lens-1.7: Lenses, Folds and Traversals

Portability Rank2Types provisional Edward Kmett Safe-Infered

Control.Lens.Setter

Description

A `Setter a b c d` is a generalization of `fmap` from `Functor`. It allows you to map into a structure and change out the contents, but it isn't strong enough to allow you to enumerate those contents. Starting with `fmap :: Functor f => (c -> d) -> f c -> f d` we monomorphize the type to obtain `(c -> d) -> a -> b` and then decorate it with `Identity` to obtain

`type `Setter` a b c d = (c -> `Identity` d) -> a -> `Identity` b`

Every `Traversal` is a valid `Setter`, since `Identity` is `Applicative`.

Everything you can do with a `Functor`, you can do with a `Setter`. There are combinators that generalize `fmap` and (`<\$`).

Synopsis

Setters

type Setter a b c d = forall f. Settable f => (c -> f d) -> a -> f bSource

The only `Lens`-like law that can apply to a `Setter` `l` is that

``` set l c (set l b a) = set l c a
```

You can't `view` a `Setter` in general, so the other two laws are irrelevant.

However, two functor laws apply to a `Setter`:

1. ``adjust` l id = id`
2. ``adjust` l f . `adjust` l g = `adjust` l (f . g)`

These an be stated more directly:

1. `l `pure` = `pure``
2. `l f . `run` . l g = l (f . `run` . g)`

You can compose a `Setter` with a `Lens` or a `Traversal` using (`.`) from the Prelude and the result is always only a `Setter` and nothing more.

class Applicative f => Settable f whereSource

Anything Settable must be isomorphic to the Identity Functor.

Methods

run :: f a -> aSource

Instances

 Settable Identity Settable Mutator Settable f => Settable (Backwards f) (Settable f, Settable g) => Settable (Compose f g)

Consuming Setters

type Setting a b c d = (c -> Mutator d) -> a -> Mutator bSource

Running a Setter instantiates it to a concrete type.

When consuming a setter, use this type.

newtype Mutator a Source

`Mutator` is just a renamed `Identity` functor to give better error messages when someone attempts to use a getter as a setter.

Constructors

 Mutator FieldsrunMutator :: a

Instances

 Functor Mutator Applicative Mutator Settable Mutator

Building Setters

sets :: ((c -> d) -> a -> b) -> Setter a b c dSource

Build a Setter from a map-like function.

Your supplied function `f` is required to satisfy:

`f id = id` `f g . f h = f (g . h)`

Equational reasoning:

``sets` . `adjust` = `id``
``adjust` . `sets` = `id``

Another way to view `sets` is that it takes a "semantic editor combinator" and transforms it into a `Setter`.

Common Setters

mapped :: Functor f => Setter (f a) (f b) a bSource

This setter can be used to map over all of the values in a `Functor`.

``fmap`        = `adjust` `mapped``
``fmapDefault` = `adjust` `traverse``
`(`<\$`)        = `set` `mapped``

Functional Combinators

adjust :: Setting a b c d -> (c -> d) -> a -> bSource

Modify the target of a `Lens` or all the targets of a `Setter` or `Traversal` with a function.

``fmap`        = `adjust` `mapped``
``fmapDefault` = `adjust` `traverse``

Free Theorems:

1. ``sets` . `adjust` = `id``
2. ``adjust` . `sets` = `id``

Another way to view `adjust` is to say that it transformers a `Setter` into a "semantic editor combinator".

``adjust` :: `Setter` a b c d -> (c -> d) -> a -> b`

mapOf :: Setting a b c d -> (c -> d) -> a -> bSource

Modify the target of a `Lens` or all the targets of a `Setter` or `Traversal` with a function. This is an alias for adjust that is provided for consistency.

``mapOf`       = `adjust``
``fmap`        = `mapOf` `mapped``
``fmapDefault` = `mapOf` `traverse``

Free Theorems:

1. ``sets` . `mapOf` = `id``
2. ``mapOf` . `sets` = `id``
``` mapOf :: Setter a b c d      -> (c -> d) -> a -> b
mapOf :: Iso a b c d         -> (c -> d) -> a -> b
mapOf :: Lens a b c d        -> (c -> d) -> a -> b
mapOf :: Traversal a b c d   -> (c -> d) -> a -> b
```

set :: Setting a b c d -> d -> a -> bSource

Replace the target of a `Lens` or all of the targets of a `Setter` or `Traversal` with a constant value.

