

When you do not need the result of the operation, (-=) is more flexible.

(<<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a


(<<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Modify the target of a Lens into your Monad's state by multipling a value and return the old value that was replaced.

When you do not need the result of the operation, (*=) is more flexible.

(<<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
(<<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a


(<<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Modify the target of a Lens into your Monads state by dividing by a value and return the old value that was replaced.

When you do not need the result of the operation, (//=) is more flexible.

(<<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
(<<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a


(<<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 Source #

Modify the target of a Lens into your Monad's state by raising it by a non-negative power and return the old value that was replaced.

When you do not need the result of the operation, (^=) is more flexible.

(<<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
(<<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> a -> m a


(<<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a infix 4 Source #

Modify the target of a Lens into your Monad's state by raising it by an integral power and return the old value that was replaced.

When you do not need the result of the operation, (^^=) is more flexible.

(<<^^=) :: (MonadState s m, Fractional a, Integral e) => Lens' s a -> e -> m a
(<<^^=) :: (MonadState s m, Fractional a, Integral e) => Iso' s a -> e -> m a


(<<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source #

Modify the target of a Lens into your Monad's state by raising it by an arbitrary power and return the old value that was replaced.

When you do not need the result of the operation, (**=) is more flexible.

(<<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
(<<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a


(<<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 Source #

Modify the target of a Lens into your Monad's state by taking its logical || with a value and return the old value that was replaced.

When you do not need the result of the operation, (||=) is more flexible.

(<<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<<||=) :: MonadState s m => Iso' s Bool -> Bool -> m Bool


(<<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 Source #

Modify the target of a Lens into your Monad's state by taking its logical && with a value and return the old value that was replaced.

When you do not need the result of the operation, (&&=) is more flexible.

(<<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
(<<&&=) :: MonadState s m => Iso' s Bool -> Bool -> m Bool


(<<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r infix 4 Source #

Modify the target of a Lens into your Monad's state by mappending a value and return the old value that was replaced.

When you do not need the result of the operation, (<>=) is more flexible.

(<<<>=) :: (MonadState s m, Monoid r) => Lens' s r -> r -> m r
(<<<>=) :: (MonadState s m, Monoid r) => Iso' s r -> r -> m r


(<<~) :: MonadState s m => ALens s s a b -> m b -> m b infixr 2 Source #

Run a monadic action, and set the target of Lens to its result.

(<<~) :: MonadState s m => Iso s s a b   -> m b -> m b
(<<~) :: MonadState s m => Lens s s a b  -> m b -> m b


NB: This is limited to taking an actual Lens than admitting a Traversal because there are potential loss of state issues otherwise.

# Cloning Lenses

cloneLens :: ALens s t a b -> Lens s t a b Source #

Cloning a Lens is one way to make sure you aren't given something weaker, such as a Traversal and can be used as a way to pass around lenses that have to be monomorphic in f.

Note: This only accepts a proper Lens.

>>> let example l x = set (cloneLens l) (x^.cloneLens l + 1) x in example _2 ("hello",1,"you")
("hello",2,"you")


cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b Source #

Clone a Lens as an IndexedPreservingLens that just passes through whatever index is on any IndexedLens, IndexedFold, IndexedGetter or IndexedTraversal it is composed with.

cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b Source #

Clone an IndexedLens as an IndexedLens with the same index.

# Arrow operators

overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t Source #

over for Arrows.

Unlike over, overA can't accept a simple Setter, but requires a full lens, or close enough.

>>> overA _1 ((+1) *** (+2)) ((1,2),6)
((2,4),6)

overA :: Arrow ar => Lens s t a b -> ar a b -> ar s t


# ALens Combinators

storing :: ALens s t a b -> b -> s -> t Source #

A version of set that works on ALens.

>>> storing _2 "world" ("hello","there")
("hello","world")


(^#) :: s -> ALens s t a b -> a infixl 8 Source #

A version of (^.) that works on ALens.

>>> ("hello","world")^#_2
"world"


(#~) :: ALens s t a b -> b -> s -> t infixr 4 Source #

A version of (.~) that works on ALens.

>>> ("hello","there") & _2 #~ "world"
("hello","world")


(#%~) :: ALens s t a b -> (a -> b) -> s -> t infixr 4 Source #

A version of (%~) that works on ALens.

>>> ("hello","world") & _2 #%~ length
("hello",5)


(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t infixr 4 Source #

A version of (%%~) that works on ALens.

