Copyright  (C) 201214 Edward Kmett 

License  BSDstyle (see the file LICENSE) 
Maintainer  Edward Kmett <ekmett@gmail.com> 
Stability  provisional 
Portability  Rank2Types 
Safe Haskell  Trustworthy 
Language  Haskell98 
A
is a generalization of Setter
s t a bfmap
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
we monomorphize the type to obtain fmap
:: Functor
f => (a > b) > f a > f b(a > b) > s > t
and then decorate it with Identity
to obtain:
typeSetter
s t a b = (a >Identity
b) > s >Identity
t
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 s t a b = forall f. Settable f => (a > f b) > s > f t
 type Setter' s a = Setter s s a a
 type IndexedSetter i s t a b = forall f p. (Indexable i p, Settable f) => p a (f b) > s > f t
 type IndexedSetter' i s a = IndexedSetter i s s a a
 type ASetter s t a b = (a > Identity b) > s > Identity t
 type ASetter' s a = ASetter s s a a
 type AnIndexedSetter i s t a b = Indexed i a (Identity b) > s > Identity t
 type AnIndexedSetter' i s a = AnIndexedSetter i s s a a
 type Setting p s t a b = p a (Identity b) > s > Identity t
 type Setting' p s a = Setting p s s a a
 sets :: (Profunctor p, Profunctor q, Settable f) => (p a b > q s t) > Optical p q f s t a b
 setting :: ((a > b) > s > t) > IndexPreservingSetter s t a b
 cloneSetter :: ASetter s t a b > Setter s t a b
 cloneIndexPreservingSetter :: ASetter s t a b > IndexPreservingSetter s t a b
 cloneIndexedSetter :: AnIndexedSetter i s t a b > IndexedSetter i s t a b
 mapped :: Functor f => Setter (f a) (f b) a b
 lifted :: Monad m => Setter (m a) (m b) a b
 contramapped :: Contravariant f => Setter (f b) (f a) a b
 argument :: Profunctor p => Setter (p b r) (p a r) a b
 over :: Profunctor p => Setting p s t a b > p a b > s > t
 set :: ASetter s t a b > b > s > t
 (.~) :: ASetter s t a b > b > s > t
 (%~) :: Profunctor p => Setting p s t a b > p a b > s > t
 (+~) :: Num a => ASetter s t a a > a > s > t
 (~) :: Num a => ASetter s t a a > a > s > t
 (*~) :: Num a => ASetter s t a a > a > s > t
 (//~) :: Fractional a => ASetter s t a a > a > s > t
 (^~) :: (Num a, Integral e) => ASetter s t a a > e > s > t
 (^^~) :: (Fractional a, Integral e) => ASetter s t a a > e > s > t
 (**~) :: Floating a => ASetter s t a a > a > s > t
 (~) :: ASetter s t Bool Bool > Bool > s > t
 (<>~) :: Monoid a => ASetter s t a a > a > s > t
 (&&~) :: ASetter s t Bool Bool > Bool > s > t
 (<.~) :: ASetter s t a b > b > s > (b, t)
 (?~) :: ASetter s t a (Maybe b) > b > s > t
 (<?~) :: ASetter s t a (Maybe b) > b > s > (b, t)
 assign :: MonadState s m => ASetter s s a b > b > m ()
 (.=) :: MonadState s m => ASetter s s a b > b > m ()
 (%=) :: (Profunctor p, MonadState s m) => Setting p s s a b > p a b > m ()
 (+=) :: (MonadState s m, Num a) => ASetter' s a > a > m ()
 (=) :: (MonadState s m, Num a) => ASetter' s a > a > m ()
 (*=) :: (MonadState s m, Num a) => ASetter' s a > a > m ()
 (//=) :: (MonadState s m, Fractional a) => ASetter' s a > a > m ()
 (^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a > e > m ()
 (^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a > e > m ()
 (**=) :: (MonadState s m, Floating a) => ASetter' s a > a > m ()
 (=) :: MonadState s m => ASetter' s Bool > Bool > m ()
 (<>=) :: (MonadState s m, Monoid a) => ASetter' s a > a > m ()
 (&&=) :: MonadState s m => ASetter' s Bool > Bool > m ()
 (<.=) :: MonadState s m => ASetter s s a b > b > m b
 (?=) :: MonadState s m => ASetter s s a (Maybe b) > b > m ()
 (<?=) :: MonadState s m => ASetter s s a (Maybe b) > b > m b
 (<~) :: MonadState s m => ASetter s s a b > m b > m ()
 scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b > b > m ()
 passing :: MonadWriter w m => Setter w w u v > m (a, u > v) > m a
 ipassing :: MonadWriter w m => IndexedSetter i w w u v > m (a, i > u > v) > m a
 censoring :: MonadWriter w m => Setter w w u v > (u > v) > m a > m a
 icensoring :: MonadWriter w m => IndexedSetter i w w u v > (i > u > v) > m a > m a
 set' :: ASetter' s a > a > s > s
 imapOf :: AnIndexedSetter i s t a b > (i > a > b) > s > t
 iover :: AnIndexedSetter i s t a b > (i > a > b) > s > t
 isets :: ((i > a > b) > s > t) > IndexedSetter i s t a b
 (%@~) :: AnIndexedSetter i s t a b > (i > a > b) > s > t
 (%@=) :: MonadState s m => AnIndexedSetter i s s a b > (i > a > b) > m ()
 assignA :: Arrow p => ASetter s t a b > p s b > p s t
 class (Applicative f, Distributive f, Traversable f) => Settable f
 newtype Identity a :: * > * = Identity {
 runIdentity :: a
 mapOf :: Profunctor p => Setting p s t a b > p a b > s > t
Setters
type Setter s t a b = forall f. Settable f => (a > f b) > s > f t Source
The only LensLike
law that can apply to a Setter
l
is that
set
l y (set
l x a) ≡set
l y 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 can 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.
