{-# LANGUAGE CPP #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE Trustworthy #-}
#if __GLASGOW_HASKELL__ >= 800
{-# LANGUAGE TypeInType #-}
#endif

#include "lens-common.h"

-------------------------------------------------------------------------------
-- |
-- Module      :  Control.Lens.Lens
-- Copyright   :  (C) 2012-16 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  provisional
-- Portability :  Rank2Types
--
-- A @'Lens' s t a b@ is a purely functional reference.
--
-- While a 'Control.Lens.Traversal.Traversal' could be used for
-- 'Control.Lens.Getter.Getting' like a valid 'Control.Lens.Fold.Fold', it
-- wasn't a valid 'Control.Lens.Getter.Getter' as a
-- 'Control.Lens.Getter.Getter' can't require an 'Applicative' constraint.
--
-- 'Functor', however, is a constraint on both.
--
-- @
-- type 'Lens' s t a b = forall f. 'Functor' f => (a -> f b) -> s -> f t
-- @
--
-- Every 'Lens' is a valid 'Control.Lens.Setter.Setter'.
--
-- Every 'Lens' can be used for 'Control.Lens.Getter.Getting' like a
-- 'Control.Lens.Fold.Fold' that doesn't use the 'Applicative' or
-- 'Contravariant'.
--
-- Every 'Lens' is a valid 'Control.Lens.Traversal.Traversal' that only uses
-- the 'Functor' part of the 'Applicative' it is supplied.
--
-- Every 'Lens' can be used for 'Control.Lens.Getter.Getting' like a valid
-- 'Control.Lens.Getter.Getter'.
--
-- Since every 'Lens' can be used for 'Control.Lens.Getter.Getting' like a
-- valid 'Control.Lens.Getter.Getter' it follows that it must view exactly one element in the
-- structure.
--
-- The 'Lens' laws follow from this property and the desire for it to act like
-- a 'Data.Traversable.Traversable' when used as a
-- 'Control.Lens.Traversal.Traversal'.
--
-- In the examples below, 'getter' and 'setter' are supplied as example getters
-- and setters, and are not actual functions supplied by this package.
-------------------------------------------------------------------------------
module Control.Lens.Lens
  (
  -- * Lenses
    Lens, Lens'
  , IndexedLens, IndexedLens'
  -- ** Concrete Lenses
  , ALens, ALens'
  , AnIndexedLens, AnIndexedLens'

  -- * Combinators
  , lens, ilens, iplens, withLens
  , (%%~), (%%=)
  , (%%@~), (%%@=)
  , (<%@~), (<%@=)
  , (<<%@~), (<<%@=)
  -- ** General Purpose Combinators
  , (&), (<&>), (??)
  , (&~)
  -- * Lateral Composition
  , choosing
  , chosen
  , alongside
  , inside

  -- * Setting Functionally with Passthrough
  , (<%~), (<+~), (<-~), (<*~), (<//~)
  , (<^~), (<^^~), (<**~)
  , (<||~), (<&&~), (<<>~)
  , (<<%~), (<<.~), (<<?~), (<<+~), (<<-~), (<<*~)
  , (<<//~), (<<^~), (<<^^~), (<<**~)
  , (<<||~), (<<&&~), (<<<>~)

  -- * Setting State with Passthrough
  , (<%=), (<+=), (<-=), (<*=), (<//=)
  , (<^=), (<^^=), (<**=)
  , (<||=), (<&&=), (<<>=)
  , (<<%=), (<<.=), (<<?=), (<<+=), (<<-=), (<<*=)
  , (<<//=), (<<^=), (<<^^=), (<<**=)
  , (<<||=), (<<&&=), (<<<>=)
  , (<<~)

  -- * Cloning Lenses
  , cloneLens
  , cloneIndexPreservingLens
  , cloneIndexedLens

  -- * Arrow operators
  , overA

  -- * ALens Combinators
  , storing
  , (^#)
  , (#~), (#%~), (#%%~), (<#~), (<#%~)
  , (#=), (#%=), (#%%=), (<#=), (<#%=)

  -- * Common Lenses
  , devoid
  , united
  , head1, last1

  -- * Context
  , Context(..)
  , Context'
  , locus

  -- * Lens fusion
  , fusing
  ) where

import Prelude ()

import Control.Arrow
import Control.Comonad
import Control.Lens.Internal.Context
import Control.Lens.Internal.Prelude
import Control.Lens.Internal.Getter
import Control.Lens.Internal.Indexed
import Control.Lens.Type
import Control.Monad.State as State
import Data.Functor.Apply
import Data.Functor.Reverse
import Data.Functor.Yoneda
import Data.Semigroup.Traversable
#if __GLASGOW_HASKELL__ >= 800
import GHC.Exts (TYPE)
#endif

-- $setup
-- >>> :set -XNoOverloadedStrings
-- >>> import Control.Lens
-- >>> import Control.Arrow
-- >>> import Control.Monad.State
-- >>> import Data.Char (chr)
-- >>> import Data.List.NonEmpty (NonEmpty ((:|)))
-- >>> import Data.Monoid (Sum (..))
-- >>> import Data.Tree (Tree (Node))
-- >>> import Debug.SimpleReflect.Expr
-- >>> import Debug.SimpleReflect.Vars as Vars hiding (f,g,h)
-- >>> 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"

infixl 8 ^#
infixr 4 %%@~, <%@~, <<%@~, %%~, <+~, <*~, <-~, <//~, <^~, <^^~, <**~, <&&~, <||~, <<>~, <%~, <<%~, <<.~, <<?~, <#~, #~, #%~, <#%~, #%%~
       , <<+~, <<-~, <<*~, <<//~, <<^~, <<^^~, <<**~, <<||~, <<&&~, <<<>~
infix  4 %%@=, <%@=, <<%@=, %%=, <+=, <*=, <-=, <//=, <^=, <^^=, <**=, <&&=, <||=, <<>=, <%=, <<%=, <<.=, <<?=, <#=, #=, #%=, <#%=, #%%=
       , <<+=, <<-=, <<*=, <<//=, <<^=, <<^^=, <<**=, <<||=, <<&&=, <<<>=
infixr 2 <<~
infixl 1 ??, &~

-------------------------------------------------------------------------------
-- Lenses
-------------------------------------------------------------------------------

-- | When you see this as an argument to a function, it expects a 'Lens'.
--
-- This type can also be used when you need to store a 'Lens' in a container,
-- since it is rank-1. You can turn them back into a 'Lens' with 'cloneLens',
-- or use it directly with combinators like 'storing' and ('^#').
type ALens s t a b = LensLike (Pretext (->) a b) s t a b

-- | @
-- type 'ALens'' = 'Simple' 'ALens'
-- @
type ALens' s a = ALens s s a a

-- | When you see this as an argument to a function, it expects an 'IndexedLens'
type AnIndexedLens i s t a b = Optical (Indexed i) (->) (Pretext (Indexed i) a b) s t a b

-- | @
-- type 'AnIndexedLens'' = 'Simple' ('AnIndexedLens' i)
-- @
type AnIndexedLens' i s a  = AnIndexedLens i s s a a

--------------------------
-- Constructing Lenses
--------------------------

-- | Build a 'Lens' from a getter and a setter.
--
-- @
-- 'lens' :: 'Functor' f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t
-- @
--
-- >>> s ^. lens getter setter
-- getter s
--
-- >>> s & lens getter setter .~ b
-- setter s b
--
-- >>> s & lens getter setter %~ f
-- setter s (f (getter s))
--
-- @
-- 'lens' :: (s -> a) -> (s -> a -> s) -> 'Lens'' s a
-- @
lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
lens sa sbt afb s = sbt s <$> afb (sa s)
{-# INLINE lens #-}

-- | Obtain a getter and a setter from a lens, reversing 'lens'.
#if __GLASGOW_HASKELL__ >= 800
withLens :: forall s t a b rep (r :: TYPE rep).
            ALens s t a b -> ((s -> a) -> (s -> b -> t) -> r) -> r
#else
withLens :: ALens s t a b -> ((s -> a) -> (s -> b -> t) -> r) -> r
#endif
withLens l f = f (^# l) (flip (storing l))
{-# INLINE withLens #-}