>>> ("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
(5,("hello","world!"))


(<#~) :: ALens s t a b -> b -> s -> (b, t) infixr 4 Source #

A version of (<.~) that works on ALens.

>>> ("hello","there") & _2 <#~ "world"
("world",("hello","world"))


(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t) infixr 4 Source #

A version of (<%~) that works on ALens.

>>> ("hello","world") & _2 <#%~ length
(5,("hello",5))


(#=) :: MonadState s m => ALens s s a b -> b -> m () infix 4 Source #

A version of (.=) that works on ALens.

(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m () infix 4 Source #

A version of (%=) that works on ALens.

(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r infix 4 Source #

A version of (%%=) that works on ALens.

(<#=) :: MonadState s m => ALens s s a b -> b -> m b infix 4 Source #

A version of (<.=) that works on ALens.

(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b infix 4 Source #

A version of (<%=) that works on ALens.

# Common Lenses

devoid :: Over p f Void Void a b Source #

There is a field for every type in the Void. Very zen.

>>> [] & mapped.devoid +~ 1
[]

>>> Nothing & mapped.devoid %~ abs
Nothing

devoid :: Lens' Void a


united :: Lens' a () Source #

We can always retrieve a () from any type.

>>> "hello"^.united
()

>>> "hello" & united .~ ()
"hello"


# Context

data Context a b t Source #

The indexed store can be used to characterize a Lens and is used by cloneLens.

Context a b t is isomorphic to newtype Context a b t = Context { runContext :: forall f. Functor f => (a -> f b) -> f t }, and to exists s. (s, Lens s t a b).

A Context is like a Lens that has already been applied to a some structure.

Constructors

 Context (b -> t) a

Instances

 Source # Methodsipos :: Context a c t -> a Source #ipeek :: c -> Context a c t -> t Source #ipeeks :: (a -> c) -> Context a c t -> t Source #iseek :: b -> Context a c t -> Context b c t Source #iseeks :: (a -> b) -> Context a c t -> Context b c t Source #iexperiment :: Functor f => (b -> f c) -> Context b c t -> f t Source #context :: Context a b t -> Context a b t Source # Source # Methodsiextract :: Context a a t -> t Source #iduplicate :: Context a c t -> Context a b (Context b c t) Source #iextend :: (Context b c t -> r) -> Context a c t -> Context a b r Source # Source # Methodsifmap :: (s -> t) -> Context a b s -> Context a b t Source # (~) * a b => ComonadStore a (Context a b) Source # Methodspos :: Context a b a -> a #peek :: a -> Context a b a -> a #peeks :: (a -> a) -> Context a b a -> a #seek :: a -> Context a b a -> Context a b a #seeks :: (a -> a) -> Context a b a -> Context a b a #experiment :: Functor f => (a -> f a) -> Context a b a -> f a # Functor (Context a b) Source # Methodsfmap :: (a -> b) -> Context a b a -> Context a b b #(<\$) :: a -> Context a b b -> Context a b a # (~) * a b => Comonad (Context a b) Source # Methodsextract :: Context a b a -> a #duplicate :: Context a b a -> Context a b (Context a b a) #extend :: (Context a b a -> b) -> Context a b a -> Context a b b # Source # Methodssell :: (LiftedRep -> LiftedRep) a (Context a b b) Source #

type Context' a = Context a a Source #

type Context' a s = Context a a s

locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b Source #

This Lens lets you view the current pos of any indexed store comonad and seek to a new position. This reduces the API for working these instances to a single Lens.

ipos w ≡ w ^. locus
iseek s w ≡ w & locus .~ s
iseeks f w ≡ w & locus %~ f

locus :: Lens' (Context' a s) a
locus :: Conjoined p => Lens' (Pretext' p a s) a
locus :: Conjoined p => Lens' (PretextT' p g a s) a


# Lens fusion

fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b Source #

Fuse a composition of lenses using Yoneda to provide fmap fusion.

In general, given a pair of lenses foo and bar

fusing (foo.bar) = foo.bar


however, foo and bar are either going to fmap internally or they are trivial.

fusing exploits the Yoneda lemma to merge these separate uses into a single fmap.

This is particularly effective when the choice of functor f is unknown at compile time or when the Lens foo.bar in the above description is recursive or complex enough to prevent inlining.

fusing :: Lens s t a b -> Lens s t a b