>>>
over traverse f [a,b,c,d]
[f a,f b,f c,f d]
>>>
over _1 f (a,b)
(f a,b)
>>>
over (traverse._1) f [(a,b),(c,d)]
[(f a,b),(f c,d)]
>>>
over both f (a,b)
(f a,f b)
>>>
over (traverse.both) f [(a,b),(c,d)]
[(f a,f b),(f c,f d)]
type IndexedSetter i s t a b = forall f p. (Indexable i p, Settable f) => p a (f b) > s > f t Source
Every IndexedSetter
is a valid Setter
.
The Setter
laws are still required to hold.
type IndexedSetter' i s a = IndexedSetter i s s a a Source
typeIndexedSetter'
i =Simple
(IndexedSetter
i)
type ASetter s t a b = (a > Identity b) > s > Identity t Source
Running a Setter
instantiates it to a concrete type.
When consuming a setter directly to perform a mapping, you can use this type, but most user code will not need to use this type.
type AnIndexedSetter i s t a b = Indexed i a (Identity b) > s > Identity t Source
Running an IndexedSetter
instantiates it to a concrete type.
When consuming a setter directly to perform a mapping, you can use this type, but most user code will not need to use this type.
type AnIndexedSetter' i s a = AnIndexedSetter i s s a a Source
typeAnIndexedSetter'
i =Simple
(AnIndexedSetter
i)
type Setting p s t a b = p a (Identity b) > s > Identity t Source
This is a convenient alias when defining highly polymorphic code that takes both
ASetter
and AnIndexedSetter
as appropriate. If a function takes this it is
expecting one of those two things based on context.
type Setting' p s a = Setting p s s a a Source
This is a convenient alias when defining highly polymorphic code that takes both
ASetter'
and AnIndexedSetter'
as appropriate. If a function takes this it is
expecting one of those two things based on context.
Building Setters
sets :: (Profunctor p, Profunctor q, Settable f) => (p a b > q s t) > Optical p q f s t a b Source
Build a Setter
, IndexedSetter
or IndexPreservingSetter
depending on your choice of Profunctor
.
sets
:: ((a > b) > s > t) >Setter
s t a b
setting :: ((a > b) > s > t) > IndexPreservingSetter s t a b Source
Build an indexpreserving Setter
from a maplike function.
Your supplied function f
is required to satisfy:
fid
≡id
f g.
f h ≡ f (g.
h)
Equational reasoning:
setting
.
over
≡id
over
.
setting
≡id
Another way to view sets
is that it takes a "semantic editor combinator"
and transforms it into a Setter
.
setting
:: ((a > b) > s > t) >Setter
s t a b
cloneIndexPreservingSetter :: ASetter s t a b > IndexPreservingSetter s t a b Source
Build an IndexPreservingSetter
from any Setter
.
cloneIndexedSetter :: AnIndexedSetter i s t a b > IndexedSetter i s t a b Source
Clone an IndexedSetter
.
Common Setters
mapped :: Functor f => Setter (f a) (f b) a b Source
This Setter
can be used to map over all of the values in a Functor
.
fmap
≡over
mapped
fmapDefault
≡over
traverse
(<$
) ≡set
mapped
>>>
over mapped f [a,b,c]
[f a,f b,f c]
>>>
over mapped (+1) [1,2,3]
[2,3,4]
>>>
set mapped x [a,b,c]
[x,x,x]
>>>
[[a,b],[c]] & mapped.mapped +~ x
[[a + x,b + x],[c + x]]
>>>
over (mapped._2) length [("hello","world"),("leaders","!!!")]
[("hello",5),("leaders",3)]
mapped
::Functor
f =>Setter
(f a) (f b) a b
If you want an IndexPreservingSetter
use
.setting
fmap
lifted :: Monad m => Setter (m a) (m b) a b Source
This setter
can be used to modify all of the values in a Monad
.