-- | Build an index-preserving 'Lens' from a 'Control.Lens.Getter.Getter' and a
-- 'Control.Lens.Setter.Setter'.
iplens :: (s -> a) -> (s -> b -> t) -> IndexPreservingLens s t a b
iplens sa sbt pafb = cotabulate $ \ws -> sbt (extract ws) <$> cosieve pafb (sa <$> ws)
{-# INLINE iplens #-}

-- | Build an 'IndexedLens' from a 'Control.Lens.Getter.Getter' and
-- a 'Control.Lens.Setter.Setter'.
ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b
ilens sia sbt iafb s = sbt s <$> uncurry (indexed iafb) (sia s)
{-# INLINE ilens #-}

-- | This can be used to chain lens operations using @op=@ syntax
-- rather than @op~@ syntax for simple non-type-changing cases.
--
-- >>> (10,20) & _1 .~ 30 & _2 .~ 40
-- (30,40)
--
-- >>> (10,20) &~ do _1 .= 30; _2 .= 40
-- (30,40)
--
-- This does not support type-changing assignment, /e.g./
--
-- >>> (10,20) & _1 .~ "hello"
-- ("hello",20)
(&~) :: s -> State s a -> s
s &~ l = execState l s
{-# INLINE (&~) #-}

-- | ('%%~') can be used in one of two scenarios:
--
-- When applied to a 'Lens', it can edit the target of the 'Lens' in a
-- structure, extracting a functorial result.
--
-- When applied to a 'Traversal', it can edit the
-- targets of the traversals, extracting an applicative summary of its
-- actions.
--
-- >>> [66,97,116,109,97,110] & each %%~ \a -> ("na", chr a)
-- ("nananananana","Batman")
--
-- For all that the definition of this combinator is just:
--
-- @
-- ('%%~') ≡ 'id'
-- @
--
-- It may be beneficial to think about it as if it had these even more
-- restricted types, however:
--
-- @
-- ('%%~') :: 'Functor' f =>     'Control.Lens.Iso.Iso' s t a b       -> (a -> f b) -> s -> f t
-- ('%%~') :: 'Functor' f =>     'Lens' s t a b      -> (a -> f b) -> s -> f t
-- ('%%~') :: 'Applicative' f => 'Control.Lens.Traversal.Traversal' s t a b -> (a -> f b) -> s -> f t
-- @
--
-- When applied to a 'Traversal', it can edit the
-- targets of the traversals, extracting a supplemental monoidal summary
-- of its actions, by choosing @f = ((,) m)@
--
-- @
-- ('%%~') ::             'Control.Lens.Iso.Iso' s t a b       -> (a -> (r, b)) -> s -> (r, t)
-- ('%%~') ::             'Lens' s t a b      -> (a -> (r, b)) -> s -> (r, t)
-- ('%%~') :: 'Monoid' m => 'Control.Lens.Traversal.Traversal' s t a b -> (a -> (m, b)) -> s -> (m, t)
-- @
(%%~) :: LensLike f s t a b -> (a -> f b) -> s -> f t
(%%~) = id
{-# INLINE (%%~) #-}

-- | Modify the target of a 'Lens' in the current state returning some extra
-- information of type @r@ or modify all targets of a
-- 'Control.Lens.Traversal.Traversal' in the current state, extracting extra
-- information of type @r@ and return a monoidal summary of the changes.
--
-- >>> runState (_1 %%= \x -> (f x, g x)) (a,b)
-- (f a,(g a,b))
--
-- @
-- ('%%=') ≡ ('state' '.')
-- @
--
-- It may be useful to think of ('%%='), instead, as having either of the
-- following more restricted type signatures:
--
-- @
-- ('%%=') :: 'MonadState' s m             => 'Control.Lens.Iso.Iso' s s a b       -> (a -> (r, b)) -> m r
-- ('%%=') :: 'MonadState' s m             => 'Lens' s s a b      -> (a -> (r, b)) -> m r
-- ('%%=') :: ('MonadState' s m, 'Monoid' r) => 'Control.Lens.Traversal.Traversal' s s a b -> (a -> (r, b)) -> m r
-- @
(%%=) :: MonadState s m => Over p ((,) r) s s a b -> p a (r, b) -> m r
#if MIN_VERSION_mtl(2,1,1)
l %%= f = State.state (l f)
#else
l %%= f = do
  (r, s) <- State.gets (l f)
  State.put s
  return r
#endif
{-# INLINE (%%=) #-}

-------------------------------------------------------------------------------
-- General Purpose Combinators
-------------------------------------------------------------------------------

-- | This is convenient to 'flip' argument order of composite functions defined as:
--
-- @
-- fab ?? a = fmap ($ a) fab
-- @
--
-- For the 'Functor' instance @f = ((->) r)@ you can reason about this function as if the definition was @('??') ≡ 'flip'@:
--
-- >>> (h ?? x) a
-- h a x
--
-- >>> execState ?? [] $ modify (1:)
-- [1]
--
-- >>> over _2 ?? ("hello","world") $ length
-- ("hello",5)
--
-- >>> over ?? length ?? ("hello","world") $ _2
-- ("hello",5)
(??) :: Functor f => f (a -> b) -> a -> f b
fab ?? a = fmap ($ a) fab
{-# INLINE (??) #-}

-------------------------------------------------------------------------------
-- Common Lenses
-------------------------------------------------------------------------------

-- | Lift a 'Lens' so it can run under a function (or other corepresentable profunctor).
--
-- @
-- 'inside' :: 'Lens' s t a b -> 'Lens' (e -> s) (e -> t) (e -> a) (e -> b)
-- @
--
--
-- >>> (\x -> (x-1,x+1)) ^. inside _1 $ 5
-- 4
--
-- >>> runState (modify (1:) >> modify (2:)) ^. (inside _2) $ []
-- [2,1]
inside :: Corepresentable p => ALens s t a b -> Lens (p e s) (p e t) (p e a) (p e b)
inside l f es = o <$> f i where
  i = cotabulate $ \ e -> ipos $ l sell (cosieve es e)
  o ea = cotabulate $ \ e -> ipeek (cosieve ea e) $ l sell (cosieve es e)
{-# INLINE inside #-}

{-
-- | Lift a 'Lens' so it can run under a function (or any other corepresentable functor).
insideF :: F.Representable f => ALens s t a b -> Lens (f s) (f t) (f a) (f b)
insideF l f es = o <$> f i where
  i = F.tabulate $ \e -> ipos $ l sell (F.index es e)
  o ea = F.tabulate $ \ e -> ipeek (F.index ea e) $ l sell (F.index es e)
{-# INLINE inside #-}
-}

-- | Merge two lenses, getters, setters, folds or traversals.
--
-- @
-- 'chosen' ≡ 'choosing' 'id' 'id'
-- @
--
-- @
-- 'choosing' :: 'Control.Lens.Getter.Getter' s a     -> 'Control.Lens.Getter.Getter' s' a     -> 'Control.Lens.Getter.Getter' ('Either' s s') a
-- 'choosing' :: 'Control.Lens.Fold.Fold' s a       -> 'Control.Lens.Fold.Fold' s' a       -> 'Control.Lens.Fold.Fold' ('Either' s s') a
-- 'choosing' :: 'Lens'' s a      -> 'Lens'' s' a      -> 'Lens'' ('Either' s s') a
-- 'choosing' :: 'Control.Lens.Traversal.Traversal'' s a -> 'Control.Lens.Traversal.Traversal'' s' a -> 'Control.Lens.Traversal.Traversal'' ('Either' s s') a
-- 'choosing' :: 'Control.Lens.Setter.Setter'' s a    -> 'Control.Lens.Setter.Setter'' s' a    -> 'Control.Lens.Setter.Setter'' ('Either' s s') a
-- @
choosing :: Functor f
       => LensLike f s t a b
       -> LensLike f s' t' a b
       -> LensLike f (Either s s') (Either t t') a b
choosing l _ f (Left a)   = Left <$> l f a
choosing _ r f (Right a') = Right <$> r f a'
{-# INLINE choosing #-}

