Portability  Rank2Types 

Stability  provisional 
Maintainer  Edward Kmett <ekmett@gmail.com> 
Safe Haskell  SafeInferred 
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 fmap ::
we monomorphize the type to obtain 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
 sets :: ((a > b) > s > t) > Setter s t a b
 mapped :: Functor f => Setter (f a) (f b) a b
 lifted :: Monad m => Setter (m a) (m b) a b
 over :: Setting s t a b > (a > b) > s > t
 mapOf :: Setting s t a b > (a > b) > s > t
 set :: Setting s t a b > b > s > t
 (.~) :: Setting s t a b > b > s > t
 (%~) :: Setting s t a b > (a > b) > s > t
 (+~) :: Num a => Setting s t a a > a > s > t
 (~) :: Num a => Setting s t a a > a > s > t
 (*~) :: Num a => Setting s t a a > a > s > t
 (//~) :: Fractional s => Setting a b s s > s > a > b
 (^~) :: (Num a, Integral e) => Setting s t a a > e > s > t
 (^^~) :: (Fractional a, Integral e) => Setting s t a a > e > s > t
 (**~) :: Floating a => Setting s t a a > a > s > t
 (~) :: Setting s t Bool Bool > Bool > s > t
 (<>~) :: Monoid a => Setting s t a a > a > s > t
 (&&~) :: Setting s t Bool Bool > Bool > s > t
 (<.~) :: Setting s t a b > b > s > (b, t)
 (?~) :: Setting s t a (Maybe b) > b > s > t
 (<?~) :: Setting s t a (Maybe b) > b > s > (b, t)
 assign :: MonadState s m => Setting s s a b > b > m ()
 (.=) :: MonadState s m => Setting s s a b > b > m ()
 (%=) :: MonadState s m => Setting s s a b > (a > b) > m ()
 (+=) :: (MonadState s m, Num a) => SimpleSetting s a > a > m ()
 (=) :: (MonadState s m, Num a) => SimpleSetting s a > a > m ()
 (*=) :: (MonadState s m, Num a) => SimpleSetting s a > a > m ()
 (//=) :: (MonadState s m, Fractional a) => SimpleSetting s a > a > m ()
 (^=) :: (MonadState s m, Num a, Integral e) => SimpleSetting s a > e > m ()
 (^^=) :: (MonadState s m, Fractional a, Integral e) => SimpleSetting s a > e > m ()
 (**=) :: (MonadState s m, Floating a) => SimpleSetting s a > a > m ()
 (=) :: MonadState s m => SimpleSetting s Bool > Bool > m ()
 (<>=) :: (MonadState s m, Monoid a) => SimpleSetting s a > a > m ()
 (&&=) :: MonadState s m => SimpleSetting s Bool > Bool > m ()
 (<.=) :: MonadState s m => Setting s s a b > b > m b
 (?=) :: MonadState s m => Setting s s a (Maybe b) > b > m ()
 (<?=) :: MonadState s m => Setting s s a (Maybe b) > b > m b
 (<~) :: MonadState s m => Setting s s a b > m b > m ()
 set' :: Setting s s a a > a > s > s
 newtype ReifiedSetter s t a b = ReifySetter {
 reflectSetter :: Setter s t a b
 type Setting s t a b = (a > Mutator b) > s > Mutator t
 type SimpleSetting s a = Setting s s a a
 type SimpleSetter s a = Setter s s a a
 type SimpleReifiedSetter s a = ReifiedSetter s s a a
 class Applicative f => Settable f
 data Mutator a
Setters
type Setter s t a b = forall f. Settable f => (a > f b) > s > f tSource
The only Lens
like 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 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.
