content: {-# LANGUAGE CPP #-}
  {-# LANGUAGE ScopedTypeVariables #-}
  {-# LANGUAGE TypeOperators #-}
  {-# LANGUAGE Rank2Types #-}
  {-# LANGUAGE MultiParamTypeClasses #-}
  {-# LANGUAGE FlexibleInstances #-}
  {-# LANGUAGE FlexibleContexts #-}
  
  #if __GLASGOW_HASKELL__ < 708
  {-# LANGUAGE Trustworthy #-}
  #endif
  -----------------------------------------------------------------------------
  -- |
  -- Module      :  Silica.Setter
  -- Copyright   :  (C) 2012-16 Edward Kmett
  -- License     :  BSD-style (see the file LICENSE)
  -- Maintainer  :  Edward Kmett <ekmett@gmail.com>
  -- Stability   :  provisional
  -- Portability :  Rank2Types
  --
  -- A @'Setter' s t a b@ 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. 
  --
  -- = Where the type comes from
  --
  -- Starting with @'fmap' :: 'Functor' f => (a -> b) -> f a -> f b@
  -- we monomorphize the type to obtain @(a -> b) -> s -> t@ and then decorate it with 'Data.Functor.Identity.Identity' to obtain:
  --
  -- @
  -- type 'Setter' s t a b = (a -> 'Data.Functor.Identity.Identity' b) -> s -> 'Data.Functor.Identity.Identity' t
  -- @
  --
  -- Every 'Traversal' is a valid 'Setter', since 'Data.Functor.Identity.Identity' is 'Applicative'.
  --
  -- Everything you can do with a 'Functor', you can do with a 'Setter'. There
  -- are combinators that generalize 'fmap' and ('<$').
  ----------------------------------------------------------------------------
  module Silica.Setter
    (
    -- * Setters
      Setter, Setter'
    , IndexedSetter, IndexedSetter'
    , R_Setter, R_Setter'
    , R_IndexedSetter, R_IndexedSetter'
    -- , R_ASetter, R_ASetter'
    -- , R_AnIndexedSetter, R_AnIndexedSetter'
    , Setting, Setting'
    -- * Building Setters
    , sets , usets, gsets
    , setting
    -- , cloneSetter
    -- , cloneR_IndexPreservingSetter
    -- , cloneIndexedSetter
    -- * Common Setters
    , mapped, lifted
    , contramapped
    , argument
    -- * Functional Combinators
    , over
    , set
    , (.~), (%~)
    , (+~), (-~), (*~), (//~), (^~), (^^~), (**~), (||~), (<>~), (&&~), (<.~), (?~), (<?~)
    -- * State Combinators
    , assign, modifying
    , (.=), (%=)
    , (+=), (-=), (*=), (//=), (^=), (^^=), (**=), (||=), (<>=), (&&=), (<.=), (?=), (<?=)
    , (<~)
    -- * Writer Combinators
    , scribe
    , passing, ipassing
    , censoring, icensoring
    -- * Simplified State Setting
    , set'
    -- * Indexed Setters
    , iover, iset, imodifying
    , isets
    , (%@~), (.@~), (%@=), (.@=)
    -- * Arrow operators
    , assignA
    -- * Deprecated
    , mapOf
    , imapOf
    ) where
  
  import Control.Applicative
  import Control.Arrow
  import Control.Comonad
  import Silica.Internal.Indexed
  import Silica.Internal.Setter
  import Silica.Type
  import Control.Monad (liftM)
  import Control.Monad.State.Class as State
  import Control.Monad.Writer.Class as Writer
  import Data.Functor.Contravariant
  import Data.Functor.Identity
  import Data.Monoid
  import Data.Profunctor
  import Data.Profunctor.Rep
  import Data.Profunctor.Sieve
  import Data.Profunctor.Unsafe
  import Prelude
  