-- | This is a 'Lens' that updates either side of an 'Either', where both sides have the same type.
--
-- @
-- 'chosen' ≡ 'choosing' 'id' 'id'
-- @
--
-- >>> Left a^.chosen
-- a
--
-- >>> Right a^.chosen
-- a
--
-- >>> Right "hello"^.chosen
-- "hello"
--
-- >>> Right a & chosen *~ b
-- Right (a * b)
--
-- @
-- 'chosen' :: 'Lens' ('Either' a a) ('Either' b b) a b
-- 'chosen' f ('Left' a)  = 'Left' '<$>' f a
-- 'chosen' f ('Right' a) = 'Right' '<$>' f a
-- @
chosen :: IndexPreservingLens (Either a a) (Either b b) a b
chosen pafb = cotabulate $ \weaa -> cosieve (either id id `lmap` pafb) weaa <&> \b -> case extract weaa of
  Left _  -> Left  b
  Right _ -> Right b
{-# INLINE chosen #-}

-- | 'alongside' makes a 'Lens' from two other lenses or a 'Getter' from two other getters
-- by executing them on their respective halves of a product.
--
-- >>> (Left a, Right b)^.alongside chosen chosen
-- (a,b)
--
-- >>> (Left a, Right b) & alongside chosen chosen .~ (c,d)
-- (Left c,Right d)
--
-- @
-- 'alongside' :: 'Lens'   s t a b -> 'Lens'   s' t' a' b' -> 'Lens'   (s,s') (t,t') (a,a') (b,b')
-- 'alongside' :: 'Getter' s   a   -> 'Getter' s'    a'    -> 'Getter' (s,s')        (a,a')
-- @
alongside :: LensLike (AlongsideLeft f b') s  t  a  b
          -> LensLike (AlongsideRight f t) s' t' a' b'
          -> LensLike f (s, s') (t, t') (a, a') (b, b')
alongside l1 l2 f (a1, a2)
  = getAlongsideRight $ l2 ?? a2 $ \b2 -> AlongsideRight
  $ getAlongsideLeft  $ l1 ?? a1 $ \b1 -> AlongsideLeft
  $ f (b1,b2)
{-# INLINE alongside #-}

-- | This 'Lens' lets you 'view' the current 'pos' of any indexed
-- store comonad and 'seek' to a new position. This reduces the API
-- for working these instances to a single 'Lens'.
--
-- @
-- 'ipos' w ≡ w 'Control.Lens.Getter.^.' 'locus'
-- 'iseek' s w ≡ w '&' 'locus' 'Control.Lens.Setter..~' s
-- 'iseeks' f w ≡ w '&' 'locus' 'Control.Lens.Setter.%~' f
-- @
--
-- @
-- 'locus' :: 'Lens'' ('Context'' a s) a
-- 'locus' :: 'Conjoined' p => 'Lens'' ('Pretext'' p a s) a
-- 'locus' :: 'Conjoined' p => 'Lens'' ('PretextT'' p g a s) a
-- @
locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b
locus f w = (`iseek` w) <$> f (ipos w)
{-# INLINE locus #-}

-------------------------------------------------------------------------------
-- Cloning Lenses
-------------------------------------------------------------------------------

-- | Cloning a 'Lens' is one way to make sure you aren't given
-- something weaker, such as a 'Control.Lens.Traversal.Traversal' and can be
-- used as a way to pass around lenses that have to be monomorphic in @f@.
--
-- Note: This only accepts a proper 'Lens'.
--
-- >>> let example l x = set (cloneLens l) (x^.cloneLens l + 1) x in example _2 ("hello",1,"you")
-- ("hello",2,"you")
cloneLens :: ALens s t a b -> Lens s t a b
cloneLens l afb s = runPretext (l sell s) afb
{-# INLINE cloneLens #-}

-- | Clone a 'Lens' as an 'IndexedPreservingLens' that just passes through whatever
-- index is on any 'IndexedLens', 'IndexedFold', 'IndexedGetter' or  'IndexedTraversal' it is composed with.
cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b
cloneIndexPreservingLens l pafb = cotabulate $ \ws -> runPretext (l sell (extract ws)) $ \a -> cosieve pafb (a <$ ws)
{-# INLINE cloneIndexPreservingLens #-}

-- | Clone an 'IndexedLens' as an 'IndexedLens' with the same index.
cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b
cloneIndexedLens l f s = runPretext (l sell s) (Indexed (indexed f))
{-# INLINE cloneIndexedLens #-}

-------------------------------------------------------------------------------
-- Setting and Remembering
-------------------------------------------------------------------------------

-- | Modify the target of a 'Lens' and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.%~') is more flexible.
--
-- @
-- ('<%~') ::             'Lens' s t a b      -> (a -> b) -> s -> (b, t)
-- ('<%~') ::             'Control.Lens.Iso.Iso' s t a b       -> (a -> b) -> s -> (b, t)
-- ('<%~') :: 'Monoid' b => 'Control.Lens.Traversal.Traversal' s t a b -> (a -> b) -> s -> (b, t)
-- @
(<%~) :: LensLike ((,) b) s t a b -> (a -> b) -> s -> (b, t)
l <%~ f = l $ (\t -> (t, t)) . f
{-# INLINE (<%~) #-}

-- | Increment the target of a numerically valued 'Lens' and return the result.
--
-- When you do not need the result of the addition, ('Control.Lens.Setter.+~') is more flexible.
--
-- @
-- ('<+~') :: 'Num' a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<+~') :: 'Num' a => 'Control.Lens.Iso.Iso'' s a  -> a -> s -> (a, s)
-- @
(<+~) :: Num a => LensLike ((,)a) s t a a -> a -> s -> (a, t)
l <+~ a = l <%~ (+ a)
{-# INLINE (<+~) #-}

-- | Decrement the target of a numerically valued 'Lens' and return the result.
--
-- When you do not need the result of the subtraction, ('Control.Lens.Setter.-~') is more flexible.
--
-- @
-- ('<-~') :: 'Num' a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<-~') :: 'Num' a => 'Control.Lens.Iso.Iso'' s a  -> a -> s -> (a, s)
-- @
(<-~) :: Num a => LensLike ((,)a) s t a a -> a -> s -> (a, t)
l <-~ a = l <%~ subtract a
{-# INLINE (<-~) #-}

-- | Multiply the target of a numerically valued 'Lens' and return the result.
--
-- When you do not need the result of the multiplication, ('Control.Lens.Setter.*~') is more
-- flexible.
--
-- @
-- ('<*~') :: 'Num' a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<*~') :: 'Num' a => 'Control.Lens.Iso.Iso''  s a -> a -> s -> (a, s)
-- @
(<*~) :: Num a => LensLike ((,)a) s t a a -> a -> s -> (a, t)
l <*~ a = l <%~ (* a)
{-# INLINE (<*~) #-}

-- | Divide the target of a fractionally valued 'Lens' and return the result.
--
-- When you do not need the result of the division, ('Control.Lens.Setter.//~') is more flexible.
--
-- @
-- ('<//~') :: 'Fractional' a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<//~') :: 'Fractional' a => 'Control.Lens.Iso.Iso''  s a -> a -> s -> (a, s)
-- @
(<//~) :: Fractional a => LensLike ((,)a) s t a a -> a -> s -> (a, t)
l <//~ a = l <%~ (/ a)
{-# INLINE (<//~) #-}

-- | Raise the target of a numerically valued 'Lens' to a non-negative
-- 'Integral' power and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.^~') is more flexible.
--
-- @
-- ('<^~') :: ('Num' a, 'Integral' e) => 'Lens'' s a -> e -> s -> (a, s)
-- ('<^~') :: ('Num' a, 'Integral' e) => 'Control.Lens.Iso.Iso'' s a -> e -> s -> (a, s)
-- @
(<^~) :: (Num a, Integral e) => LensLike ((,)a) s t a a -> e -> s -> (a, t)
l <^~ e = l <%~ (^ e)
{-# INLINE (<^~) #-}

