lens-4.15.3: Lenses, Folds and Traversals

Copyright | (C) 2012-16 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | provisional
Portability | Rank2Types
Safe Haskell | Safe
Language | Haskell98

Control.Lens.Getter

Contents

- Getters
- Building Getters
- Combinators for Getters and Folds
- Indexed Getters
  - Indexed Getter Combinators
- Implementation Details

Description

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

However, for `Getter` (but not for `Getting`) we actually permit any functor `f` which is an instance of both `Functor` and `Contravariant`:

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

A common question is whether you can combine multiple `Getter`s to retrieve multiple values. Recall that all `Getter`s are `Fold`s and that we have a ``Monoid` m => `Applicative` (`Const` m)` instance to play with. Knowing this, we can use ``<>`` to glue `Fold`s together:

    >>> import Data.Monoid
    >>> (1, 2, 3, 4, 5) ^.. (_2 <> _3 <> _5)
    [2,3,5]

Synopsis

- type Getter s a = forall f. (Contravariant f, Functor f) => (a -> f a) -> s -> f s
- type IndexedGetter i s a = forall p f. (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s
- type Getting r s a = (a -> Const r a) -> s -> Const r s
- type IndexedGetting i m s a = Indexed i a (Const m a) -> s -> Const m s
- type Accessing p m s a = p a (Const m a) -> s -> Const m s
- to :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a
- ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a
- like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a
- ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a
- (^.) :: s -> Getting a s a -> a
- view :: MonadReader s m => Getting a s a -> m a
- views :: MonadReader s m => LensLike' (Const r) s a -> (a -> r) -> m r
- use :: MonadState s m => Getting a s a -> m a
- uses :: MonadState s m => LensLike' (Const r) s a -> (a -> r) -> m r
- listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u)
- listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v)
- (^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a)
- iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a)
- iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
- iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a)
- iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r
- ilistening :: MonadWriter w m => IndexedGetting i (i, u) 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)
- class Contravariant f where
- getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a
- newtype Const k a b :: forall k. * -> k -> * = Const {
  - getConst :: a
  }

# 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 :: (Profunctor p, Contravariant f) => (s -> a) -> Optic' p f s a #

Build an (index-preserving) `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

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

ito :: (Indexable i p, Contravariant f) => (s -> (i, a)) -> Over' p f s a #

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

like :: (Profunctor p, Contravariant f, Functor f) => a -> Optic' p f s a #

Build an constant-valued (index-preserving) `Getter` from an arbitrary Haskell value.

    like a . like b ≡ like b
    a ^. like b ≡ b
    a ^. like b ≡ a ^. to (const b)

This can be useful as a second case `failing` a `Fold` e.g. `foo `failing` `like` 0`

    like :: a -> IndexPreservingGetter s a

ilike :: (Indexable i p, Contravariant f, Functor f) => i -> a -> Over' p f s a #

    ilike :: i -> a -> IndexedGetter i s a

# Combinators for Getters and Folds

(^.) :: s -> Getting a s a -> a infixl 8 #

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 :: MonadReader s m => LensLike' (Const r) s a -> (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:

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

    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 :: MonadState s m => LensLike' (Const r) s a -> (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) infixl 8 #

View the index and value of an `IndexedGetter` or `IndexedLens`.

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.

Minimal complete definition

contramap

Methods

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

(>$) :: b -> f b -> f a infixl 4 #

Replace all locations in the output with the same value. The default definition is ``contramap` . `const``, but this may be overridden with a more efficient version.