  #ifdef HLINT
  {-# ANN module "HLint: ignore Avoid lambda" #-}
  {-# ANN module "HLint: ignore Use fmap" #-}
  #endif
  
  -- $setup
  -- >>> import Silica
  -- >>> import Control.Monad.State
  -- >>> import Data.Char
  -- >>> import Data.Map as Map
  -- >>> import Debug.SimpleReflect.Expr as Expr
  -- >>> import Debug.SimpleReflect.Vars as Vars
  -- >>> let f :: Expr -> Expr; f = Debug.SimpleReflect.Vars.f
  -- >>> let g :: Expr -> Expr; g = Debug.SimpleReflect.Vars.g
  -- >>> let h :: Expr -> Expr -> Expr; h = Debug.SimpleReflect.Vars.h
  -- >>> let getter :: Expr -> Expr; getter = fun "getter"
  -- >>> let setter :: Expr -> Expr -> Expr; setter = fun "setter"
  -- >>> :set -XNoOverloadedStrings
  
  infixr 4 %@~, .@~, .~, +~, *~, -~, //~, ^~, ^^~, **~, &&~, <>~, ||~, %~, <.~, ?~, <?~
  infix  4 %@=, .@=, .=, +=, *=, -=, //=, ^=, ^^=, **=, &&=, <>=, ||=, %=, <.=, ?=, <?=
  infixr 2 <~
  
  ------------------------------------------------------------------------------
  -- Setters
  ------------------------------------------------------------------------------
  
  -- | 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 ASetter s t a b = LensLike Identity s t a b
  
  -- | This is a useful alias for use when consuming a 'Setter''.
  --
  -- Most user code will never have to use this type.
  --
  -- @
  -- type 'ASetter'' = 'Simple' 'ASetter'
  -- @
  type ASetter' s a = ASetter s s a a
  
  -- | 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 t a b = Over (Indexed i) Identity s t a b
  
  -- | @
  -- type 'AnIndexedSetter'' i = 'Simple' ('AnIndexedSetter' i)
  -- @
  type AnIndexedSetter' i s a = Over (Indexed i) Identity s s a a
  
  -- | 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 t a b = p a (Identity b) -> s -> Identity t
  
  -- | 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
  
  -----------------------------------------------------------------------------
  -- Setters
  -----------------------------------------------------------------------------
  
  -- | This 'Setter' can be used to map over all of the values in a 'Functor'.
  --
  -- @
  -- 'fmap' ≡ 'over' 'mapped'
  -- 'Data.Traversable.fmapDefault' ≡ 'over' 'Data.Traversable.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)]
  --
  -- If you want an 'IndexPreservingSetter' use @'setting' 'fmap'@.
  mapped :: Functor f => Setter (f a) (f b) a b
  mapped = sets fmap
  {-# INLINE mapped #-}
  
  -- | 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' was not a superclass of 'Monad' until
  -- GHC 7.10.
  --
  -- @
  -- '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'@.
  lifted :: Monad m => Setter (m a) (m b) a b
  lifted = sets liftM
  {-# INLINE lifted #-}
  
  -- | 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]
  --
  contramapped :: Contravariant f => Setter (f b) (f a) a b
  contramapped = sets contramap
  {-# INLINE contramapped #-}
  
  -- | 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
  -- @
  argument :: Profunctor p => Setter (p b r) (p a r) a b
  argument = sets lmap
  {-# INLINE argument #-}
  
