Portability  Rank2Types 

Stability  provisional 
Maintainer  Edward Kmett <ekmett@gmail.com> 
Safe Haskell  SafeInfered 
A
is a generalization of Setter
a b c dfmap
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 ::
we monomorphize the type to obtain Functor
f => (c > d) > f c > f d(c > d) > a > b
and then decorate it with Identity
to obtain
typeSetter
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 (<$
).
 type Setter a b c d = forall f. Settable f => (c > f d) > a > f b
 class Applicative f => Settable f where
 untainted :: f a > a
 sets :: ((c > d) > a > b) > Setter a b c d
 mapped :: Functor f => Setter (f a) (f b) a b
 over :: Setting a b c d > (c > d) > a > b
 mapOf :: Setting a b c d > (c > d) > a > b
 set :: Setting a b c d > d > a > b
 (.~) :: Setting a b c d > d > a > b
 (%~) :: Setting a b c d > (c > d) > a > b
 (+~) :: Num c => Setting a b c c > c > a > b
 (~) :: Num c => Setting a b c c > c > a > b
 (*~) :: Num c => Setting a b c c > c > a > b
 (//~) :: Fractional c => Setting a b c c > c > a > b
 (^~) :: (Num c, Integral e) => Setting a b c c > e > a > b
 (^^~) :: (Fractional c, Integral e) => Setting a b c c > e > a > b
 (**~) :: Floating c => Setting a b c c > c > a > b
 (~) :: Setting a b Bool Bool > Bool > a > b
 (&&~) :: Setting a b Bool Bool > Bool > a > b
 (<.~) :: Setting a b c d > d > a > (d, b)
 (.=) :: MonadState a m => Setting a a c d > d > m ()
 (%=) :: MonadState a m => Setting a a c d > (c > d) > m ()
 (+=) :: (MonadState a m, Num b) => SimpleSetting a b > b > m ()
 (=) :: (MonadState a m, Num b) => SimpleSetting a b > b > m ()
 (*=) :: (MonadState a m, Num b) => SimpleSetting a b > b > m ()
 (//=) :: (MonadState a m, Fractional b) => SimpleSetting a b > b > m ()
 (^=) :: (MonadState a m, Fractional b, Integral c) => SimpleSetting a b > c > m ()
 (^^=) :: (MonadState a m, Fractional b, Integral c) => SimpleSetting a b > c > m ()
 (**=) :: (MonadState a m, Floating b) => SimpleSetting a b > b > m ()
 (=) :: MonadState a m => SimpleSetting a Bool > Bool > m ()
 (&&=) :: MonadState a m => SimpleSetting a Bool > Bool > m ()
 (<.=) :: MonadState a m => Setting a a c d > d > m d
 (<~) :: MonadState a m => Setting a a c d > m d > m ()
 type Setting a b c d = (c > Mutator d) > a > Mutator b
 newtype Mutator a = Mutator {
 runMutator :: a
 type SimpleSetting a b = Setting a a b b
 type SimpleSetter a b = Setter a a b b
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
:
over
lid
=id
over
l f .over
l g =over
l (f . g)
These an be stated more directly:
lpure
=pure
l f .untainted
. l g = l (f .untainted
. 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
Building Setters
Common Setters
Functional Combinators
over :: 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
=over
mapped
fmapDefault
=over
traverse
sets
.over
=id
over
.sets
=id
Another way to view over
is to say that it transformers a Setter
into a
"semantic editor combinator".
over
::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 over
that is provided for consistency.
mapOf
=over
fmap
=mapOf
mapped
fmapDefault
=mapOf
traverse
sets
.mapOf
=id
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
>>>
import Control.Lens
>>>
set _2 "hello" (1,())
(1,"hello")
>>>
set mapped () [1,2,3,4]
[(),(),(),()]
Note: Attempting to set
a Fold
or Getter
will fail at compile time with an
relatively nice error message.