-- | Raise the target of a fractionally valued 'Lens' to an 'Integral' power
-- and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.^^~') is more flexible.
--
-- @
-- ('<^^~') :: ('Fractional' a, 'Integral' e) => 'Lens'' s a -> e -> s -> (a, s)
-- ('<^^~') :: ('Fractional' a, 'Integral' e) => 'Control.Lens.Iso.Iso'' s a -> e -> s -> (a, s)
-- @
(<^^~) :: (Fractional a, Integral e) => LensLike ((,)a) s t a a -> e -> s -> (a, t)
l <^^~ e = l <%~ (^^ e)
{-# INLINE (<^^~) #-}

-- | Raise the target of a floating-point valued 'Lens' to an arbitrary power
-- and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.**~') is more flexible.
--
-- @
-- ('<**~') :: 'Floating' a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<**~') :: 'Floating' a => 'Control.Lens.Iso.Iso'' s a  -> a -> s -> (a, s)
-- @
(<**~) :: Floating a => LensLike ((,)a) s t a a -> a -> s -> (a, t)
l <**~ a = l <%~ (** a)
{-# INLINE (<**~) #-}

-- | Logically '||' a Boolean valued 'Lens' and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.||~') is more flexible.
--
-- @
-- ('<||~') :: 'Lens'' s 'Bool' -> 'Bool' -> s -> ('Bool', s)
-- ('<||~') :: 'Control.Lens.Iso.Iso'' s 'Bool'  -> 'Bool' -> s -> ('Bool', s)
-- @
(<||~) :: LensLike ((,)Bool) s t Bool Bool -> Bool -> s -> (Bool, t)
l <||~ b = l <%~ (|| b)
{-# INLINE (<||~) #-}

-- | Logically '&&' a Boolean valued 'Lens' and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.&&~') is more flexible.
--
-- @
-- ('<&&~') :: 'Lens'' s 'Bool' -> 'Bool' -> s -> ('Bool', s)
-- ('<&&~') :: 'Control.Lens.Iso.Iso'' s 'Bool'  -> 'Bool' -> s -> ('Bool', s)
-- @
(<&&~) :: LensLike ((,)Bool) s t Bool Bool -> Bool -> s -> (Bool, t)
l <&&~ b = l <%~ (&& b)
{-# INLINE (<&&~) #-}

-- | Modify the target of a 'Lens', but return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.%~') is more flexible.
--
-- @
-- ('<<%~') ::             'Lens' s t a b      -> (a -> b) -> s -> (a, t)
-- ('<<%~') ::             'Control.Lens.Iso.Iso' s t a b       -> (a -> b) -> s -> (a, t)
-- ('<<%~') :: 'Monoid' a => 'Control.Lens.Traversal.Traversal' s t a b -> (a -> b) -> s -> (a, t)
-- @
(<<%~) :: LensLike ((,)a) s t a b -> (a -> b) -> s -> (a, t)
(<<%~) l = l . lmap (\a -> (a, a)) . second'
{-# INLINE (<<%~) #-}

-- | Replace the target of a 'Lens', but return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter..~') is more flexible.
--
-- @
-- ('<<.~') ::             'Lens' s t a b      -> b -> s -> (a, t)
-- ('<<.~') ::             'Control.Lens.Iso.Iso' s t a b       -> b -> s -> (a, t)
-- ('<<.~') :: 'Monoid' a => 'Control.Lens.Traversal.Traversal' s t a b -> b -> s -> (a, t)
-- @
(<<.~) :: LensLike ((,)a) s t a b -> b -> s -> (a, t)
l <<.~ b = l $ \a -> (a, b)
{-# INLINE (<<.~) #-}

-- | Replace the target of a 'Lens' with a 'Just' value, but return the old value.
--
-- If you do not need the old value ('Control.Lens.Setter.?~') is more flexible.
--
-- >>> import qualified Data.Map as Map
-- >>> _2.at "hello" <<?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
-- (Nothing,(42,fromList [("goodnight","gracie"),("hello","world")]))
--
-- @
-- ('<<?~') :: 'Iso' s t a ('Maybe' b)       -> b -> s -> (a, t)
-- ('<<?~') :: 'Lens' s t a ('Maybe' b)      -> b -> s -> (a, t)
-- ('<<?~') :: 'Traversal' s t a ('Maybe' b) -> b -> s -> (a, t)
-- @
(<<?~) :: LensLike ((,)a) s t a (Maybe b) -> b -> s -> (a, t)
l <<?~ b = l <<.~ Just b
{-# INLINE (<<?~) #-}

-- | Increment the target of a numerically valued 'Lens' and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.+~') is more flexible.
--
-- >>> (a,b) & _1 <<+~ c
-- (a,(a + c,b))
--
-- >>> (a,b) & _2 <<+~ c
-- (b,(a,b + c))
--
-- @
-- ('<<+~') :: 'Num' a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<<+~') :: 'Num' a => 'Iso'' s a -> a -> s -> (a, s)
-- @
(<<+~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
l <<+~ b = l $ \a -> (a, a + b)
{-# INLINE (<<+~) #-}

-- | Decrement the target of a numerically valued 'Lens' and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.-~') is more flexible.
--
-- >>> (a,b) & _1 <<-~ c
-- (a,(a - c,b))
--
-- >>> (a,b) & _2 <<-~ c
-- (b,(a,b - c))
--
-- @
-- ('<<-~') :: 'Num' a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<<-~') :: 'Num' a => 'Iso'' s a -> a -> s -> (a, s)
-- @
(<<-~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
l <<-~ b = l $ \a -> (a, a - b)
{-# INLINE (<<-~) #-}

-- | Multiply the target of a numerically valued 'Lens' and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.-~') is more flexible.
--
-- >>> (a,b) & _1 <<*~ c
-- (a,(a * c,b))
--
-- >>> (a,b) & _2 <<*~ c
-- (b,(a,b * c))
--
-- @
-- ('<<*~') :: 'Num' a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<<*~') :: 'Num' a => 'Iso'' s a -> a -> s -> (a, s)
-- @
(<<*~) :: Num a => LensLike' ((,) a) s a -> a -> s -> (a, s)
l <<*~ b = l $ \a -> (a, a * b)
{-# INLINE (<<*~) #-}

-- | Divide the target of a numerically valued 'Lens' and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.//~') is more flexible.
--
-- >>> (a,b) & _1 <<//~ c
-- (a,(a / c,b))
--
-- >>> ("Hawaii",10) & _2 <<//~ 2
-- (10.0,("Hawaii",5.0))
--
-- @
-- ('<<//~') :: Fractional a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<<//~') :: Fractional a => 'Iso'' s a -> a -> s -> (a, s)
-- @
(<<//~) :: Fractional a => LensLike' ((,) a) s a -> a -> s -> (a, s)
l <<//~ b = l $ \a -> (a, a / b)
{-# INLINE (<<//~) #-}

-- | Raise the target of a numerically valued 'Lens' to a non-negative power and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.^~') is more flexible.
--
-- @
-- ('<<^~') :: ('Num' a, 'Integral' e) => 'Lens'' s a -> e -> s -> (a, s)
-- ('<<^~') :: ('Num' a, 'Integral' e) => 'Iso'' s a -> e -> s -> (a, s)
-- @
(<<^~) :: (Num a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s)
l <<^~ e = l $ \a -> (a, a ^ e)
{-# INLINE (<<^~) #-}

-- | Raise the target of a fractionally valued 'Lens' to an integral power and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.^^~') is more flexible.
--
-- @
-- ('<<^^~') :: ('Fractional' a, 'Integral' e) => 'Lens'' s a -> e -> s -> (a, s)
-- ('<<^^~') :: ('Fractional' a, 'Integral' e) => 'Iso'' s a -> e -> S -> (a, s)
-- @
(<<^^~) :: (Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> s -> (a, s)
l <<^^~ e = l $ \a -> (a, a ^^ e)
{-# INLINE (<<^^~) #-}