You sometimes have to use this rather than mapped
 due to
temporary insanity Functor
is not a superclass of Monad
.
liftM
≡over
lifted
>>>
over lifted f [a,b,c]
[f a,f b,f c]
>>>
set lifted b (Just a)
Just b
If you want an IndexPreservingSetter
use
.setting
liftM
contramapped :: Contravariant f => Setter (f b) (f a) a b Source
This Setter
can be used to map over all of the inputs to a Contravariant
.
contramap
≡over
contramapped
>>>
getPredicate (over contramapped (*2) (Predicate even)) 5
True
>>>
getOp (over contramapped (*5) (Op show)) 100
"500"
>>>
Prelude.map ($ 1) $ over (mapped . _Unwrapping' Op . contramapped) (*12) [(*2),(+1),(^3)]
[24,13,1728]
argument :: Profunctor p => Setter (p b r) (p a r) a b Source
This Setter
can be used to map over the input of a Profunctor
.
The most common Profunctor
to use this with is (>)
.
>>>
(argument %~ f) g x
g (f x)
>>>
(argument %~ show) length [1,2,3]
7
>>>
(argument %~ f) h x y
h (f x) y
Map over the argument of the result of a function  i.e., its second argument:
>>>
(mapped.argument %~ f) h x y
h x (f y)
argument
::Setter
(b > r) (a > r) a b
Functional Combinators
over :: Profunctor p => Setting p s t a b > p a b > s > t Source
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
Given any valid Setter
l
, you can also rely on the law:
over
l f.
over
l g =over
l (f.
g)
e.g.
>>>
over mapped f (over mapped g [a,b,c]) == over mapped (f . g) [a,b,c]
True
Another way to view over
is to say that it transforms a Setter
into a
"semantic editor combinator".
>>>
over mapped f (Just a)
Just (f a)
>>>
over mapped (*10) [1,2,3]
[10,20,30]
>>>
over _1 f (a,b)
(f a,b)
>>>
over _1 show (10,20)
("10",20)
over
::Setter
s t a b > (a > b) > s > tover
::ASetter
s t a b > (a > b) > s > t
set :: ASetter s t a b > b > s > t Source
Replace the target of a Lens
or all of the targets of a Setter
or Traversal
with a constant value.
(<$
) ≡set
mapped
>>>
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
s t a b > b > s > tset
::Iso
s t a b > b > s > tset
::Lens
s t a b > b > s > tset
::Traversal
s t a b > b > s > t
(.~) :: ASetter s t a b > b > s > t infixr 4 Source
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
>>>
(a,b,c,d) & _4 .~ e
(a,b,c,e)
>>>
(42,"world") & _1 .~ "hello"
("hello","world")
>>>
(a,b) & both .~ c
(c,c)
(.~
) ::Setter
s t a b > b > s > t (.~
) ::Iso
s t a b > b > s > t (.~
) ::Lens
s t a b > b > s > t (.~
) ::Traversal
s t a b > b > s > t
(%~) :: Profunctor p => Setting p s t a b > p a b > s > t infixr 4 Source
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
>>>
(a,b,c) & _3 %~ f
(a,b,f c)
>>>
(a,b) & both %~ f
(f a,f b)
>>>
_2 %~ length $ (1,"hello")
(1,5)
>>>
traverse %~ f $ [a,b,c]
[f a,f b,f c]
>>>
traverse %~ even $ [1,2,3]
[False,True,False]
>>>
traverse.traverse %~ length $ [["hello","world"],["!!!"]]
[[5,5],[3]]
(%~
) ::Setter
s t a b > (a > b) > s > t (%~
) ::Iso
s t a b > (a > b) > s > t (%~
) ::Lens
s t a b > (a > b) > s > t (%~
) ::Traversal
s t a b > (a > b) > s > t
(+~) :: Num a => ASetter s t a a > a > s > t infixr 4 Source
Increment the target(s) of a numerically valued Lens
, Setter
or Traversal
.
>>>
(a,b) & _1 +~ c
(a + c,b)
>>>
(a,b) & both +~ c
(a + c,b + c)
>>>
(1,2) & _2 +~ 1
(1,3)
>>>
[(a,b),(c,d)] & traverse.both +~ e
[(a + e,b + e),(c + e,d + e)]
(+~
) ::Num
a =>Setter'
s a > a > s > s (+~
) ::Num
a =>Iso'
s a > a > s > s (+~
) ::Num
a =>Lens'
s a > a > s > s (+~
) ::Num
a =>Traversal'
s a > a > s > s
(~) :: Num a => ASetter s t a a > a > s > t infixr 4 Source
Decrement the target(s) of a numerically valued Lens
, Iso
, Setter
or Traversal
.
>>>
(a,b) & _1 ~ c
(a  c,b)
>>>
(a,b) & both ~ c
(a  c,b  c)
>>>
_1 ~ 2 $ (1,2)
(1,2)
>>>
mapped.mapped ~ 1 $ [[4,5],[6,7]]
[[3,4],[5,6]]
(~
) ::Num
a =>Setter'
s a > a > s > s (~
) ::Num
a =>Iso'
s a > a > s > s (~
) ::Num
a =>Lens'
s a > a > s > s (~
) ::Num
a =>Traversal'
s a > a > s > s
(*~) :: Num a => ASetter s t a a > a > s > t infixr 4 Source
Multiply the target(s) of a numerically valued Lens
, Iso
, Setter
or Traversal
.
