Control.Lens.Getter

A Getter s a is just any function (s -> a), which we've flipped into continuation passing style, (a -> r) -> s -> r and decorated with Const to obtain:

type Getting r s a = (a -> Const r a) -> s -> Const r s

If we restrict access to knowledge about the type r, we could get:

type Getter s a = forall r. Getting r s a

But we actually hide the use of Const behind a class Gettable to report error messages from type class resolution rather than at unification time, where they are much uglier.

type Getter s a = forall f. Gettable f => (a -> f a) -> s -> f s

Everything you can do with a function, you can do with a Getter, but note that because of the continuation passing style (.) composes them in the opposite order.

Since it is only a function, every Getter obviously only retrieves a single value for a given input.

Getters

type Getter s a = forall f. (Contravariant f, Functor f) => (a -> f a) -> s -> f s

A Getter describes how to retrieve a single value in a way that can be composed with other LensLike constructions.

Unlike a Lens a Getter is read-only. Since a Getter cannot be used to write back there are no Lens laws that can be applied to it. In fact, it is isomorphic to an arbitrary function from (s -> a).

Moreover, a Getter can be used directly as a Fold, since it just ignores the Applicative.

type IndexedGetter i s a = forall p f. (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s

Every IndexedGetter is a valid IndexedFold and can be used for Getting like a Getter.

type Getting r s a = (a -> Const r a) -> s -> Const r s

When you see this in a type signature it indicates that you can pass the function a Lens, Getter, Traversal, Fold, Prism, Iso, or one of the indexed variants, and it will just "do the right thing".

Most Getter combinators are able to be used with both a Getter or a Fold in limited situations, to do so, they need to be monomorphic in what we are going to extract with Const. To be compatible with Lens, Traversal and Iso we also restricted choices of the irrelevant t and b parameters.

If a function accepts a Getting r s a, then when r is a Monoid, then you can pass a Fold (or Traversal), otherwise you can only pass this a Getter or Lens.

type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s

Used to consume an IndexedFold.

type Accessing p m s a = p a (Const m a) -> s -> Const m s

This is a convenient alias used when consuming (indexed) getters and (indexed) folds in a highly general fashion.

Building Getters

to :: (s -> a) -> IndexPreservingGetter s a

Build a Getter from an arbitrary Haskell function.

 to f . to g ≡ to (g . f)

 a ^. to f ≡ f a

>>> a ^.to f
f a

>>> ("hello","world")^.to snd
"world"

>>> 5^.to succ
6

>>> (0, -5)^._2.to abs
5

ito :: (s -> (i, a)) -> IndexedGetter i s a

Combinators for Getters and Folds

(^.) :: s -> Getting a s a -> a

View the value pointed to by a Getter or Lens or the result of folding over all the results of a Fold or Traversal that points at a monoidal values.

This is the same operation as view with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be performed with (.).

>>> (a,b)^._2
b

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

>>> import Data.Complex
>>> ((0, 1 :+ 2), 3)^._1._2.to magnitude
2.23606797749979

 (^.) ::             s -> Getter s a     -> a
 (^.) :: Monoid m => s -> Fold s m       -> m
 (^.) ::             s -> Iso' s a       -> a
 (^.) ::             s -> Lens' s a      -> a
 (^.) :: Monoid m => s -> Traversal' s m -> m

view :: MonadReader s m => Getting a s a -> m a

View the value pointed to by a Getter, Iso or Lens or the result of folding over all the results of a Fold or Traversal that points at a monoidal value.

 view . to ≡ id

>>> view (to f) a
f a

>>> view _2 (1,"hello")
"hello"

>>> view (to succ) 5
6

>>> view (_2._1) ("hello",("world","!!!"))
"world"

As view is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

 view ::             Getter s a     -> s -> a
 view :: Monoid m => Fold s m       -> s -> m
 view ::             Iso' s a       -> s -> a
 view ::             Lens' s a      -> s -> a
 view :: Monoid m => Traversal' s m -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

 view :: MonadReader s m             => Getter s a     -> m a
 view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
 view :: MonadReader s m             => Iso' s a       -> m a
 view :: MonadReader s m             => Lens' s a      -> m a
 view :: (MonadReader s m, Monoid a) => Traversal' s a -> m a

views :: (Profunctor p, MonadReader s m) => Optical p (->) (Const r) s s a a -> p a r -> m r

View a function of the value pointed to by a Getter or Lens or the result of folding over the result of mapping the targets of a Fold or Traversal.

 views l f ≡ view (l . to f)

>>> views (to f) g a
g (f a)