>>>
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)]
Building Setters
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
≡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)]
Functional Combinators
over :: Setting s t a b > (a > b) > s > tSource
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 > t
set :: Setting s t a b > b > s > tSource
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
(.~) :: Setting s t a b > b > s > tSource
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
(%~) :: Setting s t a b > (a > b) > s > tSource
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 => Setting s t a a > a > s > tSource
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 =>Simple
Setter
s a > a > s > s (+~
) :: Num a =>Simple
Iso
s a > a > s > s (+~
) :: Num a =>Simple
Lens
s a > a > s > s (+~
) :: Num a =>Simple
Traversal
s a > a > s > s
(~) :: Num a => Setting s t a a > a > s > tSource
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 =>Simple
Setter
s a > a > s > s (~
) ::Num
a =>Simple
Iso
s a > a > s > s (~
) ::Num
a =>Simple
Lens
s a > a > s > s (~
) ::Num
a =>Simple
Traversal
s a > a > s > s
(*~) :: Num a => Setting s t a a > a > s > tSource
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 =>Simple
Setter
s a > a > s > s (*~
) ::Num
a =>Simple
Iso
s a > a > s > s (*~
) ::Num
a =>Simple
Lens
s a > a > s > s (*~
) ::Num
a =>Simple
Traversal
s a > a > s > s
(//~) :: Fractional s => Setting a b s s > s > a > bSource
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 =>Simple
Setter
s a > a > s > s (//~
) ::Fractional
a =>Simple
Iso
s a > a > s > s (//~
) ::Fractional
a =>Simple
Lens
s a > a > s > s (//~
) ::Fractional
a =>Simple
Traversal
s a > a > s > s
(^~) :: (Num a, Integral e) => Setting s t a a > e > s > tSource
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) =>Simple
Setter
s a > e > s > s (^~
) :: (Num
a,Integral
e) =>Simple
Iso
s a > e > s > s (^~
) :: (Num
a,Integral
e) =>Simple
Lens
s a > e > s > s (^~
) :: (Num
a,Integral
e) =>Simple
Traversal
s a > e > s > s
(^^~) :: (Fractional a, Integral e) => Setting s t a a > e > s > tSource
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) =>Simple
Setter
s a > e > s > s (^^~
) :: (Fractional
a,Integral
e) =>Simple
Iso
s a > e > s > s (^^~
) :: (Fractional
a,Integral
e) =>Simple
Lens
s a > e > s > s (^^~
) :: (Fractional
a,Integral
e) =>Simple
Traversal
s a > e > s > s
(**~) :: Floating a => Setting s t a a > a > s > tSource
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 **~ pi $ (1,3)
(1,31.54428070019754)
(**~
) ::Floating
a =>Simple
Setter
s a > a > s > s (**~
) ::Floating
a =>Simple
Iso
s a > a > s > s (**~
) ::Floating
a =>Simple
Lens
s a > a > s > s (**~
) ::Floating
a =>Simple
Traversal
s a > a > s > s
(~) :: Setting s t Bool Bool > Bool > s > tSource
Logically 
the target(s) of a Bool
valued Lens
or Setter
>>>
both ~ True $ (False,True)
(True,True)
>>>
both ~ False $ (False,True)
(False,True)
(~
) ::Simple
Setter
sBool
>Bool
> s > s (~
) ::Simple
Iso
sBool
>Bool
> s > s (~
) ::Simple
Lens
sBool
>Bool
> s > s (~
) ::Simple
Traversal
sBool
>Bool
> s > s
(<>~) :: Monoid a => Setting s t a a > a > s > tSource
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
(&&~) :: Setting s t Bool Bool > Bool > s > tSource
Logically &&
the target(s) of a Bool
valued Lens
or Setter
>>>
both &&~ True $ (False, True)
(False,True)
>>>
both &&~ False $ (False, True)
(False,False)
(&&~
) ::Simple
Setter
sBool
>Bool
> s > s (&&~
) ::Simple
Iso
sBool
>Bool
> s > s (&&~
) ::Simple
Lens
sBool
>Bool
> s > s (&&~
) ::Simple
Traversal
sBool
>Bool
> s > s
(<.~) :: Setting s t a b > b > s > (b, t)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)
(?~) :: Setting s t a (Maybe b) > b > s > tSource
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
(<?~) :: Setting s t a (Maybe b) > b > s > (b, t)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 b > (Maybe
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 => Setting 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 =>Simple
Iso
s a > a > m ()assign
::MonadState
s m =>Simple
Lens
s a > a > m ()assign
::MonadState
s m =>Simple
Traversal
s a > a > m ()assign
::MonadState
s m =>Simple
Setter
s a > a > m ()
(.=) :: MonadState s m => Setting 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 infix version of assign
.