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 over
fmap
f =mapped
%~
ffmapDefault
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 =>Setter
a b c c > c > a > b (+~) :: Num c =>Iso
a b c c > c > a > b (+~) :: Num c =>Lens
a b c c > c > a > b (+~) :: Num c =>Traversal
a b c c > c > a > b
(~) :: 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 =>Setter
a b c c > c > a > b (~) ::Num
c =>Iso
a b c c > c > a > b (~) ::Num
c =>Lens
a b c c > c > a > b (~) ::Num
c =>Traversal
a b c c > c > a > b
(*~) :: 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)
(*~) ::Num
c =>Setter
a b c c > c > a > b (*~) ::Num
c =>Iso
a b c c > c > a > b (*~) ::Num
c =>Lens
a b c c > c > a > b (*~) ::Num
c =>Traversal
a b c c > c > a > b
(//~) :: Fractional c => Setting a b c c > c > a > bSource
Divide the target(s) of a numerically valued Lens
, Iso
, Setter
or Traversal
(~) ::Fractional
c =>Setter
a b c c > c > a > b (~) ::Fractional
c =>Iso
a b c c > c > a > b (~) ::Fractional
c =>Lens
a b c c > c > a > b (~) ::Fractional
c =>Traversal
a b c c > c > a > b
(^^~) :: (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)
(^^~) :: (Fractional
c,Integral
e) =>Setter
a b c c > e > a > b (^^~) :: (Fractional
c,Integral
e) =>Iso
a b c c > e > a > b (^^~) :: (Fractional
c,Integral
e) =>Lens
a b c c > e > a > b (^^~) :: (Fractional
c,Integral
e) =>Traversal
a b c c > e > a > b
(**~) :: Floating c => Setting a b c c > c > a > bSource
Raise the target(s) of a floatingpoint valued Lens
, Setter
or Traversal
to an arbitrary power.
>>>
import Control.Lens
>>>
_2 **~ pi $ (1,3)
(1,31.54428070019754)
(**~) ::Floating
c =>Setter
a b c c > c > a > b (**~) ::Floating
c =>Iso
a b c c > c > a > b (**~) ::Floating
c =>Lens
a b c c > c > a > b (**~) ::Floating
c =>Traversal
a b c c > c > a > b
(~) :: Setting a b Bool Bool > Bool > a > bSource
Logically 
the target(s) of a Bool
valued Lens
or Setter
>>>
:m + Control.Lens Data.Pair.Lens
>>>
both ~ True $ (False,True)
(True,True)
>>>
both ~ False $ (False,True)
(False,True)
(~)::Setter
a bBool
Bool
>Bool
> a > b (~)::Iso
a bBool
Bool
>Bool
> a > b (~)::Lens
a bBool
Bool
>Bool
> a > b (~)::Traversal
a bBool
Bool
>Bool
> a > b
(&&~) :: Setting a b Bool Bool > Bool > a > bSource
Logically &&
the target(s) of a Bool
valued Lens
or Setter
>>>
:m + Control.Lens Data.Pair.Lens
>>>
both &&~ True $ (False, True)
(False,True)
>>>
both &&~ False $ (False, True)
(False,False)
(&&~)::Setter
a bBool
Bool
>Bool
> a > b (&&~)::Iso
a bBool
Bool
>Bool
> a > b (&&~)::Lens
a bBool
Bool
>Bool
> a > b (&&~)::Traversal
a bBool
Bool
>Bool
> a > b
(<.~) :: Setting a b c d > d > a > (d, b)Source
Set with passthrough
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
directly is a good idea.
.~
d
(<.~) ::Setter
a b c d > d > a > (d, b) (<.~) ::Iso
a b c d > d > a > (d, b) (<.~) ::Lens
a b c d > d > a > (d, b) (<.~) ::Traversal
a b c d > d > a > (d, b)
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 :: MonadState Int m => m Int fresh = doid
+=
1use
id
(+=) :: (MonadState
a m,Num
b) =>Simple
Setter
a b > b > m () (+=) :: (MonadState
a m,Num
b) =>Simple
Iso
a b > b > m () (+=) :: (MonadState
a m,Num
b) =>Simple
Lens
a b > b > m () (+=) :: (MonadState
a m,Num
b) =>Simple
Traversal
a b > b > 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 subtracting a value
(=) :: (MonadState
a m,Num
b) =>Simple
Setter
a b > b > m () (=) :: (MonadState
a m,Num
b) =>Simple
Iso
a b > b > m () (=) :: (MonadState
a m,Num
b) =>Simple
Lens
a b > b > m () (=) :: (MonadState
a m,Num
b) =>Simple
Traversal
a b > b > 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 multiplying by value.