>>> views _2 length (1,"hello")
5

As views is commonly used to access the target of a Getter or obtain a monoidal summary of the targets of a Fold, It may be useful to think of it as having one of these more restricted signatures:

 views ::             Getter s a     -> (a -> r) -> s -> r
 views :: Monoid m => Fold s a       -> (a -> m) -> s -> m
 views ::             Iso' s a       -> (a -> r) -> s -> r
 views ::             Lens' s a      -> (a -> r) -> s -> r
 views :: Monoid m => Traversal' s a -> (a -> m) -> s -> m

In a more general setting, such as when working with a Monad transformer stack you can use:

 view :: MonadReader s m             => Getter s a     -> m a
 view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
 view :: MonadReader s m             => Iso' s a       -> m a
 view :: MonadReader s m             => Lens' s a      -> m a
 view :: (MonadReader s m, Monoid a) => Traversal' s a -> m a

 views :: MonadReader s m => Getting r s a -> (a -> r) -> m r

use :: MonadState s m => Getting a s a -> m a

Use the target of a Lens, Iso, or Getter in the current state, or use a summary of a Fold or Traversal that points to a monoidal value.

>>> evalState (use _1) (a,b)
a

>>> evalState (use _1) ("hello","world")
"hello"

 use :: MonadState s m             => Getter s a     -> m a
 use :: (MonadState s m, Monoid r) => Fold s r       -> m r
 use :: MonadState s m             => Iso' s a       -> m a
 use :: MonadState s m             => Lens' s a      -> m a
 use :: (MonadState s m, Monoid r) => Traversal' s r -> m r

uses :: (Profunctor p, MonadState s m) => Optical p (->) (Const r) s s a a -> p a r -> m r

Use the target of a Lens, Iso or Getter in the current state, or use a summary of a Fold or Traversal that points to a monoidal value.

>>> evalState (uses _1 length) ("hello","world")
5

 uses :: MonadState s m             => Getter s a     -> (a -> r) -> m r
 uses :: (MonadState s m, Monoid r) => Fold s a       -> (a -> r) -> m r
 uses :: MonadState s m             => Lens' s a      -> (a -> r) -> m r
 uses :: MonadState s m             => Iso' s a       -> (a -> r) -> m r
 uses :: (MonadState s m, Monoid r) => Traversal' s a -> (a -> r) -> m r

 uses :: MonadState s m => Getting r s t a b -> (a -> r) -> m r

listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u)

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

 listening :: MonadWriter w m             => Getter w u     -> m a -> m (a, u)
 listening :: MonadWriter w m             => Lens' w u      -> m a -> m (a, u)
 listening :: MonadWriter w m             => Iso' w u       -> m a -> m (a, u)
 listening :: (MonadWriter w m, Monoid u) => Fold w u       -> m a -> m (a, u)
 listening :: (MonadWriter w m, Monoid u) => Traversal' w u -> m a -> m (a, u)
 listening :: (MonadWriter w m, Monoid u) => Prism' w u     -> m a -> m (a, u)

listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v)

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

 listenings :: MonadWriter w m             => Getter w u     -> (u -> v) -> m a -> m (a, v)
 listenings :: MonadWriter w m             => Lens' w u      -> (u -> v) -> m a -> m (a, v)
 listenings :: MonadWriter w m             => Iso' w u       -> (u -> v) -> m a -> m (a, v)
 listenings :: (MonadWriter w m, Monoid v) => Fold w u       -> (u -> v) -> m a -> m (a, v)
 listenings :: (MonadWriter w m, Monoid v) => Traversal' w u -> (u -> v) -> m a -> m (a, v)
 listenings :: (MonadWriter w m, Monoid v) => Prism' w u     -> (u -> v) -> m a -> m (a, v)

Indexed Getters

Indexed Getter Combinators

(^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a)

View the value pointed to by a Getter or Lens.

This is the same operation as iview with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be performed with (.).

 (^@.) :: s -> IndexedGetter i s a -> (i, a)
 (^@.) :: s -> IndexedLens' i s a  -> (i, a)

The result probably doesn't have much meaning when applied to an IndexedFold.

iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a)

View the index and value of an IndexedGetter into the current environment as a pair.

When applied to an IndexedFold the result will most likely be a nonsensical monoidal summary of the indices tupled with a monoidal summary of the values and probably not whatever it is you wanted.

iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r

View a function of the index and value of an IndexedGetter into the current environment.

When applied to an IndexedFold the result will be a monoidal summary instead of a single answer.

 iviews ≡ ifoldMapOf

iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a)

Use the index and value of an IndexedGetter into the current state as a pair.