  -- | Build an index-preserving '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:
  --
  -- @
  -- '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
  -- @
  
  setting :: ((a -> b) -> s -> t) -> Setter s t a b
  setting = usetting
  {-# INLINE setting #-}
  
  usetting :: ((a -> b) -> s -> t) -> Setter s t a b
  usetting = psetting
  {-# INLINE usetting #-}
  
  xsetting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b
  xsetting l = Optic (rsetting l)
  {-# INLINE xsetting #-}
  
  gsetting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b
  gsetting = xsetting
  {-# INLINE gsetting #-}
  
  psetting
    :: (A_IndexPreserving A_Setter <: k)
    => ((a -> b) -> s -> t)
    -> Optic k s t a b
  psetting l = sub (xsetting l)
  {-# INLINE psetting #-}
  
  rsetting :: ((a -> b) -> s -> t) -> R_IndexPreservingSetter s t a b
  rsetting l pafb = cotabulate
    $ \ws -> pure $ l (\a -> untainted (cosieve pafb (a <$ ws))) (extract ws)
  {-# INLINE rsetting #-}
  
  -- | Build a 'R_Setter', 'R_IndexedSetter' or 'R_IndexPreservingSetter' depending on your choice of 'Profunctor'.
  --
  -- @
  -- 'gsets' :: ((a -> b) -> s -> t) -> 'R_Setter' s t a b
  -- @
  
  -- | Build a 'Setter'.
  sets :: ((a -> b) -> s -> t) -> Setter s t a b
  sets = usets
  {-# INLINE sets #-}
  
  usets :: ((a -> b) -> s -> t) -> Setter s t a b
  usets f = Optic (rsets f)
  {-# INLINE usets #-}
  
  gsets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Optical p q f s t a b
  gsets f = Optic (rsets f)
  {-# INLINE gsets #-}
  
  rsets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> R_Optical p q f s t a b
  rsets f g = taintedDot (f (untaintedDot g))
  {-# INLINE rsets #-}
  
  -----------------------------------------------------------------------------
  -- Using Setters
  -----------------------------------------------------------------------------
  
  -- | Modify the target of a 'Lens' or all the targets of a 'Setter' or 'Traversal'
  -- with a function.
  --
  -- @
  -- 'fmap' ≡ 'over' 'mapped'
  -- 'Data.Traversable.fmapDefault' ≡ 'over' 'Data.Traversable.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
  -- 'over' :: 'ASetter' s t a b -> (a -> b) -> s -> t
  -- @
  over :: AsSetter k => Optic k s t a b -> (a -> b) -> s -> t
  over l f = runIdentity #. runSetter l (Identity #. f)
  {-# INLINE over #-}
  
  asSetter :: AsSetter k => Optic k s t a b -> Setter s t a b
  asSetter = sub
  
  runSetter :: AsSetter k => Optic k s t a b -> R_Setter s t a b
  runSetter = runOptic . asSetter
  
  asIndexedSetter :: AsIndexedSetter i k => Optic k s t a b -> IndexedSetter i s t a b
  asIndexedSetter = sub
  
  -- | 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 -> t
  -- 'set' :: 'Iso' s t a b       -> b -> s -> t
  -- 'set' :: 'Lens' s t a b      -> b -> s -> t
  -- 'set' :: 'Traversal' s t a b -> b -> s -> t
  -- @
  set :: AsSetter k => Optic k s t a b -> b -> s -> t
  set l b = runIdentity #. runSetter l (\_ -> Identity b)
  {-# INLINE set #-}
  
  -- | 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 -> s
  -- 'set'' :: 'Iso'' s a       -> a -> s -> s
  -- 'set'' :: 'Lens'' s a      -> a -> s -> s
  -- 'set'' :: 'Traversal'' s a -> a -> s -> s
  -- @
  set' :: AsSetter k => Optic' k s a -> a -> s -> s
  set' l b = runIdentity #. runSetter l (\_ -> Identity b)
  {-# INLINE set' #-}
  
  -- | 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' '%~' f
  -- 'Data.Traversable.fmapDefault' f ≡ 'Data.Traversable.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
  -- @
  (%~) :: AsSetter k => Optic k s t a b -> (a -> b) -> s -> t
  (%~) = over
  {-# INLINE (%~) #-}
  
  -- | 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
  -- @
  (.~) :: AsSetter k => Optic k s t a b -> b -> s -> t
  (.~) = set
  {-# INLINE (.~) #-}
  