>>>
(a,b) & _1 *~ c
(a * c,b)
>>>
(a,b) & both *~ c
(a * c,b * c)
>>>
(1,2) & _2 *~ 4
(1,8)
>>>
Just 24 & mapped *~ 2
Just 48
(*~
) ::Num
a =>Setter'
s a > a > s > s (*~
) ::Num
a =>Iso'
s a > a > s > s (*~
) ::Num
a =>Lens'
s a > a > s > s (*~
) ::Num
a =>Traversal'
s a > a > s > s
(//~) :: Fractional a => ASetter s t a a > a > s > t infixr 4 Source
Divide the target(s) of a numerically valued Lens
, Iso
, Setter
or Traversal
.
>>>
(a,b) & _1 //~ c
(a / c,b)
>>>
(a,b) & both //~ c
(a / c,b / c)
>>>
("Hawaii",10) & _2 //~ 2
("Hawaii",5.0)
(//~
) ::Fractional
a =>Setter'
s a > a > s > s (//~
) ::Fractional
a =>Iso'
s a > a > s > s (//~
) ::Fractional
a =>Lens'
s a > a > s > s (//~
) ::Fractional
a =>Traversal'
s a > a > s > s
(^~) :: (Num a, Integral e) => ASetter s t a a > e > s > t infixr 4 Source
Raise the target(s) of a numerically valued Lens
, Setter
or Traversal
to a nonnegative integral power.
>>>
(1,3) & _2 ^~ 2
(1,9)
(^~
) :: (Num
a,Integral
e) =>Setter'
s a > e > s > s (^~
) :: (Num
a,Integral
e) =>Iso'
s a > e > s > s (^~
) :: (Num
a,Integral
e) =>Lens'
s a > e > s > s (^~
) :: (Num
a,Integral
e) =>Traversal'
s a > e > s > s
(^^~) :: (Fractional a, Integral e) => ASetter s t a a > e > s > t infixr 4 Source
Raise the target(s) of a fractionally valued Lens
, Setter
or Traversal
to an integral power.
>>>
(1,2) & _2 ^^~ (1)
(1,0.5)
(^^~
) :: (Fractional
a,Integral
e) =>Setter'
s a > e > s > s (^^~
) :: (Fractional
a,Integral
e) =>Iso'
s a > e > s > s (^^~
) :: (Fractional
a,Integral
e) =>Lens'
s a > e > s > s (^^~
) :: (Fractional
a,Integral
e) =>Traversal'
s a > e > s > s
(**~) :: Floating a => ASetter s t a a > a > s > t infixr 4 Source
Raise the target(s) of a floatingpoint valued Lens
, Setter
or Traversal
to an arbitrary power.
>>>
(a,b) & _1 **~ c
(a**c,b)
>>>
(a,b) & both **~ c
(a**c,b**c)
>>>
_2 **~ 10 $ (3,2)
(3,1024.0)
(**~
) ::Floating
a =>Setter'
s a > a > s > s (**~
) ::Floating
a =>Iso'
s a > a > s > s (**~
) ::Floating
a =>Lens'
s a > a > s > s (**~
) ::Floating
a =>Traversal'
s a > a > s > s
(~) :: ASetter s t Bool Bool > Bool > s > t infixr 4 Source
Logically 
the target(s) of a Bool
valued Lens
or Setter
.
>>>
both ~ True $ (False,True)
(True,True)
>>>
both ~ False $ (False,True)
(False,True)
(~
) ::Setter'
sBool
>Bool
> s > s (~
) ::Iso'
sBool
>Bool
> s > s (~
) ::Lens'
sBool
>Bool
> s > s (~
) ::Traversal'
sBool
>Bool
> s > s
(<>~) :: Monoid a => ASetter s t a a > a > s > t infixr 4 Source
Modify the target of a monoidally valued by mappend
ing another value.
>>>
(Sum a,b) & _1 <>~ Sum c
(Sum {getSum = a + c},b)
>>>
(Sum a,Sum b) & both <>~ Sum c
(Sum {getSum = a + c},Sum {getSum = b + c})
>>>
both <>~ "!!!" $ ("hello","world")
("hello!!!","world!!!")
(<>~
) ::Monoid
a =>Setter
s t a a > a > s > t (<>~
) ::Monoid
a =>Iso
s t a a > a > s > t (<>~
) ::Monoid
a =>Lens
s t a a > a > s > t (<>~
) ::Monoid
a =>Traversal
s t a a > a > s > t
(&&~) :: ASetter s t Bool Bool > Bool > s > t infixr 4 Source
Logically &&
the target(s) of a Bool
valued Lens
or Setter
.