When applied to an IndexedFold the result will most likely be a nonsensical monoidal summary of the indices tupled with a monoidal summary of the values and probably not whatever it is you wanted.

iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r

Use a function of the index and value of an IndexedGetter into the current state.

When applied to an IndexedFold the result will be a monoidal summary instead of a single answer.

ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u))

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

 ilistening :: MonadWriter w m             => IndexedGetter i w u     -> m a -> m (a, (i, u))
 ilistening :: MonadWriter w m             => IndexedLens' i w u      -> m a -> m (a, (i, u))
 ilistening :: (MonadWriter w m, Monoid u) => IndexedFold i w u       -> m a -> m (a, (i, u))
 ilistening :: (MonadWriter w m, Monoid u) => IndexedTraversal' i w u -> m a -> m (a, (i, u))

ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v)

This is a generalized form of listen that only extracts the portion of the log that is focused on by a Getter. If given a Fold or a Traversal then a monoidal summary of the parts of the log that are visited will be returned.

 ilistenings :: MonadWriter w m             => IndexedGetter w u     -> (i -> u -> v) -> m a -> m (a, v)
 ilistenings :: MonadWriter w m             => IndexedLens' w u      -> (i -> u -> v) -> m a -> m (a, v)
 ilistenings :: (MonadWriter w m, Monoid v) => IndexedFold w u       -> (i -> u -> v) -> m a -> m (a, v)
 ilistenings :: (MonadWriter w m, Monoid v) => IndexedTraversal' w u -> (i -> u -> v) -> m a -> m (a, v)

Implementation Details

class Contravariant f where

Any instance should be subject to the following laws:

 contramap id = id
 contramap f . contramap g = contramap (g . f)

Note, that the second law follows from the free theorem of the type of contramap and the first law, so you need only check that the former condition holds.

Methods

contramap :: (a -> b) -> f b -> f a

Instances

Contravariant Predicate

A Predicate is a Contravariant Functor, because contramap can apply its function argument to the input of the predicate.

Contravariant Comparison

A Comparison is a Contravariant Functor, because contramap can apply its function argument to each input to each input to the comparison function.

Contravariant Equivalence

Equivalence relations are Contravariant, because you can apply the contramapped function to each input to the equivalence relation.

Contravariant (Const a)

Contravariant (Op a)

Contravariant (Proxy *)

Contravariant f => Contravariant (Reverse f)

Contravariant f => Contravariant (Backwards f)

Contravariant (Constant a)

Contravariant f => Contravariant (Indexing64 f)

Contravariant f => Contravariant (Indexing f)

(Contravariant f, Contravariant g) => Contravariant (Coproduct f g)

(Functor f, Contravariant g) => Contravariant (ComposeFC f g)

(Contravariant f, Functor g) => Contravariant (ComposeCF f g)

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

(Contravariant f, Contravariant g) => Contravariant (Product f g)

Contravariant (Effect m r)

Contravariant f => Contravariant (AlongsideRight f a)

Contravariant f => Contravariant (AlongsideLeft f b)

(Profunctor p, Contravariant g) => Contravariant (PretextT p g a b)

(Profunctor p, Contravariant g) => Contravariant (BazaarT1 p g a b)

(Profunctor p, Contravariant g) => Contravariant (BazaarT p g a b)

Contravariant f => Contravariant (TakingWhile p f a b)

Contravariant (EffectRWS w st m s)

coerce :: (Contravariant f, Functor f) => f a -> f b

This Generalizes Const so we can apply simple Applicative transformations to it and so we can get nicer error messages.

A Functor you can coerce ignores its argument, which it carries solely as a phantom type parameter.

By the Functor and Contravariant laws, an instance of Gettable will necessarily satisfy:

id = fmap f = coerce = contramap g

coerced :: (Functor f, Contravariant f) => LensLike f s t a b -> LensLike' f s a

Coerce a Gettable LensLike to a Simple LensLike. This is useful when using a Traversal that is not simple as a Getter or a Fold.

newtype Const a b

Constructors

Const

Fields

getConst :: a

Instances

Bitraversable Const

Bifunctor Const

Bifoldable Const

Effective Identity r (Const r)

Functor (Const m)

Monoid m => Applicative (Const m)

Foldable (Const m)

Traversable (Const m)

Contravariant (Const a)

Semigroup m => Apply (Const m)

Semigroup a => Semigroup (Const a b)

Wrapped (Const a x)

~ * t (Const a' x') => Rewrapped (Const a x) t

class (Contravariant f, Functor f) => Gettable f

This class is provided mostly for backwards compatibility with lens 3.8, but it can also shorten type signatures.

Instances

(Contravariant f, Functor f) => Gettable f