Instances

Contravariant V1 |
Methods contramap :: (a -> b) -> V1 b -> V1 a # (>$) :: b -> V1 b -> V1 a #
Contravariant U1 |
Methods contramap :: (a -> b) -> U1 b -> U1 a # (>$) :: b -> U1 b -> U1 a #
Contravariant SettableStateVar |
Methods contramap :: (a -> b) -> SettableStateVar b -> SettableStateVar a # (>$) :: b -> SettableStateVar b -> SettableStateVar a #
Contravariant Predicate | A `Predicate` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to the input of the predicate.
Methods contramap :: (a -> b) -> Predicate b -> Predicate a # (>$) :: b -> Predicate b -> Predicate a #
Contravariant Comparison | A `Comparison` is a `Contravariant` `Functor`, because `contramap` can apply its function argument to each input of the comparison function.
Methods contramap :: (a -> b) -> Comparison b -> Comparison a # (>$) :: b -> Comparison b -> Comparison a #
Contravariant Equivalence | Equivalence relations are `Contravariant`, because you can apply the contramapped function to each input to the equivalence relation.
Methods contramap :: (a -> b) -> Equivalence b -> Equivalence a # (>$) :: b -> Equivalence b -> Equivalence a #
Contravariant f => Contravariant (Rec1 f) |
Methods contramap :: (a -> b) -> Rec1 f b -> Rec1 f a # (>$) :: b -> Rec1 f b -> Rec1 f a #
Contravariant (Op a) |
Methods contramap :: (a -> b) -> Op a b -> Op a a # (>$) :: b -> Op a b -> Op a a #
Contravariant (Proxy *) |
Methods contramap :: (a -> b) -> Proxy * b -> Proxy * a # (>$) :: b -> Proxy * b -> Proxy * a #
Contravariant m => Contravariant (ListT m) |
Methods contramap :: (a -> b) -> ListT m b -> ListT m a # (>$) :: b -> ListT m b -> ListT m a #
Contravariant m => Contravariant (MaybeT m) |
Methods contramap :: (a -> b) -> MaybeT m b -> MaybeT m a # (>$) :: b -> MaybeT m b -> MaybeT m a #
Contravariant f => Contravariant (Indexing64 f) # |
Methods contramap :: (a -> b) -> Indexing64 f b -> Indexing64 f a # (>$) :: b -> Indexing64 f b -> Indexing64 f a #
Contravariant f => Contravariant (Indexing f) # |
Methods contramap :: (a -> b) -> Indexing f b -> Indexing f a # (>$) :: b -> Indexing f b -> Indexing f a #
Contravariant (K1 i c) |
Methods contramap :: (a -> b) -> K1 i c b -> K1 i c a # (>$) :: b -> K1 i c b -> K1 i c a #
(Contravariant f, Contravariant g) => Contravariant ((:+:) f g) |
Methods contramap :: (a -> b) -> (f :+: g) b -> (f :+: g) a # (>$) :: b -> (f :+: g) b -> (f :+: g) a #
(Contravariant f, Contravariant g) => Contravariant ((:*:) f g) |
Methods contramap :: (a -> b) -> (f :*: g) b -> (f :*: g) a # (>$) :: b -> (f :*: g) b -> (f :*: g) a #
(Functor f, Contravariant g) => Contravariant ((:.:) f g) |
Methods contramap :: (a -> b) -> (f :.: g) b -> (f :.: g) a # (>$) :: b -> (f :.: g) b -> (f :.: g) a #
Contravariant (Const * a) |
Methods contramap :: (a -> b) -> Const * a b -> Const * a a # (>$) :: b -> Const * a b -> Const * a a #
Contravariant f => Contravariant (Alt * f) |
Methods contramap :: (a -> b) -> Alt * f b -> Alt * f a # (>$) :: b -> Alt * f b -> Alt * f a #
Contravariant f => Contravariant (IdentityT * f) |
Methods contramap :: (a -> b) -> IdentityT * f b -> IdentityT * f a # (>$) :: b -> IdentityT * f b -> IdentityT * f a #
(Functor f, Contravariant g) => Contravariant (ComposeFC f g) |
Methods contramap :: (a -> b) -> ComposeFC f g b -> ComposeFC f g a # (>$) :: b -> ComposeFC f g b -> ComposeFC f g a #
(Contravariant f, Functor g) => Contravariant (ComposeCF f g) |
Methods contramap :: (a -> b) -> ComposeCF f g b -> ComposeCF f g a # (>$) :: b -> ComposeCF f g b -> ComposeCF f g a #
Contravariant m => Contravariant (ErrorT e m) |
Methods contramap :: (a -> b) -> ErrorT e m b -> ErrorT e m a # (>$) :: b -> ErrorT e m b -> ErrorT e m a #
Contravariant m => Contravariant (ExceptT e m) |
Methods contramap :: (a -> b) -> ExceptT e m b -> ExceptT e m a # (>$) :: b -> ExceptT e m b -> ExceptT e m a #