  -- | 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
  -- @
  (?~) :: AsSetter k => Optic k s t a (Maybe b) -> b -> s -> t
  l ?~ b = set l (Just b)
  {-# INLINE (?~) #-}
  
  -- | Set with pass-through.
  --
  -- This is mostly present for consistency, but may be useful for chaining assignments.
  --
  -- If you do not need a copy of the intermediate result, then using @l '.~' t@ directly is a good idea.
  --
  -- >>> (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)
  -- @
  (<.~) :: AsSetter k => Optic k s t a b -> b -> s -> (b, t)
  l <.~ b = \s -> (b, set l b s)
  {-# INLINE (<.~) #-}
  
  -- | Set to 'Just' a value 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.
  --
  -- >>> 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)
  -- @
  (<?~) :: AsSetter k => Optic k s t a (Maybe b) -> b -> s -> (b, t)
  l <?~ b = \s -> (b, set l (Just b) s)
  {-# INLINE (<?~) #-}
  
  -- | 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, AsSetter k) => Optic k s t a a -> a -> s -> t
  l +~ n = over l (+ n)
  {-# INLINE (+~) #-}
  
  -- | 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
  -- @
  (*~) :: (Num a, AsSetter k) => Optic k s t a a -> a -> s -> t
  l *~ n = over l (* n)
  {-# INLINE (*~) #-}
  
  -- | 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, AsSetter k) => Optic k s t a a -> a -> s -> t
  l -~ n = over l (subtract n)
  {-# INLINE (-~) #-}
  
  -- | 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
  -- @
  (//~) :: (Fractional a, AsSetter k) => Optic k s t a a -> a -> s -> t
  l //~ n = over l (/ n)
  {-# INLINE (//~) #-}
  
  -- | Raise the target(s) of a numerically valued 'Lens', 'Setter' or 'Traversal' to a non-negative 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
  -- @
  (^~) :: (Num a, Integral e, AsSetter k) => Optic k s t a a -> e -> s -> t
  l ^~ n = over l (^ n)
  {-# INLINE (^~) #-}
  
  -- | 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
  -- @
  --
  (^^~) :: (Fractional a, Integral e, AsSetter k) => Optic k s t a a -> e -> s -> t
  l ^^~ n = over l (^^ n)
  {-# INLINE (^^~) #-}
  
  -- | Raise the target(s) of a floating-point 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
  -- @
  (**~) :: (Floating a, AsSetter k) => Optic k s t a a -> a -> s -> t
  l **~ n = over l (** n)
  {-# INLINE (**~) #-}
  
  -- | Logically '||' the target(s) of a 'Bool'-valued 'Lens' or 'Setter'.
  --
  -- >>> both ||~ True $ (False,True)
  -- (True,True)
  --
  -- >>> both ||~ False $ (False,True)
  -- (False,True)
  --
  -- @
  -- ('||~') :: 'Setter'' s 'Bool'    -> 'Bool' -> s -> s
  -- ('||~') :: 'Iso'' s 'Bool'       -> 'Bool' -> s -> s
  -- ('||~') :: 'Lens'' s 'Bool'      -> 'Bool' -> s -> s
  -- ('||~') :: 'Traversal'' s 'Bool' -> 'Bool' -> s -> s
  -- @
  (||~):: AsSetter k => Optic k s t Bool Bool -> Bool -> s -> t
  l ||~ n = over l (|| n)
  {-# INLINE (||~) #-}
  