>>>
execState (do _1 .= c; _2 .= d) (a,b)
(c,d)
>>>
execState (both .= c) (a,b)
(c,c)
(.=
) ::MonadState
s m =>Simple
Iso
s a > a > m () (.=
) ::MonadState
s m =>Simple
Lens
s a > a > m () (.=
) ::MonadState
s m =>Simple
Traversal
s a > a > m () (.=
) ::MonadState
s m =>Simple
Setter
s a > a > m ()
(%=) :: MonadState s m => Setting s s a b > (a > b) > m ()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 =>Simple
Iso
s a > (a > a) > m () (%=
) ::MonadState
s m =>Simple
Lens
s a > (a > a) > m () (%=
) ::MonadState
s m =>Simple
Traversal
s a > (a > a) > m () (%=
) ::MonadState
s m =>Simple
Setter
s a > (a > a) > m ()
(+=) :: (MonadState s m, Num a) => SimpleSetting s a > a > 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
>>>
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) =>Simple
Setter
s a > a > m () (+=
) :: (MonadState
s m,Num
a) =>Simple
Iso
s a > a > m () (+=
) :: (MonadState
s m,Num
a) =>Simple
Lens
s a > a > m () (+=
) :: (MonadState
s m,Num
a) =>Simple
Traversal
s a > a > m ()
(=) :: (MonadState s m, Num a) => SimpleSetting s a > a > m ()Source
Modify the target(s) of a Simple
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) =>Simple
Setter
s a > a > m () (=
) :: (MonadState
s m,Num
a) =>Simple
Iso
s a > a > m () (=
) :: (MonadState
s m,Num
a) =>Simple
Lens
s a > a > m () (=
) :: (MonadState
s m,Num
a) =>Simple
Traversal
s a > a > m ()
(*=) :: (MonadState s m, Num a) => SimpleSetting s a > a > m ()Source
Modify the target(s) of a Simple
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) =>Simple
Setter
s a > a > m () (*=
) :: (MonadState
s m,Num
a) =>Simple
Iso
s a > a > m () (*=
) :: (MonadState
s m,Num
a) =>Simple
Lens
s a > a > m () (*=
) :: (MonadState
s m,Num
a) =>Simple
Traversal
s a > a > m ()
(//=) :: (MonadState s m, Fractional a) => SimpleSetting s a > a > m ()Source
Modify the target(s) of a Simple
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) =>Simple
Setter
s a > a > m () (//=
) :: (MonadState
s m,Fractional
a) =>Simple
Iso
s a > a > m () (//=
) :: (MonadState
s m,Fractional
a) =>Simple
Lens
s a > a > m () (//=
) :: (MonadState
s m,Fractional
a) =>Simple
Traversal
s a > a > m ()
(^=) :: (MonadState s m, Num a, Integral e) => SimpleSetting s a > e > m ()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) =>Simple
Setter
s a > e > m () (^=
) :: (MonadState
s m,Num
a,Integral
e) =>Simple
Iso
s a > e > m () (^=
) :: (MonadState
s m,Num
a,Integral
e) =>Simple
Lens
s a > e > m () (^=
) :: (MonadState
s m,Num
a,Integral
e) =>Simple
Traversal
s a > e > m ()
(^^=) :: (MonadState s m, Fractional a, Integral e) => SimpleSetting s a > e > m ()Source
Raise the target(s) of a numerically valued Lens
, Setter
or Traversal
to an integral power.