Contravariant m => Contravariant (StateT s m) |
Methods contramap :: (a -> b) -> StateT s m b -> StateT s m a # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant m => Contravariant (StateT s m) |
Methods contramap :: (a -> b) -> StateT s m b -> StateT s m a # (>$) :: b -> StateT s m b -> StateT s m a #
Contravariant m => Contravariant (WriterT w m) |
Methods contramap :: (a -> b) -> WriterT w m b -> WriterT w m a # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant m => Contravariant (WriterT w m) |
Methods contramap :: (a -> b) -> WriterT w m b -> WriterT w m a # (>$) :: b -> WriterT w m b -> WriterT w m a #
Contravariant f => Contravariant (Reverse * f) |
Methods contramap :: (a -> b) -> Reverse * f b -> Reverse * f a # (>$) :: b -> Reverse * f b -> Reverse * f a #
Contravariant f => Contravariant (Backwards * f) |
Methods contramap :: (a -> b) -> Backwards * f b -> Backwards * f a # (>$) :: b -> Backwards * f b -> Backwards * f a #
Contravariant (Constant * a) |
Methods contramap :: (a -> b) -> Constant * a b -> Constant * a a # (>$) :: b -> Constant * a b -> Constant * a a #
Contravariant (Effect m r) # |
Methods contramap :: (a -> b) -> Effect m r b -> Effect m r a # (>$) :: b -> Effect m r b -> Effect m r a #
Contravariant f => Contravariant (AlongsideRight f a) # |
Methods contramap :: (a -> b) -> AlongsideRight f a b -> AlongsideRight f a a # (>$) :: b -> AlongsideRight f a b -> AlongsideRight f a a #
Contravariant f => Contravariant (AlongsideLeft f b) # |
Methods contramap :: (a -> b) -> AlongsideLeft f b b -> AlongsideLeft f b a # (>$) :: b -> AlongsideLeft f b b -> AlongsideLeft f b a #
Contravariant f => Contravariant (M1 i c f) |
Methods contramap :: (a -> b) -> M1 i c f b -> M1 i c f a # (>$) :: b -> M1 i c f b -> M1 i c f a #
(Contravariant f, Contravariant g) => Contravariant (Sum * f g) |
Methods contramap :: (a -> b) -> Sum * f g b -> Sum * f g a # (>$) :: b -> Sum * f g b -> Sum * f g a #
(Contravariant f, Contravariant g) => Contravariant (Product * f g) |
Methods contramap :: (a -> b) -> Product * f g b -> Product * f g a # (>$) :: b -> Product * f g b -> Product * f g a #
Contravariant m => Contravariant (ReaderT * r m) |
Methods contramap :: (a -> b) -> ReaderT * r m b -> ReaderT * r m a # (>$) :: b -> ReaderT * r m b -> ReaderT * r m a #
(Functor f, Contravariant g) => Contravariant (Compose * * f g) |
Methods contramap :: (a -> b) -> Compose * * f g b -> Compose * * f g a # (>$) :: b -> Compose * * f g b -> Compose * * f g a #
Contravariant m => Contravariant (RWST r w s m) |
Methods contramap :: (a -> b) -> RWST r w s m b -> RWST r w s m a # (>$) :: b -> RWST r w s m b -> RWST r w s m a #
Contravariant m => Contravariant (RWST r w s m) |
Methods contramap :: (a -> b) -> RWST r w s m b -> RWST r w s m a # (>$) :: b -> RWST r w s m b -> RWST r w s m a #
Contravariant (EffectRWS w st m s) # |
Methods contramap :: (a -> b) -> EffectRWS w st m s b -> EffectRWS w st m s a # (>$) :: b -> EffectRWS w st m s b -> EffectRWS w st m s a #
(Profunctor p, Contravariant g) => Contravariant (PretextT p g a b) # |
Methods contramap :: (a -> b) -> PretextT p g a b b -> PretextT p g a b a # (>$) :: b -> PretextT p g a b b -> PretextT p g a b a #
(Profunctor p, Contravariant g) => Contravariant (BazaarT1 p g a b) # |
Methods contramap :: (a -> b) -> BazaarT1 p g a b b -> BazaarT1 p g a b a # (>$) :: b -> BazaarT1 p g a b b -> BazaarT1 p g a b a #
(Profunctor p, Contravariant g) => Contravariant (BazaarT p g a b) # |
Methods contramap :: (a -> b) -> BazaarT p g a b b -> BazaarT p g a b a # (>$) :: b -> BazaarT p g a b b -> BazaarT p g a b a #
Contravariant f => Contravariant (TakingWhile p f a b) # |
Methods contramap :: (a -> b) -> TakingWhile p f a b b -> TakingWhile p f a b a # (>$) :: b -> TakingWhile p f a b b -> TakingWhile p f a b a #