  -- | Logically '&&' the target(s) of a 'Bool'-valued 'Lens' or 'Setter'.
  --
  -- >>> both &&~ True $ (False, True)
  -- (False,True)
  --
  -- >>> both &&~ False $ (False, True)
  -- (False,False)
  --
  -- @
  -- ('&&~') :: 'Setter'' s 'Bool'    -> 'Bool' -> s -> s
  -- ('&&~') :: 'Iso'' s 'Bool'       -> 'Bool' -> s -> s
  -- ('&&~') :: 'Lens'' s 'Bool'      -> 'Bool' -> s -> s
  -- ('&&~') :: 'Traversal'' s 'Bool' -> 'Bool' -> s -> s
  -- @
  (&&~) :: AsSetter k => Optic k s t Bool Bool -> Bool -> s -> t
  l &&~ n = over l (&& n)
  {-# INLINE (&&~) #-}
  
  ------------------------------------------------------------------------------
  -- Using Setters with State
  ------------------------------------------------------------------------------
  
  -- | 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 ()
  -- @
  assign :: (MonadState s m, AsSetter k) => Optic k s s a b -> b -> m ()
  assign l b = State.modify (set l b)
  {-# INLINE assign #-}
  
  -- | 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./
  (.=) :: (MonadState s m, AsSetter k) => Optic k s s a b -> b -> m ()
  l .= b = State.modify (l .~ b)
  {-# INLINE (.=) #-}
  
  -- | 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, AsSetter k) => Optic k s s a b -> (a -> b) -> m ()
  l %= f = State.modify (l %~ f)
  {-# INLINE (%=) #-}
  
  -- | This is an alias for ('%=').
  modifying :: (MonadState s m, AsSetter k) => Optic k s s a b -> (a -> b) -> m ()
  modifying l f = State.modify (over l f)
  {-# INLINE modifying #-}
  
  -- | 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, AsSetter k) => Optic k s s a (Maybe b) -> b -> m ()
  l ?= b = State.modify (l ?~ b)
  {-# INLINE (?=) #-}
  
  -- | Modify the target(s) of a 'Lens'', 'Iso', 'Setter' or 'Traversal' by adding a value.
  --
  -- Example:
  --
  -- @
  -- 'fresh' :: 'MonadState' 'Int' m => m 'Int'
  -- 'fresh' = do
  --   'id' '+=' 1
  --   'Control.Lens.Getter.use' '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, AsSetter k) => Optic' k s a -> a -> m ()
  l += b = State.modify (l +~ b)
  {-# INLINE (+=) #-}
  
  -- | 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, AsSetter k) => Optic' k s a -> a -> m ()
  l -= b = State.modify (l -~ b)
  {-# INLINE (-=) #-}
  
  -- | 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, Num a, AsSetter k) => Optic' k s a -> a -> m ()
  l *= b = State.modify (l *~ b)
  {-# INLINE (*=) #-}
  
  -- | 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, Fractional a, AsSetter k) => Optic' k s a -> a -> m ()
  l //= a = State.modify (l //~ a)
  {-# INLINE (//=) #-}
  
  -- | Raise the target(s) of a numerically valued 'Lens', 'Setter' or 'Traversal' to a non-negative 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, Num a, Integral e, AsSetter k) => Optic' k s a -> e -> m ()
  l ^= e = State.modify (l ^~ e)
  {-# INLINE (^=) #-}
  
  -- | 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, Fractional a, Integral e, AsSetter k) => Optic' k s a -> e -> m ()
  l ^^= e = State.modify (l ^^~ e)
  {-# INLINE (^^=) #-}
  
  -- | 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, Floating a, AsSetter k) => Optic' k s a -> a -> m ()
  l **= a = State.modify (l **~ a)
  {-# INLINE (**=) #-}
  
  -- | 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'' s 'Bool'    -> 'Bool' -> m ()
  -- ('&&=') :: 'MonadState' s m => 'Iso'' s 'Bool'       -> 'Bool' -> m ()
  -- ('&&=') :: 'MonadState' s m => 'Lens'' s 'Bool'      -> 'Bool' -> m ()
  -- ('&&=') :: 'MonadState' s m => 'Traversal'' s 'Bool' -> 'Bool' -> m ()
  -- @
  (&&=):: (MonadState s m, AsSetter k) => Optic' k s Bool -> Bool -> m ()
  l &&= b = State.modify (l &&~ b)
  {-# INLINE (&&=) #-}
  