(^^=
) :: (MonadState
s m,Fractional
a,Integral
e) =>Simple
Setter
s a > e > m () (^^=
) :: (MonadState
s m,Fractional
a,Integral
e) =>Simple
Iso
s a > e > m () (^^=
) :: (MonadState
s m,Fractional
a,Integral
e) =>Simple
Lens
s a > e > m () (^^=
) :: (MonadState
s m,Fractional
a,Integral
e) =>Simple
Traversal
s a > e > m ()
(**=) :: (MonadState s m, Floating a) => SimpleSetting s a > a > m ()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) =>Simple
Setter
s a > a > m () (**=
) :: (MonadState
s m,Floating
a) =>Simple
Iso
s a > a > m () (**=
) :: (MonadState
s m,Floating
a) =>Simple
Lens
s a > a > m () (**=
) :: (MonadState
s m,Floating
a) =>Simple
Traversal
s a > a > m ()
(=) :: MonadState s m => SimpleSetting s Bool > Bool > m ()Source
Modify the target(s) of a Simple
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 =>Simple
Setter
sBool
>Bool
> m () (=
) ::MonadState
s m =>Simple
Iso
sBool
>Bool
> m () (=
) ::MonadState
s m =>Simple
Lens
sBool
>Bool
> m () (=
) ::MonadState
s m =>Simple
Traversal
sBool
>Bool
> m ()
(<>=) :: (MonadState s m, Monoid a) => SimpleSetting s a > a > m ()Source
Modify the target(s) of a Simple
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) =>Simple
Setter
s a > a > m () (<>=
) :: (MonadState
s m,Monoid
a) =>Simple
Iso
s a > a > m () (<>=
) :: (MonadState
s m,Monoid
a) =>Simple
Lens
s a > a > m () (<>=
) :: (MonadState
s m,Monoid
a) =>Simple
Traversal
s a > a > m ()
(&&=) :: MonadState s m => SimpleSetting s Bool > Bool > m ()Source
Modify the target(s) of a Simple
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 =>Simple
Setter
sBool
>Bool
> m () (&&=
) ::MonadState
s m =>Simple
Iso
sBool
>Bool
> m () (&&=
) ::MonadState
s m =>Simple
Lens
sBool
>Bool
> m () (&&=
) ::MonadState
s m =>Simple
Traversal
sBool
>Bool
> m ()
(<.=) :: MonadState s m => Setting s s a b > b > m bSource
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
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 => Setting s s a (Maybe 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 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 =>Simple
Iso
s (Maybe
a) > a > m () (?=
) ::MonadState
s m =>Simple
Lens
s (Maybe
a) > a > m () (?=
) ::MonadState
s m =>Simple
Traversal
s (Maybe
a) > a > m () (?=
) ::MonadState
s m =>Simple
Setter
s (Maybe
a) > a > m ()
(<?=) :: MonadState s m => Setting s s a (Maybe b) > b > m bSource
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 ?= d
will avoid unused binding warnings
(<?=
) ::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 => Setting s s a b > m b > m ()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
...
Simplified State Setting
set' :: Setting s s a a > a > s > sSource
Replace the target of a Lens
or all of the targets of a Simple
Setter
or Simple
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'
::Simple
Setter
s a > a > s > sset'
::Simple
Iso
s a > a > s > sset'
::Simple
Lens
s a > a > s > sset'
::Simple
Traversal
s a > a > s > s
Storing Setters
newtype ReifiedSetter s t a b Source
Reify a setter so it can be stored safely in a container.
ReifySetter  

Setter Internals
type SimpleSetting s a = Setting s s a aSource
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 s a = Setter s s a aSource
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
type SimpleReifiedSetter s a = ReifiedSetter s s a aSource
Exported for legible error messages
class Applicative f => Settable f Source