getting :: (Profunctor p, Profunctor q, Functor f, Contravariant f) => Optical p q f s t a b -> Optical' p q f s a #

Coerce a `Getter`-compatible `Optical` to an `Optical'`. This is useful when using a `Traversal` that is not simple as a `Getter` or a `Fold`.

    getting :: Traversal s t a b          -> Fold s a
    getting :: Lens s t a b               -> Getter s a
    getting :: IndexedTraversal i s t a b -> IndexedFold i s a
    getting :: IndexedLens i s t a b      -> IndexedGetter i s a

newtype Const k a b :: forall k. * -> k -> * #

The `Const` functor.

Constructors

Const |
Fields getConst :: a

Instances

Eq2 (Const *) |
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const * a c -> Const * b d -> Bool #
Ord2 (Const *) |
Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const * a c -> Const * b d -> Ordering #
Read2 (Const *) |
Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const * a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const * a b] #
Show2 (Const *) |
Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Const * a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Const * a b] -> ShowS #
Bifunctor (Const *) |
Methods bimap :: (a -> b) -> (c -> d) -> Const * a c -> Const * b d # first :: (a -> b) -> Const * a c -> Const * b c # second :: (b -> c) -> Const * a b -> Const * a c #
Biapplicative (Const *) |
Methods bipure :: a -> b -> Const * a b # (<<*>>) :: Const * (a -> b) (c -> d) -> Const * a c -> Const * b d # (*>>) :: Const * a b -> Const * c d -> Const * c d # (<<*) :: Const * a b -> Const * c d -> Const * a b #
Bitraversable (Const *) |
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const * a b -> f (Const * c d) #
Bifoldable (Const *) |
Methods bifold :: Monoid m => Const * m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Const * a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Const * a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Const * a b -> c #
Hashable2 (Const *) |
Methods liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Const * a b -> Int #
Bitraversable1 (Const *) |
Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Const * a c -> f (Const * b d) # bisequence1 :: Apply f => Const * (f a) (f b) -> f (Const * a b) #
Biapply (Const *) |
Methods (<<.>>) :: Const * (a -> b) (c -> d) -> Const * a c -> Const * b d # (.>>) :: Const * a b -> Const * c d -> Const * c d # (<<.) :: Const * a b -> Const * c d -> Const * a b #
Bifoldable1 (Const *) |
Methods bifold1 :: Semigroup m => Const * m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Const * a b -> m #
Semigroupoid * (Const *) |
Methods o :: c j k1 -> c i j -> c i k1 #
Sieve (Forget r) (Const * r) |
Methods sieve :: Forget r a b -> a -> Const * r b #
Functor (Const * m) |
Methods fmap :: (a -> b) -> Const * m a -> Const * m b # (<$) :: a -> Const * m b -> Const * m a #
Monoid m => Applicative (Const * m) |
Methods pure :: a -> Const * m a # (<*>) :: Const * m (a -> b) -> Const * m a -> Const * m b # (*>) :: Const * m a -> Const * m b -> Const * m b # (<*) :: Const * m a -> Const * m b -> Const * m a #
Foldable (Const * m) |