-- | Raise the target of a floating-point valued 'Lens' to an arbitrary power and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.**~') is more flexible.
--
-- >>> (a,b) & _1 <<**~ c
-- (a,(a**c,b))
--
-- >>> (a,b) & _2 <<**~ c
-- (b,(a,b**c))
--
-- @
-- ('<<**~') :: 'Floating' a => 'Lens'' s a -> a -> s -> (a, s)
-- ('<<**~') :: 'Floating' a => 'Iso'' s a -> a -> s -> (a, s)
-- @
(<<**~) :: Floating a => LensLike' ((,) a) s a -> a -> s -> (a, s)
l <<**~ e = l $ \a -> (a, a ** e)
{-# INLINE (<<**~) #-}

-- | Logically '||' the target of a 'Bool'-valued 'Lens' and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.||~') is more flexible.
--
-- >>> (False,6) & _1 <<||~ True
-- (False,(True,6))
--
-- >>> ("hello",True) & _2 <<||~ False
-- (True,("hello",True))
--
-- @
-- ('<<||~') :: 'Lens'' s 'Bool' -> 'Bool' -> s -> ('Bool', s)
-- ('<<||~') :: 'Iso'' s 'Bool' -> 'Bool' -> s -> ('Bool', s)
-- @
(<<||~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s)
l <<||~ b = l $ \a -> (a, b || a)
{-# INLINE (<<||~) #-}

-- | Logically '&&' the target of a 'Bool'-valued 'Lens' and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.&&~') is more flexible.
--
-- >>> (False,6) & _1 <<&&~ True
-- (False,(False,6))
--
-- >>> ("hello",True) & _2 <<&&~ False
-- (True,("hello",False))
--
-- @
-- ('<<&&~') :: 'Lens'' s Bool -> Bool -> s -> (Bool, s)
-- ('<<&&~') :: 'Iso'' s Bool -> Bool -> s -> (Bool, s)
-- @
(<<&&~) :: LensLike' ((,) Bool) s Bool -> Bool -> s -> (Bool, s)
l <<&&~ b = l $ \a -> (a, b && a)
{-# INLINE (<<&&~) #-}

-- | Modify the target of a monoidally valued 'Lens' by using ('<>') a new value and return the old value.
--
-- When you do not need the old value, ('Control.Lens.Setter.<>~') is more flexible.
--
-- >>> (Sum a,b) & _1 <<<>~ Sum c
-- (Sum {getSum = a},(Sum {getSum = a + c},b))
--
-- >>> _2 <<<>~ ", 007" $ ("James", "Bond")
-- ("Bond",("James","Bond, 007"))
--
-- @
-- ('<<<>~') :: 'Semigroup' r => 'Lens'' s r -> r -> s -> (r, s)
-- ('<<<>~') :: 'Semigroup' r => 'Iso'' s r -> r -> s -> (r, s)
-- @
(<<<>~) :: Semigroup r => LensLike' ((,) r) s r -> r -> s -> (r, s)
l <<<>~ b = l $ \a -> (a, a <> b)
{-# INLINE (<<<>~) #-}

-------------------------------------------------------------------------------
-- Setting and Remembering State
-------------------------------------------------------------------------------

-- | Modify the target of a 'Lens' into your 'Monad''s state by a user supplied
-- function and return the result.
--
-- When applied to a 'Control.Lens.Traversal.Traversal', it this will return a monoidal summary of all of the intermediate
-- results.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.%=') is more flexible.
--
-- @
-- ('<%=') :: 'MonadState' s m             => 'Lens'' s a      -> (a -> a) -> m a
-- ('<%=') :: 'MonadState' s m             => 'Control.Lens.Iso.Iso'' s a       -> (a -> a) -> m a
-- ('<%=') :: ('MonadState' s m, 'Monoid' a) => 'Control.Lens.Traversal.Traversal'' s a -> (a -> a) -> m a
-- @
(<%=) :: MonadState s m => LensLike ((,)b) s s a b -> (a -> b) -> m b
l <%= f = l %%= (\b -> (b, b)) . f
{-# INLINE (<%=) #-}


-- | Add to the target of a numerically valued 'Lens' into your 'Monad''s state
-- and return the result.
--
-- When you do not need the result of the addition, ('Control.Lens.Setter.+=') is more
-- flexible.
--
-- @
-- ('<+=') :: ('MonadState' s m, 'Num' a) => 'Lens'' s a -> a -> m a
-- ('<+=') :: ('MonadState' s m, 'Num' a) => 'Control.Lens.Iso.Iso'' s a -> a -> m a
-- @
(<+=) :: (MonadState s m, Num a) => LensLike' ((,)a) s a -> a -> m a
l <+= a = l <%= (+ a)
{-# INLINE (<+=) #-}

-- | Subtract from the target of a numerically valued 'Lens' into your 'Monad''s
-- state and return the result.
--
-- When you do not need the result of the subtraction, ('Control.Lens.Setter.-=') is more
-- flexible.
--
-- @
-- ('<-=') :: ('MonadState' s m, 'Num' a) => 'Lens'' s a -> a -> m a
-- ('<-=') :: ('MonadState' s m, 'Num' a) => 'Control.Lens.Iso.Iso'' s a -> a -> m a
-- @
(<-=) :: (MonadState s m, Num a) => LensLike' ((,)a) s a -> a -> m a
l <-= a = l <%= subtract a
{-# INLINE (<-=) #-}

-- | Multiply the target of a numerically valued 'Lens' into your 'Monad''s
-- state and return the result.
--
-- When you do not need the result of the multiplication, ('Control.Lens.Setter.*=') is more
-- flexible.
--
-- @
-- ('<*=') :: ('MonadState' s m, 'Num' a) => 'Lens'' s a -> a -> m a
-- ('<*=') :: ('MonadState' s m, 'Num' a) => 'Control.Lens.Iso.Iso'' s a -> a -> m a
-- @
(<*=) :: (MonadState s m, Num a) => LensLike' ((,)a) s a -> a -> m a
l <*= a = l <%= (* a)
{-# INLINE (<*=) #-}

-- | Divide the target of a fractionally valued 'Lens' into your 'Monad''s state
-- and return the result.
--
-- When you do not need the result of the division, ('Control.Lens.Setter.//=') is more flexible.
--
-- @
-- ('<//=') :: ('MonadState' s m, 'Fractional' a) => 'Lens'' s a -> a -> m a
-- ('<//=') :: ('MonadState' s m, 'Fractional' a) => 'Control.Lens.Iso.Iso'' s a -> a -> m a
-- @
(<//=) :: (MonadState s m, Fractional a) => LensLike' ((,)a) s a -> a -> m a
l <//= a = l <%= (/ a)
{-# INLINE (<//=) #-}

-- | Raise the target of a numerically valued 'Lens' into your 'Monad''s state
-- to a non-negative 'Integral' power and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.^=') is more flexible.
--
-- @
-- ('<^=') :: ('MonadState' s m, 'Num' a, 'Integral' e) => 'Lens'' s a -> e -> m a
-- ('<^=') :: ('MonadState' s m, 'Num' a, 'Integral' e) => 'Control.Lens.Iso.Iso'' s a -> e -> m a
-- @
(<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,)a) s a -> e -> m a
l <^= e = l <%= (^ e)
{-# INLINE (<^=) #-}

-- | Raise the target of a fractionally valued 'Lens' into your 'Monad''s state
-- to an 'Integral' power and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.^^=') is more flexible.
--
-- @
-- ('<^^=') :: ('MonadState' s m, 'Fractional' b, 'Integral' e) => 'Lens'' s a -> e -> m a
-- ('<^^=') :: ('MonadState' s m, 'Fractional' b, 'Integral' e) => 'Control.Lens.Iso.Iso'' s a  -> e -> m a
-- @
(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,)a) s a -> e -> m a
l <^^= e = l <%= (^^ e)
{-# INLINE (<^^=) #-}