>>>
both &&~ True $ (False, True)
(False,True)
>>>
both &&~ False $ (False, True)
(False,False)
(&&~
) ::Setter'
sBool
>Bool
> s > s (&&~
) ::Iso'
sBool
>Bool
> s > s (&&~
) ::Lens'
sBool
>Bool
> s > s (&&~
) ::Traversal'
sBool
>Bool
> s > s
(<.~) :: ASetter s t a b > b > s > (b, t) infixr 4 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..~
t
>>>
(a,b) & _1 <.~ c
(c,(c,b))
>>>
("good","morning","vietnam") & _3 <.~ "world"
("world",("good","morning","world"))
>>>
(42,Map.fromList [("goodnight","gracie")]) & _2.at "hello" <.~ Just "world"
(Just "world",(42,fromList [("goodnight","gracie"),("hello","world")]))
(<.~
) ::Setter
s t a b > b > s > (b, t) (<.~
) ::Iso
s t a b > b > s > (b, t) (<.~
) ::Lens
s t a b > b > s > (b, t) (<.~
) ::Traversal
s t a b > b > s > (b, t)
(?~) :: ASetter s t a (Maybe b) > b > s > t infixr 4 Source
Set the target of a Lens
, Traversal
or Setter
to Just
a value.
l?~
t ≡set
l (Just
t)
>>>
Nothing & id ?~ a
Just a
>>>
Map.empty & at 3 ?~ x
fromList [(3,x)]
(?~
) ::Setter
s t a (Maybe
b) > b > s > t (?~
) ::Iso
s t a (Maybe
b) > b > s > t (?~
) ::Lens
s t a (Maybe
b) > b > s > t (?~
) ::Traversal
s t a (Maybe
b) > b > s > t
(<?~) :: ASetter s t a (Maybe b) > b > s > (b, t) infixr 4 Source
Set to Just
a value 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
>>>
import Data.Map as Map
>>>
_2.at "hello" <?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
("world",(42,fromList [("goodnight","gracie"),("hello","world")]))
(<?~
) ::Setter
s t a (Maybe
b) > b > s > (b, t) (<?~
) ::Iso
s t a (Maybe
b) > b > s > (b, t) (<?~
) ::Lens
s t a (Maybe
b) > b > s > (b, t) (<?~
) ::Traversal
s t a (Maybe
b) > b > s > (b, t)
State Combinators
assign :: MonadState s m => ASetter s s a b > b > 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.
This is an alias for (.=
).
>>>
execState (do assign _1 c; assign _2 d) (a,b)
(c,d)
>>>
execState (both .= c) (a,b)
(c,c)
assign
::MonadState
s m =>Iso'
s a > a > m ()assign
::MonadState
s m =>Lens'
s a > a > m ()assign
::MonadState
s m =>Traversal'
s a > a > m ()assign
::MonadState
s m =>Setter'
s a > a > m ()
(.=) :: MonadState s m => ASetter s s a b > b > m () infix 4 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.
This is an infix version of assign
.
>>>
execState (do _1 .= c; _2 .= d) (a,b)
(c,d)
>>>
execState (both .= c) (a,b)
(c,c)
(.=
) ::MonadState
s m =>Iso'
s a > a > m () (.=
) ::MonadState
s m =>Lens'
s a > a > m () (.=
) ::MonadState
s m =>Traversal'
s a > a > m () (.=
) ::MonadState
s m =>Setter'
s a > a > m ()
It puts the state in the monad or it gets the hose again.
(%=) :: (Profunctor p, MonadState s m) => Setting p s s a b > p a b > m () infix 4 Source
Map over the target of a Lens
or all of the targets of a Setter
or Traversal
in our monadic state.
>>>
execState (do _1 %= f;_2 %= g) (a,b)
(f a,g b)
>>>
execState (do both %= f) (a,b)
(f a,f b)
(%=
) ::MonadState
s m =>Iso'
s a > (a > a) > m () (%=
) ::MonadState
s m =>Lens'
s a > (a > a) > m () (%=
) ::MonadState
s m =>Traversal'
s a > (a > a) > m () (%=
) ::MonadState
s m =>Setter'
s a > (a > a) > m ()
(%=
) ::MonadState
s m =>ASetter
s s a b > (a > b) > m ()
(+=) :: (MonadState s m, Num a) => ASetter' s a > a > m () infix 4 Source
Modify the target(s) of a Lens'
, Iso
, Setter
or Traversal
by adding a value.
Example:
fresh
::MonadState
Int
m => mInt
fresh
= doid
+=
1use
id
>>>
execState (do _1 += c; _2 += d) (a,b)
(a + c,b + d)
>>>
execState (do _1.at 1.non 0 += 10) (Map.fromList [(2,100)],"hello")
(fromList [(1,10),(2,100)],"hello")
(+=
) :: (MonadState
s m,Num
a) =>Setter'
s a > a > m () (+=
) :: (MonadState
s m,Num
a) =>Iso'
s a > a > m () (+=
) :: (MonadState
s m,Num
a) =>Lens'
s a > a > m () (+=
) :: (MonadState
s m,Num
a) =>Traversal'
s a > a > m ()
(=) :: (MonadState s m, Num a) => ASetter' s a > a > m () infix 4 Source
Modify the target(s) of a Lens'
, Iso
, Setter
or Traversal
by subtracting a value.