`(`<\$`) = `set` `mapped``
``` set :: Setter a b c d    -> d -> a -> b
set :: Iso a b c d       -> d -> a -> b
set :: Lens a b c d      -> d -> a -> b
set :: Traversal a b c d -> d -> a -> b
```

(.~) :: Setting a b c d -> d -> a -> bSource

Replace the target of a `Lens` or all of the targets of a `Setter` or `Traversal` with a constant value.

This is an infix version of `set`, provided for consistency with (`.=`)

`f `<\$` a = `mapped` `.~` f `\$` a`
````>>> ````import Control.Lens
````>>> ````_1 .~ "hello" \$ (42,"world")
```("hello","world")
```
``` (.~) :: Setter a b c d    -> d -> a -> b
(.~) :: Iso a b c d       -> d -> a -> b
(.~) :: Lens a b c d      -> d -> a -> b
(.~) :: Traversal a b c d -> d -> a -> b
```

(%~) :: Setting a b c d -> (c -> d) -> a -> bSource

Modifies the target of a `Lens` or all of the targets of a `Setter` or `Traversal` with a user supplied function.

This is an infix version of `adjust`

``fmap` f = `mapped` `%~` f`
``fmapDefault` f = `traverse` `%~` f`
````>>> ````import Control.Lens
````>>> ````_2 %~ length \$ (1,"hello")
```(1,5)
```
``` (%~) :: Setter a b c d    -> (c -> d) -> a -> b
(%~) :: Iso a b c d       -> (c -> d) -> a -> b
(%~) :: Lens a b c d      -> (c -> d) -> a -> b
(%~) :: Traversal a b c d -> (c -> d) -> a -> b
```

(+~) :: Num c => Setting a b c c -> c -> a -> bSource

Increment the target(s) of a numerically valued `Lens`, `Setter` or `Traversal`

````>>> ````import Control.Lens
````>>> ````_1 +~ 1 \$ (1,2)
```(2,2)
```

(-~) :: Num c => Setting a b c c -> c -> a -> bSource

Decrement the target(s) of a numerically valued `Lens`, `Iso`, `Setter` or `Traversal`

````>>> ````import Control.Lens
````>>> ````_1 -~ 2 \$ (1,2)
```(-1,2)
```

(*~) :: Num c => Setting a b c c -> c -> a -> bSource

Multiply the target(s) of a numerically valued `Lens`, `Iso`, `Setter` or `Traversal`

````>>> ````import Control.Lens
````>>> ````_2 *~ 4 \$ (1,2)
```(1,8)
```

(//~) :: Fractional c => Setting a b c c -> c -> a -> bSource

Divide the target(s) of a numerically valued `Lens`, `Iso`, `Setter` or `Traversal`

(^~) :: (Num c, Integral e) => Setting a b c c -> e -> a -> bSource

Raise the target(s) of a numerically valued `Lens`, `Setter` or `Traversal` to a non-negative integral power

````>>> ````import Control.Lens
````>>> ````_2 ^~ 2 \$ (1,3)
```(1,9)
```

(^^~) :: (Fractional c, Integral e) => Setting a b c c -> e -> a -> bSource

Raise the target(s) of a fractionally valued `Lens`, `Setter` or `Traversal` to an integral power

````>>> ````import Control.Lens
````>>> ````_2 ^^~ (-1) \$ (1,2)
```(1,0.5)
```

(**~) :: Floating c => Setting a b c c -> c -> a -> bSource

Raise the target(s) of a floating-point valued `Lens`, `Setter` or `Traversal` to an arbitrary power.

````>>> ````import Control.Lens
````>>> ````_2 **~ pi \$ (1,3)
```(1,31.54428070019754)
```

(||~) :: Setting a b Bool Bool -> Bool -> a -> bSource

Logically `||` the target(s) of a `Bool`-valued `Lens` or `Setter`

(&&~) :: Setting a b Bool Bool -> Bool -> a -> bSource

Logically `&&` the target(s) of a `Bool`-valued `Lens` or `Setter`

(<>~) :: Monoid c => Setting a b c c -> c -> a -> bSource

Modify the target of a monoidally valued by `mappend`ing another value.

(<.~) :: Setting a b c d -> d -> a -> (d, b)Source

Set with pass-through

This is mostly present for consistency, but may be useful for for chaining assignments

If you do not need a copy of the intermediate result, then using `l .~ d` directly is a good idea.