Methods fold :: Monoid m => Const * m m -> m # foldMap :: Monoid m => (a -> m) -> Const * m a -> m # foldr :: (a -> b -> b) -> b -> Const * m a -> b # foldr' :: (a -> b -> b) -> b -> Const * m a -> b # foldl :: (b -> a -> b) -> b -> Const * m a -> b # foldl' :: (b -> a -> b) -> b -> Const * m a -> b # foldr1 :: (a -> a -> a) -> Const * m a -> a # foldl1 :: (a -> a -> a) -> Const * m a -> a # toList :: Const * m a -> [a] # null :: Const * m a -> Bool # length :: Const * m a -> Int # elem :: Eq a => a -> Const * m a -> Bool # maximum :: Ord a => Const * m a -> a # minimum :: Ord a => Const * m a -> a # sum :: Num a => Const * m a -> a # product :: Num a => Const * m a -> a #
Traversable (Const * m) |
Methods traverse :: Applicative f => (a -> f b) -> Const * m a -> f (Const * m b) # sequenceA :: Applicative f => Const * m (f a) -> f (Const * m a) # mapM :: Monad m => (a -> m b) -> Const * m a -> m (Const * m b) # sequence :: Monad m => Const * m (m a) -> m (Const * m a) #
Generic1 (Const * a) |
Associated Types type Rep1 (Const * a :: * -> *) :: * -> * # Methods from1 :: Const * a a -> Rep1 (Const * a) a # to1 :: Rep1 (Const * a) a -> Const * a a #
Contravariant (Const * a) |
Methods contramap :: (a -> b) -> Const * a b -> Const * a a # (>$) :: b -> Const * a b -> Const * a a #
Eq a => Eq1 (Const * a) |
Methods liftEq :: (a -> b -> Bool) -> Const * a a -> Const * a b -> Bool #
Ord a => Ord1 (Const * a) |
Methods liftCompare :: (a -> b -> Ordering) -> Const * a a -> Const * a b -> Ordering #
Read a => Read1 (Const * a) |
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Const * a a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Const * a a] #
Show a => Show1 (Const * a) |
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Const * a a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Const * a a] -> ShowS #
Hashable a => Hashable1 (Const * a) |
Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> Const * a a -> Int #
Semigroup m => Apply (Const * m) |
Methods (<.>) :: Const * m (a -> b) -> Const * m a -> Const * m b # (.>) :: Const * m a -> Const * m b -> Const * m b # (<.) :: Const * m a -> Const * m b -> Const * m a #
Bounded a => Bounded (Const k a b) |
Methods minBound :: Const k a b # maxBound :: Const k a b #
Enum a => Enum (Const k a b) |
Methods succ :: Const k a b -> Const k a b # pred :: Const k a b -> Const k a b # toEnum :: Int -> Const k a b # fromEnum :: Const k a b -> Int # enumFrom :: Const k a b -> [Const k a b] # enumFromThen :: Const k a b -> Const k a b -> [Const k a b] # enumFromTo :: Const k a b -> Const k a b -> [Const k a b] # enumFromThenTo :: Const k a b -> Const k a b -> Const k a b -> [Const k a b] #
Eq a => Eq (Const k a b) |
Methods (==) :: Const k a b -> Const k a b -> Bool # (/=) :: Const k a b -> Const k a b -> Bool #
Floating a => Floating (Const k a b) |
Methods pi :: Const k a b # exp :: Const k a b -> Const k a b # log :: Const k a b -> Const k a b # sqrt :: Const k a b -> Const k a b # (**) :: Const k a b -> Const k a b -> Const k a b # logBase :: Const k a b -> Const k a b -> Const k a b # sin :: Const k a b -> Const k a b # cos :: Const k a b -> Const k a b # tan :: Const k a b -> Const k a b # asin :: Const k a b -> Const k a b # acos :: Const k a b -> Const k a b # atan :: Const k a b -> Const k a b # sinh :: Const k a b -> Const k a b # cosh :: Const k a b -> Const k a b # tanh :: Const k a b -> Const k a b # asinh :: Const k a b -> Const k a b # acosh :: Const k a b -> Const k a b # atanh :: Const k a b -> Const k a b # log1p :: Const k a b -> Const k a b # expm1 :: Const k a b -> Const k a b # log1pexp :: Const k a b -> Const k a b # log1mexp :: Const k a b -> Const k a b #