>>>
execState (do _1 = c; _2 = d) (a,b)
(a  c,b  d)
(=
) :: (MonadState
s m,Num
a) =>Setter'
s a > a > m () (=
) :: (MonadState
s m,Num
a) =>Iso'
s a > a > m () (=
) :: (MonadState
s m,Num
a) =>Lens'
s a > a > m () (=
) :: (MonadState
s m,Num
a) =>Traversal'
s a > a > m ()
(*=) :: (MonadState s m, Num a) => ASetter' s a > a > m () infix 4 Source
Modify the target(s) of a Lens'
, Iso
, Setter
or Traversal
by multiplying by value.
>>>
execState (do _1 *= c; _2 *= d) (a,b)
(a * c,b * d)
(*=
) :: (MonadState
s m,Num
a) =>Setter'
s a > a > m () (*=
) :: (MonadState
s m,Num
a) =>Iso'
s a > a > m () (*=
) :: (MonadState
s m,Num
a) =>Lens'
s a > a > m () (*=
) :: (MonadState
s m,Num
a) =>Traversal'
s a > a > m ()
(//=) :: (MonadState s m, Fractional a) => ASetter' s a > a > m () infix 4 Source
Modify the target(s) of a Lens'
, Iso
, Setter
or Traversal
by dividing by a value.
>>>
execState (do _1 //= c; _2 //= d) (a,b)
(a / c,b / d)
(//=
) :: (MonadState
s m,Fractional
a) =>Setter'
s a > a > m () (//=
) :: (MonadState
s m,Fractional
a) =>Iso'
s a > a > m () (//=
) :: (MonadState
s m,Fractional
a) =>Lens'
s a > a > m () (//=
) :: (MonadState
s m,Fractional
a) =>Traversal'
s a > a > m ()
(^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a > e > m () infix 4 Source
Raise the target(s) of a numerically valued Lens
, Setter
or Traversal
to a nonnegative integral power.
(^=
) :: (MonadState
s m,Num
a,Integral
e) =>Setter'
s a > e > m () (^=
) :: (MonadState
s m,Num
a,Integral
e) =>Iso'
s a > e > m () (^=
) :: (MonadState
s m,Num
a,Integral
e) =>Lens'
s a > e > m () (^=
) :: (MonadState
s m,Num
a,Integral
e) =>Traversal'
s a > e > m ()
(^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a > e > m () infix 4 Source
Raise the target(s) of a numerically valued Lens
, Setter
or Traversal
to an integral power.
(^^=
) :: (MonadState
s m,Fractional
a,Integral
e) =>Setter'
s a > e > m () (^^=
) :: (MonadState
s m,Fractional
a,Integral
e) =>Iso'
s a > e > m () (^^=
) :: (MonadState
s m,Fractional
a,Integral
e) =>Lens'
s a > e > m () (^^=
) :: (MonadState
s m,Fractional
a,Integral
e) =>Traversal'
s a > e > m ()
(**=) :: (MonadState s m, Floating a) => ASetter' s a > a > m () infix 4 Source
Raise the target(s) of a numerically valued Lens
, Setter
or Traversal
to an arbitrary power
>>>
execState (do _1 **= c; _2 **= d) (a,b)
(a**c,b**d)
(**=
) :: (MonadState
s m,Floating
a) =>Setter'
s a > a > m () (**=
) :: (MonadState
s m,Floating
a) =>Iso'
s a > a > m () (**=
) :: (MonadState
s m,Floating
a) =>Lens'
s a > a > m () (**=
) :: (MonadState
s m,Floating
a) =>Traversal'
s a > a > m ()
(=) :: MonadState s m => ASetter' s Bool > Bool > m () infix 4 Source
Modify the target(s) of a Lens'
, 'Iso, Setter
or Traversal
by taking their logical 
with a value.
>>>
execState (do _1 = True; _2 = False; _3 = True; _4 = False) (True,True,False,False)
(True,True,True,False)
(=
) ::MonadState
s m =>Setter'
sBool
>Bool
> m () (=
) ::MonadState
s m =>Iso'
sBool
>Bool
> m () (=
) ::MonadState
s m =>Lens'
sBool
>Bool
> m () (=
) ::MonadState
s m =>Traversal'
sBool
>Bool
> m ()
(<>=) :: (MonadState s m, Monoid a) => ASetter' s a > a > m () infix 4 Source
Modify the target(s) of a Lens'
, Iso
, Setter
or Traversal
by mappend
ing a value.
>>>
execState (do _1 <>= Sum c; _2 <>= Product d) (Sum a,Product b)
(Sum {getSum = a + c},Product {getProduct = b * d})
>>>
execState (both <>= "!!!") ("hello","world")
("hello!!!","world!!!")