  -- | 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'' s 'Bool'    -> 'Bool' -> m ()
  -- ('||=') :: 'MonadState' s m => 'Iso'' s 'Bool'       -> 'Bool' -> m ()
  -- ('||=') :: 'MonadState' s m => 'Lens'' s 'Bool'      -> 'Bool' -> m ()
  -- ('||=') :: 'MonadState' s m => 'Traversal'' s 'Bool' -> 'Bool' -> m ()
  -- @
  (||=) :: (MonadState s m, AsSetter k) => Optic' k s Bool -> Bool -> m ()
  l ||= b = State.modify (l ||~ b)
  {-# INLINE (||=) #-}
  
  -- | 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
  --    ...
  -- @
  --
  -- will store the result in a 'Lens', 'Setter', or 'Traversal'.
  (<~) :: (MonadState s m, AsSetter k) => Optic k s s a b -> m b -> m ()
  l <~ mb = mb >>= (l .=)
  {-# INLINE (<~) #-}
  
  -- | Set with pass-through
  --
  -- This is useful for chaining assignment without round-tripping through your 'Monad' stack.
  --
  -- @
  -- do x <- 'Control.Lens.Tuple._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, AsSetter k) => Optic k s s a b -> b -> m b
  l <.= b = do
    l .= b
    return b
  {-# INLINE (<.=) #-}
  
  -- | Set 'Just' a value with pass-through
  --
  -- This is useful for chaining assignment without round-tripping through your 'Monad' stack.
  --
  -- @
  -- do x <- 'Control.Lens.At.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, AsSetter k) => Optic k s s a (Maybe b) -> b -> m b
  l <?= b = do
    l ?= b
    return b
  {-# INLINE (<?=) #-}
  
  -- | 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
  -- @
  (<>~) :: (Monoid a, AsSetter k) => Optic k s t a a -> a -> s -> t
  l <>~ n = over l (`mappend` n)
  {-# INLINE (<>~) #-}
  
  -- | 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, Monoid a, AsSetter k) => Optic' k s a -> a -> m ()
  l <>= a = State.modify (l <>~ a)
  {-# INLINE (<>=) #-}
  
  -----------------------------------------------------------------------------
  -- Writer Operations
  ----------------------------------------------------------------------------
  
  -- | Write to a fragment of a larger 'Writer' format.
  scribe :: (MonadWriter t m, Monoid s, AsSetter k) => Optic k s t a b -> b -> m ()
  scribe l b = tell (set l b mempty)
  {-# INLINE scribe #-}
  
  -- | This is a generalization of 'pass' that alows you to modify just a
  -- portion of the resulting 'MonadWriter'.
  passing :: (MonadWriter w m, AsSetter k) => Optic k w w u v -> m (a, u -> v) -> m a
  passing l m = pass $ do
    (a, uv) <- m
    return (a, over l uv)
  {-# INLINE passing #-}
  
  -- | 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'.
  ipassing :: (MonadWriter w m, AsIndexedSetter i k) => Optic k w w u v -> m (a, i -> u -> v) -> m a
  ipassing l m = pass $ do
    (a, uv) <- m
    return (a, iover l uv)
  {-# INLINE ipassing #-}
  
  -- | This is a generalization of 'censor' that alows you to 'censor' just a
  -- portion of the resulting 'MonadWriter'.
  censoring :: (MonadWriter w m, AsSetter k) => Optic k w w u v -> (u -> v) -> m a -> m a
  censoring l uv = censor (over l uv)
  {-# INLINE censoring #-}
  
  -- | 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'.
  icensoring :: (MonadWriter w m, AsIndexedSetter i k) => Optic k w w u v -> (i -> u -> v) -> m a -> m a
  icensoring l uv = censor (iover l uv)
  {-# INLINE icensoring #-}
  