Fractional a => Fractional (Const k a b) |
Methods (/) :: Const k a b -> Const k a b -> Const k a b # recip :: Const k a b -> Const k a b # fromRational :: Rational -> Const k a b #
Integral a => Integral (Const k a b) |
Methods quot :: Const k a b -> Const k a b -> Const k a b # rem :: Const k a b -> Const k a b -> Const k a b # div :: Const k a b -> Const k a b -> Const k a b # mod :: Const k a b -> Const k a b -> Const k a b # quotRem :: Const k a b -> Const k a b -> (Const k a b, Const k a b) # divMod :: Const k a b -> Const k a b -> (Const k a b, Const k a b) # toInteger :: Const k a b -> Integer #
Num a => Num (Const k a b) |
Methods (+) :: Const k a b -> Const k a b -> Const k a b # (-) :: Const k a b -> Const k a b -> Const k a b # (*) :: Const k a b -> Const k a b -> Const k a b # negate :: Const k a b -> Const k a b # abs :: Const k a b -> Const k a b # signum :: Const k a b -> Const k a b # fromInteger :: Integer -> Const k a b #
Ord a => Ord (Const k a b) |
Methods compare :: Const k a b -> Const k a b -> Ordering # (<) :: Const k a b -> Const k a b -> Bool # (<=) :: Const k a b -> Const k a b -> Bool # (>) :: Const k a b -> Const k a b -> Bool # (>=) :: Const k a b -> Const k a b -> Bool # max :: Const k a b -> Const k a b -> Const k a b # min :: Const k a b -> Const k a b -> Const k a b #
Read a => Read (Const k a b) | This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed
Methods readsPrec :: Int -> ReadS (Const k a b) # readList :: ReadS [Const k a b] # readPrec :: ReadPrec (Const k a b) # readListPrec :: ReadPrec [Const k a b] #
Real a => Real (Const k a b) |
Methods toRational :: Const k a b -> Rational #
RealFloat a => RealFloat (Const k a b) |
Methods floatRadix :: Const k a b -> Integer # floatDigits :: Const k a b -> Int # floatRange :: Const k a b -> (Int, Int) # decodeFloat :: Const k a b -> (Integer, Int) # encodeFloat :: Integer -> Int -> Const k a b # exponent :: Const k a b -> Int # significand :: Const k a b -> Const k a b # scaleFloat :: Int -> Const k a b -> Const k a b # isNaN :: Const k a b -> Bool # isInfinite :: Const k a b -> Bool # isDenormalized :: Const k a b -> Bool # isNegativeZero :: Const k a b -> Bool # isIEEE :: Const k a b -> Bool # atan2 :: Const k a b -> Const k a b -> Const k a b #
RealFrac a => RealFrac (Const k a b) |
Methods properFraction :: Integral b => Const k a b -> (b, Const k a b) # truncate :: Integral b => Const k a b -> b # round :: Integral b => Const k a b -> b # ceiling :: Integral b => Const k a b -> b # floor :: Integral b => Const k a b -> b #
Show a => Show (Const k a b) | This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed
Methods showsPrec :: Int -> Const k a b -> ShowS # show :: Const k a b -> String # showList :: [Const k a b] -> ShowS #
Ix a => Ix (Const k a b) |