(<>=
) :: (MonadState
s m,Monoid
a) =>Setter'
s a > a > m () (<>=
) :: (MonadState
s m,Monoid
a) =>Iso'
s a > a > m () (<>=
) :: (MonadState
s m,Monoid
a) =>Lens'
s a > a > m () (<>=
) :: (MonadState
s m,Monoid
a) =>Traversal'
s a > a > m ()
(&&=) :: MonadState s m => ASetter' s Bool > Bool > m () infix 4 Source
Modify the target(s) of a Lens'
, Iso
, Setter
or Traversal
by taking their logical &&
with a value.
>>>
execState (do _1 &&= True; _2 &&= False; _3 &&= True; _4 &&= False) (True,True,False,False)
(True,False,False,False)
(&&=
) ::MonadState
s m =>Setter'
sBool
>Bool
> m () (&&=
) ::MonadState
s m =>Iso'
sBool
>Bool
> m () (&&=
) ::MonadState
s m =>Lens'
sBool
>Bool
> m () (&&=
) ::MonadState
s m =>Traversal'
sBool
>Bool
> m ()
(<.=) :: MonadState s m => ASetter s s a b > b > m b infix 4 Source
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
will avoid unused binding warnings..=
d
(<.=
) ::MonadState
s m =>Setter
s s a b > b > m b (<.=
) ::MonadState
s m =>Iso
s s a b > b > m b (<.=
) ::MonadState
s m =>Lens
s s a b > b > m b (<.=
) ::MonadState
s m =>Traversal
s s a b > b > m b
(?=) :: MonadState s m => ASetter s s a (Maybe b) > b > m () infix 4 Source
Replace the target of a Lens
or all of the targets of a Setter
or Traversal
in our monadic
state with Just
a new value, irrespective of the old.
>>>
execState (do at 1 ?= a; at 2 ?= b) Map.empty
fromList [(1,a),(2,b)]
>>>
execState (do _1 ?= b; _2 ?= c) (Just a, Nothing)
(Just b,Just c)
(?=
) ::MonadState
s m =>Iso'
s (Maybe
a) > a > m () (?=
) ::MonadState
s m =>Lens'
s (Maybe
a) > a > m () (?=
) ::MonadState
s m =>Traversal'
s (Maybe
a) > a > m () (?=
) ::MonadState
s m =>Setter'
s (Maybe
a) > a > m ()
(<?=) :: MonadState s m => ASetter s s a (Maybe b) > b > m b infix 4 Source
Set Just
a value with passthrough
This is useful for chaining assignment without roundtripping through your Monad
stack.
do x <at
"foo"<?=
ninety_nine_bottles_of_beer_on_the_wall
If you do not need a copy of the intermediate result, then using l
will avoid unused binding warnings.?=
d
(<?=
) ::MonadState
s m =>Setter
s s a (Maybe
b) > b > m b (<?=
) ::MonadState
s m =>Iso
s s a (Maybe
b) > b > m b (<?=
) ::MonadState
s m =>Lens
s s a (Maybe
b) > b > m b (<?=
) ::MonadState
s m =>Traversal
s s a (Maybe
b) > b > m b
(<~) :: MonadState s m => ASetter s s a b > m b > m () infixr 2 Source
Run a monadic action, and set all of the targets of a Lens
, Setter
or Traversal
to its result.
(<~
) ::MonadState
s m =>Iso
s s a b > m b > m () (<~
) ::MonadState
s m =>Lens
s s a b > m b > m () (<~
) ::MonadState
s m =>Traversal
s s a b > m b > m () (<~
) ::MonadState
s m =>Setter
s s a b > m b > 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
...
Writer Combinators
scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b > b > m () Source
Write to a fragment of a larger Writer
format.
passing :: MonadWriter w m => Setter w w u v > m (a, u > v) > m a Source
This is a generalization of pass
that alows you to modify just a
portion of the resulting MonadWriter
.
ipassing :: MonadWriter w m => IndexedSetter i w w u v > m (a, i > u > v) > m a Source
This is a generalization of pass
that alows you to modify just a
portion of the resulting MonadWriter
with access to the index of an
IndexedSetter
.
censoring :: MonadWriter w m => Setter w w u v > (u > v) > m a > m a Source
This is a generalization of censor
that alows you to censor
just a
portion of the resulting MonadWriter
.
icensoring :: MonadWriter w m => IndexedSetter i w w u v > (i > u > v) > m a > m a Source
This is a generalization of censor
that alows you to censor
just a
portion of the resulting MonadWriter
, with access to the index of an
IndexedSetter
.
Simplified State Setting
set' :: ASetter' s a > a > s > s Source
Replace the target of a Lens
or all of the targets of a Setter'
or Traversal
with a constant value, without changing its type.
This is a type restricted version of set
, which retains the type of the original.