-- | Raise the target of a floating-point valued 'Lens' into your 'Monad''s
-- state to an arbitrary power and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.**=') is more flexible.
--
-- @
-- ('<**=') :: ('MonadState' s m, 'Floating' a) => 'Lens'' s a -> a -> m a
-- ('<**=') :: ('MonadState' s m, 'Floating' a) => 'Control.Lens.Iso.Iso'' s a -> a -> m a
-- @
(<**=) :: (MonadState s m, Floating a) => LensLike' ((,)a) s a -> a -> m a
l <**= a = l <%= (** a)
{-# INLINE (<**=) #-}

-- | Logically '||' a Boolean valued 'Lens' into your 'Monad''s state and return
-- the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.||=') is more flexible.
--
-- @
-- ('<||=') :: 'MonadState' s m => 'Lens'' s 'Bool' -> 'Bool' -> m 'Bool'
-- ('<||=') :: 'MonadState' s m => 'Control.Lens.Iso.Iso'' s 'Bool'  -> 'Bool' -> m 'Bool'
-- @
(<||=) :: MonadState s m => LensLike' ((,)Bool) s Bool -> Bool -> m Bool
l <||= b = l <%= (|| b)
{-# INLINE (<||=) #-}

-- | Logically '&&' a Boolean valued 'Lens' into your 'Monad''s state and return
-- the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.&&=') is more flexible.
--
-- @
-- ('<&&=') :: 'MonadState' s m => 'Lens'' s 'Bool' -> 'Bool' -> m 'Bool'
-- ('<&&=') :: 'MonadState' s m => 'Control.Lens.Iso.Iso'' s 'Bool'  -> 'Bool' -> m 'Bool'
-- @
(<&&=) :: MonadState s m => LensLike' ((,)Bool) s Bool -> Bool -> m Bool
l <&&= b = l <%= (&& b)
{-# INLINE (<&&=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by a user supplied
-- function and return the /old/ value that was replaced.
--
-- When applied to a 'Control.Lens.Traversal.Traversal', this will return a monoidal summary of all of the old values
-- present.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.%=') is more flexible.
--
-- @
-- ('<<%=') :: 'MonadState' s m             => 'Lens'' s a      -> (a -> a) -> m a
-- ('<<%=') :: 'MonadState' s m             => 'Control.Lens.Iso.Iso'' s a       -> (a -> a) -> m a
-- ('<<%=') :: ('MonadState' s m, 'Monoid' a) => 'Control.Lens.Traversal.Traversal'' s a -> (a -> a) -> m a
-- @
--
-- @('<<%=') :: 'MonadState' s m => 'LensLike' ((,)a) s s a b -> (a -> b) -> m a@
(<<%=) :: (Strong p, MonadState s m) => Over p ((,)a) s s a b -> p a b -> m a
l <<%= f = l %%= lmap (\a -> (a,a)) (second' f)
{-# INLINE (<<%=) #-}

-- | Replace the target of a 'Lens' into your 'Monad''s state with a user supplied
-- value and return the /old/ value that was replaced.
--
-- When applied to a 'Control.Lens.Traversal.Traversal', this will return a monoidal summary of all of the old values
-- present.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter..=') is more flexible.
--
-- @
-- ('<<.=') :: 'MonadState' s m             => 'Lens'' s a      -> a -> m a
-- ('<<.=') :: 'MonadState' s m             => 'Control.Lens.Iso.Iso'' s a       -> a -> m a
-- ('<<.=') :: ('MonadState' s m, 'Monoid' a) => 'Control.Lens.Traversal.Traversal'' s a -> a -> m a
-- @
(<<.=) :: MonadState s m => LensLike ((,)a) s s a b -> b -> m a
l <<.= b = l %%= \a -> (a,b)
{-# INLINE (<<.=) #-}

-- | Replace the target of a 'Lens' into your 'Monad''s state with 'Just' a user supplied
-- value and return the /old/ value that was replaced.
--
-- When applied to a 'Control.Lens.Traversal.Traversal', this will return a monoidal summary of all of the old values
-- present.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.?=') is more flexible.
--
-- @
-- ('<<?=') :: 'MonadState' s m             => 'Lens' s t a (Maybe b)      -> b -> m a
-- ('<<?=') :: 'MonadState' s m             => 'Control.Lens.Iso.Iso' s t a (Maybe b)       -> b -> m a
-- ('<<?=') :: ('MonadState' s m, 'Monoid' a) => 'Control.Lens.Traversal.Traversal' s t a (Maybe b) -> b -> m a
-- @
(<<?=) :: MonadState s m => LensLike ((,)a) s s a (Maybe b) -> b -> m a
l <<?= b = l <<.= Just b
{-# INLINE (<<?=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by adding a value
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.+=') is more flexible.
--
-- @
-- ('<<+=') :: ('MonadState' s m, 'Num' a) => 'Lens'' s a -> a -> m a
-- ('<<+=') :: ('MonadState' s m, 'Num' a) => 'Iso'' s a -> a -> m a
-- @
(<<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
l <<+= n = l %%= \a -> (a, a + n)
{-# INLINE (<<+=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by subtracting a value
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.-=') is more flexible.
--
-- @
-- ('<<-=') :: ('MonadState' s m, 'Num' a) => 'Lens'' s a -> a -> m a
-- ('<<-=') :: ('MonadState' s m, 'Num' a) => 'Iso'' s a -> a -> m a
-- @
(<<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
l <<-= n = l %%= \a -> (a, a - n)
{-# INLINE (<<-=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by multipling a value
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.*=') is more flexible.
--
-- @
-- ('<<*=') :: ('MonadState' s m, 'Num' a) => 'Lens'' s a -> a -> m a
-- ('<<*=') :: ('MonadState' s m, 'Num' a) => 'Iso'' s a -> a -> m a
-- @
(<<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
l <<*= n = l %%= \a -> (a, a * n)
{-# INLINE (<<*=) #-}

-- | Modify the target of a 'Lens' into your 'Monad'\s state by dividing by a value
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.//=') is more flexible.
--
-- @
-- ('<<//=') :: ('MonadState' s m, 'Fractional' a) => 'Lens'' s a -> a -> m a
-- ('<<//=') :: ('MonadState' s m, 'Fractional' a) => 'Iso'' s a -> a -> m a
-- @
(<<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a
l <<//= n = l %%= \a -> (a, a / n)
{-# INLINE (<<//=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by raising it by a non-negative power
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.^=') is more flexible.
--
-- @
-- ('<<^=') :: ('MonadState' s m, 'Num' a, 'Integral' e) => 'Lens'' s a -> e -> m a
-- ('<<^=') :: ('MonadState' s m, 'Num' a, 'Integral' e) => 'Iso'' s a -> a -> m a
-- @
(<<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
l <<^= n = l %%= \a -> (a, a ^ n)
{-# INLINE (<<^=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by raising it by an integral power
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.^^=') is more flexible.
--
-- @
-- ('<<^^=') :: ('MonadState' s m, 'Fractional' a, 'Integral' e) => 'Lens'' s a -> e -> m a
-- ('<<^^=') :: ('MonadState' s m, 'Fractional' a, 'Integral' e) => 'Iso'' s a -> e -> m a
-- @
(<<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
l <<^^= n = l %%= \a -> (a, a ^^ n)
{-# INLINE (<<^^=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by raising it by an arbitrary power
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.**=') is more flexible.
--
-- @
-- ('<<**=') :: ('MonadState' s m, 'Floating' a) => 'Lens'' s a -> a -> m a
-- ('<<**=') :: ('MonadState' s m, 'Floating' a) => 'Iso'' s a -> a -> m a
-- @
(<<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a
l <<**= n = l %%= \a -> (a, a ** n)
{-# INLINE (<<**=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by taking its logical '||' with a value
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.||=') is more flexible.
--
-- @
-- ('<<||=') :: 'MonadState' s m => 'Lens'' s 'Bool' -> 'Bool' -> m 'Bool'
-- ('<<||=') :: 'MonadState' s m => 'Iso'' s 'Bool' -> 'Bool' -> m 'Bool'
-- @
(<<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
l <<||= b = l %%= \a -> (a, a || b)
{-# INLINE (<<||=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by taking its logical '&&' with a value
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.&&=') is more flexible.
--
-- @
-- ('<<&&=') :: 'MonadState' s m => 'Lens'' s 'Bool' -> 'Bool' -> m 'Bool'
-- ('<<&&=') :: 'MonadState' s m => 'Iso'' s 'Bool' -> 'Bool' -> m 'Bool'
-- @
(<<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
l <<&&= b = l %%= \a -> (a, a && b)
{-# INLINE (<<&&=) #-}