Methods range :: (Const k a b, Const k a b) -> [Const k a b] # index :: (Const k a b, Const k a b) -> Const k a b -> Int # unsafeIndex :: (Const k a b, Const k a b) -> Const k a b -> Int inRange :: (Const k a b, Const k a b) -> Const k a b -> Bool # rangeSize :: (Const k a b, Const k a b) -> Int # unsafeRangeSize :: (Const k a b, Const k a b) -> Int
Generic (Const k a b) |
Associated Types type Rep (Const k a b) :: * -> * # Methods from :: Const k a b -> Rep (Const k a b) x # to :: Rep (Const k a b) x -> Const k a b #
Semigroup a => Semigroup (Const k a b) |
Methods (<>) :: Const k a b -> Const k a b -> Const k a b # sconcat :: NonEmpty (Const k a b) -> Const k a b # stimes :: Integral b => b -> Const k a b -> Const k a b #
Monoid a => Monoid (Const k a b) |
Methods mempty :: Const k a b # mappend :: Const k a b -> Const k a b -> Const k a b # mconcat :: [Const k a b] -> Const k a b #
Storable a => Storable (Const k a b) |
Methods sizeOf :: Const k a b -> Int # alignment :: Const k a b -> Int # peekElemOff :: Ptr (Const k a b) -> Int -> IO (Const k a b) # pokeElemOff :: Ptr (Const k a b) -> Int -> Const k a b -> IO () # peekByteOff :: Ptr b -> Int -> IO (Const k a b) # pokeByteOff :: Ptr b -> Int -> Const k a b -> IO () # peek :: Ptr (Const k a b) -> IO (Const k a b) # poke :: Ptr (Const k a b) -> Const k a b -> IO () #
Bits a => Bits (Const k a b) |
Methods (.&.) :: Const k a b -> Const k a b -> Const k a b # (.|.) :: Const k a b -> Const k a b -> Const k a b # xor :: Const k a b -> Const k a b -> Const k a b # complement :: Const k a b -> Const k a b # shift :: Const k a b -> Int -> Const k a b # rotate :: Const k a b -> Int -> Const k a b # zeroBits :: Const k a b # bit :: Int -> Const k a b # setBit :: Const k a b -> Int -> Const k a b # clearBit :: Const k a b -> Int -> Const k a b # complementBit :: Const k a b -> Int -> Const k a b # testBit :: Const k a b -> Int -> Bool # bitSizeMaybe :: Const k a b -> Maybe Int # bitSize :: Const k a b -> Int # isSigned :: Const k a b -> Bool # shiftL :: Const k a b -> Int -> Const k a b # unsafeShiftL :: Const k a b -> Int -> Const k a b # shiftR :: Const k a b -> Int -> Const k a b # unsafeShiftR :: Const k a b -> Int -> Const k a b # rotateL :: Const k a b -> Int -> Const k a b # rotateR :: Const k a b -> Int -> Const k a b # popCount :: Const k a b -> Int #
FiniteBits a => FiniteBits (Const k a b) |
Methods finiteBitSize :: Const k a b -> Int # countLeadingZeros :: Const k a b -> Int # countTrailingZeros :: Const k a b -> Int #
Hashable a => Hashable (Const * a b) |
Methods hashWithSalt :: Int -> Const * a b -> Int # hash :: Const * a b -> Int #
Wrapped (Const k a x) # |
Associated Types type Unwrapped (Const k a x) :: * # Methods _Wrapped' :: Iso' (Const k a x) (Unwrapped (Const k a x)) #
(~) * t (Const k1 a' x') => Rewrapped (Const k a x) t # |
type Rep1 (Const * a) |
type Rep1 (Const * a) = D1 (MetaData "Const" "Data.Functor.Const" "base" True) (C1 (MetaCons "Const" PrefixI True) (S1 (MetaSel (Just Symbol "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep (Const k a b) |
type Rep (Const k a b) = D1 (MetaData "Const" "Data.Functor.Const" "base" True) (C1 (MetaCons "Const" PrefixI True) (S1 (MetaSel (Just Symbol "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Unwrapped (Const k a x) # |
type Unwrapped (Const k a x) = a