  -----------------------------------------------------------------------------
  -- Indexed Setters
  ----------------------------------------------------------------------------
  
  
  -- | 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 -> t
  -- 'iover' :: 'IndexedLens' i s t a b      -> (i -> a -> b) -> s -> t
  -- 'iover' :: 'IndexedTraversal' i s t a b -> (i -> a -> b) -> s -> t
  -- @
  iover :: AsIndexedSetter i k => Optic k s t a b -> (i -> a -> b) -> s -> t
  iover l f = runIdentity #. runOptic (asIndexedSetter l) (Identity #. Indexed f)
  {-# INLINE iover #-}
  
  -- | Set with index. Equivalent to 'iover' with the current value ignored.
  --
  -- When you do not need access to the index, then 'set' is more liberal in what it can accept.
  --
  -- @
  -- 'set' l ≡ 'iset' l '.' 'const'
  -- @
  --
  -- @
  -- 'iset' :: 'IndexedSetter' i s t a b    -> (i -> b) -> s -> t
  -- 'iset' :: 'IndexedLens' i s t a b      -> (i -> b) -> s -> t
  -- 'iset' :: 'IndexedTraversal' i s t a b -> (i -> b) -> s -> t
  -- @
  iset :: (AsIndexedSetter i k) => Optic k s t a b -> (i -> b) -> s -> t
  iset l = iover l . (const .)
  {-# INLINE iset #-}
  
  -- | Build an 'IndexedSetter' from an 'Control.Lens.Indexed.imap'-like function.
  --
  -- Your supplied function @f@ is required to satisfy:
  --
  -- @
  -- f 'id' ≡ 'id'
  -- f g '.' f h ≡ f (g '.' h)
  -- @
  --
  -- Equational reasoning:
  --
  -- @
  -- 'isets' '.' 'iover' ≡ 'id'
  -- 'iover' '.' 'isets' ≡ 'id'
  -- @
  --
  -- Another way to view 'isets' is that it takes a \"semantic editor combinator\"
  -- which has been modified to carry an index and transforms it into a 'IndexedSetter'.
  isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b
  isets f = Optic (rsets (f . indexed))
  {-# INLINE isets #-}
  
  -- | Adjust every target of an 'IndexedSetter', 'IndexedLens' or 'IndexedTraversal'
  -- with access to the index.
  --
  -- @
  -- ('%@~') ≡ 'iover'
  -- @
  --
  -- 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
  -- @
  (%@~) :: AsIndexedSetter i k => Optic k s t a b -> (i -> a -> b) -> s -> t
  (%@~) = iover
  {-# INLINE (%@~) #-}
  
  -- | Replace every target of an 'IndexedSetter', 'IndexedLens' or 'IndexedTraversal'
  -- with access to the index.
  --
  -- @
  -- ('.@~') ≡ 'iset'
  -- @
  --
  -- When you do not need access to the index then ('.~') is more liberal in what it can accept.
  --
  -- @
  -- l '.~' b ≡ l '.@~' 'const' b
  -- @
  --
  -- @
  -- ('.@~') :: 'IndexedSetter' i s t a b    -> (i -> b) -> s -> t
  -- ('.@~') :: 'IndexedLens' i s t a b      -> (i -> b) -> s -> t
  -- ('.@~') :: 'IndexedTraversal' i s t a b -> (i -> b) -> s -> t
  -- @
  (.@~) :: AsIndexedSetter i k => Optic k s t a b -> (i -> b) -> s -> t
  l .@~ f = runIdentity #. runOptic (asIndexedSetter l) (Identity #. Indexed (const . f))
  {-# INLINE (.@~) #-}
  
  -- | 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 ()
  -- @
  (%@=) :: (MonadState s m, AsIndexedSetter i k) => Optic k s s a b -> (i -> a -> b) -> m ()
  l %@= f = State.modify (l %@~ f)
  {-# INLINE (%@=) #-}
  