ballSpeed.
both
*=
speedMultiplier
(*=) :: (MonadState
a m,Num
b) =>Simple
Setter
a b > b > m () (*=) :: (MonadState
a m,Num
b) =>Simple
Iso
a b > b > m () (*=) :: (MonadState
a m,Num
b) =>Simple
Lens
a b > b > m () (*=) :: (MonadState
a m,Num
b) =>Simple
Traversal
a b > b > m ()
(//=) :: (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) =>Simple
Setter
a b > b > m () (=) :: (MonadState
a m,Fractional
b) =>Simple
Iso
a b > b > m () (=) :: (MonadState
a m,Fractional
b) =>Simple
Lens
a b > b > m () (=) :: (MonadState
a m,Fractional
b) =>Simple
Traversal
a b > b > m ()
(^=) :: (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 nonnegative integral power.
(^=) :: (MonadState
a m,Fractional
b,Integral
c) =>Simple
Setter
a b > c > m () (^=) :: (MonadState
a m,Fractional
b,Integral
c) =>Simple
Iso
a b > c > m () (^=) :: (MonadState
a m,Fractional
b,Integral
c) =>Simple
Lens
a b > c > m () (^=) :: (MonadState
a m,Fractional
b,Integral
c) =>Simple
Traversal
a b > c > m ()
(^^=) :: (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,Fractional
b,Integral
c) =>Simple
Setter
a b > c > m () (^^=) :: (MonadState
a m,Fractional
b,Integral
c) =>Simple
Iso
a b > c > m () (^^=) :: (MonadState
a m,Fractional
b,Integral
c) =>Simple
Lens
a b > c > m () (^^=) :: (MonadState
a m,Fractional
b,Integral
c) =>Simple
Traversal
a b > c > m ()
(**=) :: (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,Floating
b) =>Simple
Setter
a b > b > m () (**=) :: (MonadState
a m,Floating
b) =>Simple
Iso
a b > b > m () (**=) :: (MonadState
a m,Floating
b) =>Simple
Lens
a b > b > m () (**=) :: (MonadState
a m,Floating
b) =>Simple
Traversal
a b > b > m ()
(=) :: 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 =>Simple
Setter
aBool
>Bool
> m () (=)::MonadState
a m =>Simple
Iso
aBool
>Bool
> m () (=)::MonadState
a m =>Simple
Lens
aBool
>Bool
> m () (=)::MonadState
a m =>Simple
Traversal
aBool
>Bool
> m ()
(&&=) :: 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 =>Simple
Setter
aBool
>Bool
> m () (&&=)::MonadState
a m =>Simple
Iso
aBool
>Bool
> m () (&&=)::MonadState
a m =>Simple
Lens
aBool
>Bool
> m () (&&=)::MonadState
a m =>Simple
Traversal
aBool
>Bool
> m ()
(<.=) :: MonadState a m => Setting a a c d > d > m dSource
Set with passthrough
This is useful for chaining assignment without roundtripping through your monad stack.
do x < _2
<.= ninety_nine_bottles_of_beer_on_the_wall
If you do not need a copy of the intermediate result, then using l .= d
will avoid unused binding warnings
(<.=) ::MonadState
a m =>Setter
a a c d > d > m d (<.=) ::MonadState
a m =>Iso
a a c d > d > m d (<.=) ::MonadState
a m =>Lens
a a c d > d > m d (<.=) ::MonadState
a m =>Traversal
a a c d > d > m d
(<~) :: 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 ...
Setter Internals
Mutator
is just a renamed Identity
functor to give better error
messages when someone attempts to use a getter as a setter.
Most user code will never need to see this type.
Mutator  

type SimpleSetting a b = Setting a a b bSource
This is a useful alias for use when consuming a SimpleSetter
.
Most user code will never have to use this type.
typeSimpleSetting
m =Simple
Setting
Simplicity
type SimpleSetter a b = Setter a a b bSource
A Simple Setter is just a Setter
that doesn't change the types.
These are particularly common when talking about monomorphic containers. e.g.
sets
Data.Text.map ::SimpleSetter
Text
Char
typeSimpleSetter
=Simple
Setter