>>>
set' mapped x [a,b,c,d]
[x,x,x,x]
>>>
set' _2 "hello" (1,"world")
(1,"hello")
>>>
set' mapped 0 [1,2,3,4]
[0,0,0,0]
Note: Attempting to adjust set'
a Fold
or Getter
will fail at compile time with an
relatively nice error message.
set'
::Setter'
s a > a > s > sset'
::Iso'
s a > a > s > sset'
::Lens'
s a > a > s > sset'
::Traversal'
s a > a > s > s
Indexed Setters
imapOf :: AnIndexedSetter i s t a b > (i > a > b) > s > t Source
Deprecated: Use iover
Map with index. (Deprecated alias for iover
).
When you do not need access to the index, then mapOf
is more liberal in what it can accept.
mapOf
l ≡imapOf
l.
const
imapOf
::IndexedSetter
i s t a b > (i > a > b) > s > timapOf
::IndexedLens
i s t a b > (i > a > b) > s > timapOf
::IndexedTraversal
i s t a b > (i > a > b) > s > t
iover :: AnIndexedSetter i s t a b > (i > a > b) > s > t Source
Map with index. This is an alias for imapOf
.
When you do not need access to the index, then over
is more liberal in what it can accept.
over
l ≡iover
l.
const
iover
l ≡over
l.
Indexed
iover
::IndexedSetter
i s t a b > (i > a > b) > s > tiover
::IndexedLens
i s t a b > (i > a > b) > s > tiover
::IndexedTraversal
i s t a b > (i > a > b) > s > t
isets :: ((i > a > b) > s > t) > IndexedSetter i s t a b Source
(%@~) :: AnIndexedSetter i s t a b > (i > a > b) > s > t infixr 4 Source
Adjust every target of an IndexedSetter
, IndexedLens
or IndexedTraversal
with access to the index.
(%@~
) ≡imapOf
When you do not need access to the index then (%@~
) is more liberal in what it can accept.
l%~
f ≡ l%@~
const
f
(%@~
) ::IndexedSetter
i s t a b > (i > a > b) > s > t (%@~
) ::IndexedLens
i s t a b > (i > a > b) > s > t (%@~
) ::IndexedTraversal
i s t a b > (i > a > b) > s > t
(%@=) :: MonadState s m => AnIndexedSetter i s s a b > (i > a > b) > m () infix 4 Source
Adjust every target in the current state of an IndexedSetter
, IndexedLens
or IndexedTraversal
with access to the index.
When you do not need access to the index then (%=
) is more liberal in what it can accept.
l%=
f ≡ l%@=
const
f
(%@=
) ::MonadState
s m =>IndexedSetter
i s s a b > (i > a > b) > m () (%@=
) ::MonadState
s m =>IndexedLens
i s s a b > (i > a > b) > m () (%@=
) ::MonadState
s m =>IndexedTraversal
i s t a b > (i > a > b) > m ()
Arrow operators
assignA :: Arrow p => ASetter s t a b > p s b > p s t Source
Run an arrow command and use the output to set all the targets of
a Lens
, Setter
or Traversal
to the result.
assignA
can be used very similarly to (<~
), except that the type of
the object being modified can change; for example:
runKleisli action ((), (), ()) where action = assignA _1 (Kleisli (const getVal1)) >>> assignA _2 (Kleisli (const getVal2)) >>> assignA _3 (Kleisli (const getVal3)) getVal1 :: Either String Int getVal1 = ... getVal2 :: Either String Bool getVal2 = ... getVal3 :: Either String Char getVal3 = ...
has the type Either
String
(Int
, Bool
, Char
)
assignA
::Arrow
p =>Iso
s t a b > p s b > p s tassignA
::Arrow
p =>Lens
s t a b > p s b > p s tassignA
::Arrow
p =>Traversal
s t a b > p s b > p s tassignA
::Arrow
p =>Setter
s t a b > p s b > p s t
Exported for legible error messages
class (Applicative f, Distributive f, Traversable f) => Settable f Source
newtype Identity a :: * > *
Identity functor and monad.
Identity  

Monad Identity  
Functor Identity  
MonadFix Identity  
Applicative Identity  
Foldable Identity  
Traversable Identity  
Comonad Identity  
ComonadApply Identity  
Distributive Identity  
Traversable1 Identity  
Foldable1 Identity  
Apply Identity  
Bind Identity  
Extend Identity  
Eq1 Identity  
Ord1 Identity  
Read1 Identity  
Show1 Identity  
Settable Identity  So you can pass our 
TraversableWithIndex () Identity  
FoldableWithIndex () Identity  
FunctorWithIndex () Identity  
Effective Identity r (Const r)  
Eq a => Eq (Identity a)  
Ord a => Ord (Identity a)  
Read a => Read (Identity a)  
Show a => Show (Identity a)  
Wrapped (Identity a)  
Ixed (Identity a)  
(~) * t (Identity b) => Rewrapped (Identity a) t  
Field1 (Identity a) (Identity b) a b  
Each (Identity a) (Identity b) a b 

type Unwrapped (Identity a) = a  
type IxValue (Identity a) = a  
type Index (Identity a) = () 