State Combinators

(.=) :: MonadState a m => Setting a a c d -> d -> m ()Source

Replace the target of a `Lens` or all of the targets of a `Setter` or `Traversal` in our monadic state with a new value, irrespective of the old.

``` (.=) :: MonadState a m => Iso a a c d             -> d -> m ()
(.=) :: MonadState a m => Lens a a c d            -> d -> m ()
(.=) :: MonadState a m => Traversal a a c d       -> d -> m ()
(.=) :: MonadState a m => Setter a a c d          -> d -> m ()
```

(%=) :: MonadState a m => Setting a a c d -> (c -> d) -> m ()Source

Map over the target of a `Lens` or all of the targets of a `Setter` or `Traversal` in our monadic state.

``` (%=) :: MonadState a m => Iso a a c d             -> (c -> d) -> m ()
(%=) :: MonadState a m => Lens a a c d            -> (c -> d) -> m ()
(%=) :: MonadState a m => Traversal a a c d       -> (c -> d) -> m ()
(%=) :: MonadState a m => Setter a a c d          -> (c -> d) -> m ()
```

(+=) :: (MonadState a m, Num b) => SimpleSetting a b -> b -> m ()Source

Modify the target(s) of a `Simple` `Lens`, `Iso`, `Setter` or `Traversal` by adding a value

Example:

``` fresh = do
id += 1
access id
```

(-=) :: (MonadState a m, Num b) => SimpleSetting a b -> b -> m ()Source

Modify the target(s) of a `Simple` `Lens`, `Iso`, `Setter` or `Traversal` by subtracting a value

(*=) :: (MonadState a m, Num b) => SimpleSetting a b -> b -> m ()Source

Modify the target(s) of a `Simple` `Lens`, `Iso`, `Setter` or `Traversal` by multiplying by value

(//=) :: (MonadState a m, Fractional b) => SimpleSetting a b -> b -> m ()Source

Modify the target(s) of a `Simple` `Lens`, `Iso`, `Setter` or `Traversal` by dividing by a value

(^=) :: (MonadState a m, Fractional b, Integral c) => SimpleSetting a b -> c -> m ()Source

Raise the target(s) of a numerically valued `Lens`, `Setter` or `Traversal` to a non-negative integral power

(^^=) :: (MonadState a m, Fractional b, Integral c) => SimpleSetting a b -> c -> m ()Source

Raise the target(s) of a numerically valued `Lens`, `Setter` or `Traversal` to an integral power

(**=) :: (MonadState a m, Floating b) => SimpleSetting a b -> b -> m ()Source

Raise the target(s) of a numerically valued `Lens`, `Setter` or `Traversal` to an arbitrary power

(||=) :: MonadState a m => SimpleSetting a Bool -> Bool -> m ()Source

Modify the target(s) of a `Simple` `Lens`, 'Iso, `Setter` or `Traversal` by taking their logical `||` with a value

(&&=) :: MonadState a m => SimpleSetting a Bool -> Bool -> m ()Source

Modify the target(s) of a `Simple` `Lens`, `Iso`, `Setter` or `Traversal` by taking their logical `&&` with a value

(<>=) :: (MonadState a m, Monoid b) => SimpleSetting a b -> b -> m ()Source

Modify the target(s) of a `Simple` `Lens`, `Iso`, `Setter` or `Traversal` by `mappend`ing a value.

(<.=) :: MonadState a m => Setting a a c d -> d -> m dSource

Set with pass-through

This is useful for chaining assignment

``` do x <- _2 <.= (an expensive expression)
```

If you do not need a copy of the intermediate result, then using `l .= d` will avoid unused binding warnings

(<~) :: MonadState a m => Setting a a c d -> m d -> m ()Source

Run a monadic action, and set all of the targets of a `Lens`, `Setter` or `Traversal` to its result.

``` (<~) :: MonadState a m => Iso a a c d       -> m d -> m ()
(<~) :: MonadState a m => Lens a a c d      -> m d -> m ()
(<~) :: MonadState a m => Traversal a a c d -> m d -> m ()
(<~) :: MonadState a m => Setter a a c d    -> m d -> m ()
```

As a reasonable mnemonic, this lets you store the result of a monadic action in a lens rather than in a local variable.

``` do foo <- bar
...
```

will store the result in a variable, while

``` do foo <~ bar
...
```

will store the result in a `Lens`, `Setter`, or `Traversal`.

whisper :: (MonadWriter b m, Monoid a) => Setting a b c d -> d -> m ()Source

Tell a part of a value to a `MonadWriter`, filling in the rest from `mempty`

``` whisper l d = tell (set l d mempty)
```

Simplicity

type SimpleSetter a b = Setter a a b bSource

``` 'SimpleSetter' = 'Simple' 'Setter'
```

type SimpleSetting a b = Setting a a b bSource

``` 'SimpleSetting' m = 'Simple' 'Setting'
```