-- | Modify the target of a 'Lens' into your 'Monad''s state by using ('<>')
-- and return the /old/ value that was replaced.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.<>=') is more flexible.
--
-- @
-- ('<<<>=') :: ('MonadState' s m, 'Semigroup' r) => 'Lens'' s r -> r -> m r
-- ('<<<>=') :: ('MonadState' s m, 'Semigroup' r) => 'Iso'' s r -> r -> m r
-- @
(<<<>=) :: (MonadState s m, Semigroup r) => LensLike' ((,) r) s r -> r -> m r
l <<<>= b = l %%= \a -> (a, a <> b)
{-# INLINE (<<<>=) #-}

-- | Run a monadic action, and set the target of 'Lens' to its result.
--
-- @
-- ('<<~') :: 'MonadState' s m => 'Control.Lens.Iso.Iso' s s a b   -> m b -> m b
-- ('<<~') :: 'MonadState' s m => 'Lens' s s a b  -> m b -> m b
-- @
--
-- NB: This is limited to taking an actual 'Lens' than admitting a 'Control.Lens.Traversal.Traversal' because
-- there are potential loss of state issues otherwise.
(<<~) :: MonadState s m => ALens s s a b -> m b -> m b
l <<~ mb = do
  b <- mb
  modify $ \s -> ipeek b (l sell s)
  return b
{-# INLINE (<<~) #-}

-- | ('<>') a 'Semigroup' value onto the end of the target of a 'Lens' and
-- return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.<>~') is more flexible.
(<<>~) :: Semigroup m => LensLike ((,)m) s t m m -> m -> s -> (m, t)
l <<>~ m = l <%~ (<> m)
{-# INLINE (<<>~) #-}

-- | ('<>') a 'Semigroup' value onto the end of the target of a 'Lens' into
-- your 'Monad''s state and return the result.
--
-- When you do not need the result of the operation, ('Control.Lens.Setter.<>=') is more flexible.
(<<>=) :: (MonadState s m, Semigroup r) => LensLike' ((,)r) s r -> r -> m r
l <<>= r = l <%= (<> r)
{-# INLINE (<<>=) #-}

------------------------------------------------------------------------------
-- Arrow operators
------------------------------------------------------------------------------

-- | 'Control.Lens.Setter.over' for Arrows.
--
-- Unlike 'Control.Lens.Setter.over', 'overA' can't accept a simple
-- 'Control.Lens.Setter.Setter', but requires a full lens, or close
-- enough.
--
-- >>> overA _1 ((+1) *** (+2)) ((1,2),6)
-- ((2,4),6)
--
-- @
-- overA :: Arrow ar => Lens s t a b -> ar a b -> ar s t
-- @
overA :: Arrow ar => LensLike (Context a b) s t a b -> ar a b -> ar s t
overA l p = arr (\s -> let (Context f a) = l sell s in (f, a))
            >>> second p
            >>> arr (uncurry id)

------------------------------------------------------------------------------
-- Indexed
------------------------------------------------------------------------------

-- | Adjust the target of an 'IndexedLens' returning the intermediate result, or
-- adjust all of the targets of an 'Control.Lens.Traversal.IndexedTraversal' and return a monoidal summary
-- along with the answer.
--
-- @
-- l '<%~' f ≡ l '<%@~' 'const' f
-- @
--
-- When you do not need access to the index then ('<%~') is more liberal in what it can accept.
--
-- If you do not need the intermediate result, you can use ('Control.Lens.Setter.%@~') or even ('Control.Lens.Setter.%~').
--
-- @
-- ('<%@~') ::             'IndexedLens' i s t a b      -> (i -> a -> b) -> s -> (b, t)
-- ('<%@~') :: 'Monoid' b => 'Control.Lens.Traversal.IndexedTraversal' i s t a b -> (i -> a -> b) -> s -> (b, t)
-- @
(<%@~) :: Over (Indexed i) ((,) b) s t a b -> (i -> a -> b) -> s -> (b, t)
l <%@~ f = l (Indexed $ \i a -> let b = f i a in (b, b))
{-# INLINE (<%@~) #-}

-- | Adjust the target of an 'IndexedLens' returning the old value, or
-- adjust all of the targets of an 'Control.Lens.Traversal.IndexedTraversal' and return a monoidal summary
-- of the old values along with the answer.
--
-- @
-- ('<<%@~') ::             'IndexedLens' i s t a b      -> (i -> a -> b) -> s -> (a, t)
-- ('<<%@~') :: 'Monoid' a => 'Control.Lens.Traversal.IndexedTraversal' i s t a b -> (i -> a -> b) -> s -> (a, t)
-- @
(<<%@~) :: Over (Indexed i) ((,) a) s t a b -> (i -> a -> b) -> s -> (a, t)
l <<%@~ f = l $ Indexed $ \i a -> second' (f i) (a,a)

{-# INLINE (<<%@~) #-}

-- | Adjust the target of an 'IndexedLens' returning a supplementary result, or
-- adjust all of the targets of an 'Control.Lens.Traversal.IndexedTraversal' and return a monoidal summary
-- of the supplementary results and the answer.
--
-- @
-- ('%%@~') ≡ 'Control.Lens.Indexed.withIndex'
-- @
--
-- @
-- ('%%@~') :: 'Functor' f => 'IndexedLens' i s t a b      -> (i -> a -> f b) -> s -> f t
-- ('%%@~') :: 'Applicative' f => 'Control.Lens.Traversal.IndexedTraversal' i s t a b -> (i -> a -> f b) -> s -> f t
-- @
--
-- In particular, it is often useful to think of this function as having one of these even more
-- restricted type signatures:
--
-- @
-- ('%%@~') ::             'IndexedLens' i s t a b      -> (i -> a -> (r, b)) -> s -> (r, t)
-- ('%%@~') :: 'Monoid' r => 'Control.Lens.Traversal.IndexedTraversal' i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)
-- @
(%%@~) :: Over (Indexed i) f s t a b -> (i -> a -> f b) -> s -> f t
(%%@~) l = l .# Indexed
{-# INLINE (%%@~) #-}

-- | Adjust the target of an 'IndexedLens' returning a supplementary result, or
-- adjust all of the targets of an 'Control.Lens.Traversal.IndexedTraversal' within the current state, and
-- return a monoidal summary of the supplementary results.
--
-- @
-- l '%%@=' f ≡ 'state' (l '%%@~' f)
-- @
--
-- @
-- ('%%@=') :: 'MonadState' s m                 => 'IndexedLens' i s s a b      -> (i -> a -> (r, b)) -> s -> m r
-- ('%%@=') :: ('MonadState' s m, 'Monoid' r) => 'Control.Lens.Traversal.IndexedTraversal' i s s a b -> (i -> a -> (r, b)) -> s -> m r
-- @
(%%@=) :: MonadState s m => Over (Indexed i) ((,) r) s s a b -> (i -> a -> (r, b)) -> m r
#if MIN_VERSION_mtl(2,1,0)
l %%@= f = State.state (l %%@~ f)
#else
l %%@= f = do
  (r, s) <- State.gets (l %%@~ f)
  State.put s
  return r
#endif
{-# INLINE (%%@=) #-}