  -- | This is an alias for ('%@=').
  imodifying :: (MonadState s m, AsIndexedSetter i k) => Optic k s s a b -> (i -> a -> b) -> m ()
  imodifying l f = State.modify (iover l f)
  {-# INLINE imodifying #-}
  
  -- | Replace 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 '.=' b ≡ l '.@=' 'const' b
  -- @
  --
  -- @
  -- ('.@=') :: 'MonadState' s m => 'IndexedSetter' i s s a b    -> (i -> b) -> m ()
  -- ('.@=') :: 'MonadState' s m => 'IndexedLens' i s s a b      -> (i -> b) -> m ()
  -- ('.@=') :: 'MonadState' s m => 'IndexedTraversal' i s t a b -> (i -> b) -> m ()
  -- @
  (.@=) :: (MonadState s m, AsIndexedSetter i k) => Optic k s s a b -> (i -> b) -> m ()
  l .@= f = State.modify (l .@~ f)
  {-# INLINE (.@=) #-}
  
  ------------------------------------------------------------------------------
  -- Arrows
  ------------------------------------------------------------------------------
  
  -- | 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 t
  -- 'assignA' :: 'Arrow' p => 'Lens' s t a b      -> p s b -> p s t
  -- 'assignA' :: 'Arrow' p => 'Traversal' s t a b -> p s b -> p s t
  -- 'assignA' :: 'Arrow' p => 'Setter' s t a b    -> p s b -> p s t
  -- @
  assignA :: (Arrow p, AsSetter k) => Optic k s t a b -> p s b -> p s t
  assignA l p = arr (flip $ set l) &&& p >>> arr (uncurry id)
  {-# INLINE assignA #-}
  
  ------------------------------------------------------------------------------
  -- Deprecated
  ------------------------------------------------------------------------------
  
  -- | 'mapOf' is a deprecated alias for 'over'.
  mapOf :: AsSetter k => Optic k s t a b -> (a -> b) -> s -> t
  mapOf = over
  {-# INLINE mapOf #-}
  {-# DEPRECATED mapOf "Use `over`" #-}
  
  -- | 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 -> t
  -- 'imapOf' :: 'IndexedLens' i s t a b      -> (i -> a -> b) -> s -> t
  -- 'imapOf' :: 'IndexedTraversal' i s t a b -> (i -> a -> b) -> s -> t
  -- @
  imapOf :: AsIndexedSetter i k => Optic k s t a b -> (i -> a -> b) -> s -> t
  imapOf = iover
  {-# INLINE imapOf #-}
  {-# DEPRECATED imapOf "Use `iover`" #-}
  
  -- -- | Restore 'ASetter' to a full 'Setter'.
  -- cloneSetter :: R_ASetter s t a b -> Setter s t a b
  -- cloneSetter l = Optic (\afb -> taintedDot $ runIdentity #. l (Identity #. untaintedDot afb))
  -- {-# INLINE cloneSetter #-}
  
  -- -- | Build an 'IndexPreservingSetter' from any 'Setter'.
  -- cloneR_IndexPreservingSetter :: R_ASetter s t a b -> R_IndexPreservingSetter s t a b
  -- cloneR_IndexPreservingSetter l pafb = cotabulate $ \ws ->
  --     taintedDot runIdentity $ l (\a -> Identity (untainted (cosieve pafb (a <$ ws)))) (extract ws)
  -- {-# INLINE cloneR_IndexPreservingSetter #-}
  
  -- -- | Clone an 'IndexedSetter'.
  -- cloneIndexedSetter :: R_AnIndexedSetter i s t a b -> IndexedSetter i s t a b
  -- cloneIndexedSetter l = 
  --   Optic (\pafb -> taintedDot (runIdentity #. l (Indexed $ \i -> Identity #. untaintedDot (indexed pafb i))))
  -- {-# INLINE cloneIndexedSetter #-}
  
  