-- | Adjust the target of an 'IndexedLens' returning the intermediate result, or
-- adjust all of the targets of an 'Control.Lens.Traversal.IndexedTraversal' within the current state, and
-- return a monoidal summary of the intermediate results.
--
-- @
-- ('<%@=') :: 'MonadState' s m                 => 'IndexedLens' i s s a b      -> (i -> a -> b) -> m b
-- ('<%@=') :: ('MonadState' s m, 'Monoid' b) => 'Control.Lens.Traversal.IndexedTraversal' i s s a b -> (i -> a -> b) -> m b
-- @
(<%@=) :: MonadState s m => Over (Indexed i) ((,) b) s s a b -> (i -> a -> b) -> m b
l <%@= f = l %%@= \ i a -> let b = f i a in (b, b)
{-# INLINE (<%@=) #-}

-- | Adjust the target of an 'IndexedLens' returning the old value, or
-- adjust all of the targets of an 'Control.Lens.Traversal.IndexedTraversal' within the current state, and
-- return a monoidal summary of the old values.
--
-- @
-- ('<<%@=') :: 'MonadState' s m                 => 'IndexedLens' i s s a b      -> (i -> a -> b) -> m a
-- ('<<%@=') :: ('MonadState' s m, 'Monoid' b) => 'Control.Lens.Traversal.IndexedTraversal' i s s a b -> (i -> a -> b) -> m a
-- @
(<<%@=) :: MonadState s m => Over (Indexed i) ((,) a) s s a b -> (i -> a -> b) -> m a
#if MIN_VERSION_mtl(2,1,0)
l <<%@= f = State.state (l (Indexed $ \ i a -> (a, f i a)))
#else
l <<%@= f = do
  (r, s) <- State.gets (l (Indexed $ \ i a -> (a, f i a)))
  State.put s
  return r
#endif
{-# INLINE (<<%@=) #-}

------------------------------------------------------------------------------
-- ALens Combinators
------------------------------------------------------------------------------

-- | A version of ('Control.Lens.Getter.^.') that works on 'ALens'.
--
-- >>> ("hello","world")^#_2
-- "world"
(^#) :: s -> ALens s t a b -> a
s ^# l = ipos (l sell s)
{-# INLINE (^#) #-}

-- | A version of 'Control.Lens.Setter.set' that works on 'ALens'.
--
-- >>> storing _2 "world" ("hello","there")
-- ("hello","world")
storing :: ALens s t a b -> b -> s -> t
storing l b s = ipeek b (l sell s)
{-# INLINE storing #-}

-- | A version of ('Control.Lens.Setter..~') that works on 'ALens'.
--
-- >>> ("hello","there") & _2 #~ "world"
-- ("hello","world")
(#~) :: ALens s t a b -> b -> s -> t
(#~) l b s = ipeek b (l sell s)
{-# INLINE (#~) #-}

-- | A version of ('Control.Lens.Setter.%~') that works on 'ALens'.
--
-- >>> ("hello","world") & _2 #%~ length
-- ("hello",5)
(#%~) :: ALens s t a b -> (a -> b) -> s -> t
(#%~) l f s = ipeeks f (l sell s)
{-# INLINE (#%~) #-}

-- | A version of ('%%~') that works on 'ALens'.
--
-- >>> ("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
-- (5,("hello","world!"))
(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t
(#%%~) l f s = runPretext (l sell s) f
{-# INLINE (#%%~) #-}

-- | A version of ('Control.Lens.Setter..=') that works on 'ALens'.
(#=) :: MonadState s m => ALens s s a b -> b -> m ()
l #= f = modify (l #~ f)
{-# INLINE (#=) #-}

-- | A version of ('Control.Lens.Setter.%=') that works on 'ALens'.
(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m ()
l #%= f = modify (l #%~ f)
{-# INLINE (#%=) #-}

-- | A version of ('<%~') that works on 'ALens'.
--
-- >>> ("hello","world") & _2 <#%~ length
-- (5,("hello",5))
(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t)
l <#%~ f = \s -> runPretext (l sell s) $ \a -> let b = f a in (b, b)
{-# INLINE (<#%~) #-}

-- | A version of ('<%=') that works on 'ALens'.
(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b
l <#%= f = l #%%= \a -> let b = f a in (b, b)
{-# INLINE (<#%=) #-}

-- | A version of ('%%=') that works on 'ALens'.
(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r
#if MIN_VERSION_mtl(2,1,1)
l #%%= f = State.state $ \s -> runPretext (l sell s) f
#else
l #%%= f = do
  p <- State.gets (l sell)
  let (r, t) = runPretext p f
  State.put t
  return r
#endif
{-# INLINE (#%%=) #-}

-- | A version of ('Control.Lens.Setter.<.~') that works on 'ALens'.
--
-- >>> ("hello","there") & _2 <#~ "world"
-- ("world",("hello","world"))
(<#~) :: ALens s t a b -> b -> s -> (b, t)
l <#~ b = \s -> (b, storing l b s)
{-# INLINE (<#~) #-}

-- | A version of ('Control.Lens.Setter.<.=') that works on 'ALens'.
(<#=) :: MonadState s m => ALens s s a b -> b -> m b
l <#= b = do
  l #= b
  return b
{-# INLINE (<#=) #-}

-- | There is a field for every type in the 'Void'. Very zen.
--
-- >>> [] & mapped.devoid +~ 1
-- []
--
-- >>> Nothing & mapped.devoid %~ abs
-- Nothing
--
-- @
-- 'devoid' :: 'Lens'' 'Void' a
-- @
devoid :: Over p f Void Void a b
devoid _ = absurd
{-# INLINE devoid #-}

-- | We can always retrieve a @()@ from any type.
--
-- >>> "hello"^.united
-- ()
--
-- >>> "hello" & united .~ ()
-- "hello"
united :: Lens' a ()
united f v = f () <&> \ () -> v
{-# INLINE united #-}

data First1 f a = First1 (f a) a

instance (Functor f) => Functor (First1 f) where
  fmap f (First1 fa a) = First1 (f <$> fa) (f a)
  {-# INLINE fmap #-}

instance (Functor f) => Apply (First1 f) where
  First1 ff f <.> First1 _ x = First1 (($ x) <$> ff) (f x)
  {-# INLINE (<.>) #-}

getFirst1 :: First1 f a -> f a
getFirst1 (First1 fa _) = fa
{-# INLINE getFirst1 #-}

-- | A 'Lens' focusing on the first element of a 'Traversable1' container.
--
-- >>> 2 :| [3, 4] & head1 +~ 10
-- 12 :| [3,4]
--
-- >>> Identity True ^. head1
-- True
head1 :: (Traversable1 t) => Lens' (t a) a
head1 f = getFirst1 . traverse1 (\a -> First1 (f a) a)
{-# INLINE head1 #-}

-- | A 'Lens' focusing on the last element of a 'Traversable1' container.
--
-- >>> 2 :| [3, 4] & last1 +~ 10
-- 2 :| [3,14]
--
-- >>> Node 'a' [Node 'b' [], Node 'c' []] ^. last1
-- 'c'
last1 :: (Traversable1 t) => Lens' (t a) a
last1 f = fmap getReverse . head1 f . Reverse
{-# INLINE last1 #-}

-- | Fuse a composition of lenses using 'Yoneda' to provide 'fmap' fusion.
--
-- In general, given a pair of lenses 'foo' and 'bar'
--
-- @
-- fusing (foo.bar) = foo.bar
-- @
--
-- however, @foo@ and @bar@ are either going to 'fmap' internally or they are trivial.
--
-- 'fusing' exploits the 'Yoneda' lemma to merge these separate uses into a single 'fmap'.
--
-- This is particularly effective when the choice of functor 'f' is unknown at compile
-- time or when the 'Lens' @foo.bar@ in the above description is recursive or complex
-- enough to prevent inlining.
--
-- @
-- 'fusing' :: 'Lens' s t a b -> 'Lens' s t a b
-- @
fusing :: Functor f => LensLike (Yoneda f) s t a b -> LensLike f s t a b
fusing t = \f -> lowerYoneda . t (liftYoneda . f)
{-# INLINE fusing #-}
