/usr/share/doc/libghc-lens-doc/html/Control-Lens-Lens.html is in libghc-lens-doc 4.13-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 | <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Control.Lens.Lens</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><script src="haddock-util.js" type="text/javascript"></script><script type="text/javascript">//<![CDATA[
window.onload = function () {pageLoad();setSynopsis("mini_Control-Lens-Lens.html");};
//]]>
</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Control-Lens-Lens.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">lens-4.13: Lenses, Folds and Traversals</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Copyright</th><td>(C) 2012-15 Edward Kmett</td></tr><tr><th>License</th><td>BSD-style (see the file LICENSE)</td></tr><tr><th>Maintainer</th><td>Edward Kmett <ekmett@gmail.com></td></tr><tr><th>Stability</th><td>provisional</td></tr><tr><th>Portability</th><td>Rank2Types</td></tr><tr><th>Safe Haskell</th><td>Safe</td></tr><tr><th>Language</th><td>Haskell98</td></tr></table><p class="caption">Control.Lens.Lens</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Lenses</a><ul><li><a href="#g:2">Concrete Lenses</a></li></ul></li><li><a href="#g:3">Combinators</a><ul><li><a href="#g:4">General Purpose Combinators</a></li></ul></li><li><a href="#g:5">Lateral Composition</a></li><li><a href="#g:6">Setting Functionally with Passthrough</a></li><li><a href="#g:7">Setting State with Passthrough</a></li><li><a href="#g:8">Cloning Lenses</a></li><li><a href="#g:9">Arrow operators</a></li><li><a href="#g:10">ALens Combinators</a></li><li><a href="#g:11">Common Lenses</a></li><li><a href="#g:12">Context</a></li><li><a href="#g:13">Lens fusion</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A <code><code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b</code> is a purely functional reference.</p><p>While a <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> could be used for
<code><a href="Control-Lens-Getter.html#v:Getting">Getting</a></code> like a valid <code><a href="Control-Lens-Fold.html#v:Fold">Fold</a></code>, it
wasn't a valid <code><a href="Control-Lens-Getter.html#v:Getter">Getter</a></code> as a
<code><a href="Control-Lens-Getter.html#v:Getter">Getter</a></code> can't require an <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> constraint.</p><p><code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code>, however, is a constraint on both.</p><pre>type <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b = forall f. <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> f => (a -> f b) -> s -> f t
</pre><p>Every <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> is a valid <code><a href="Control-Lens-Setter.html#v:Setter">Setter</a></code>.</p><p>Every <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> can be used for <code><a href="Control-Lens-Getter.html#v:Getting">Getting</a></code> like a
<code><a href="Control-Lens-Fold.html#v:Fold">Fold</a></code> that doesn't use the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> or
<code>Contravariant</code>.</p><p>Every <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> is a valid <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> that only uses
the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> part of the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> it is supplied.</p><p>Every <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> can be used for <code><a href="Control-Lens-Getter.html#v:Getting">Getting</a></code> like a valid
<code><a href="Control-Lens-Getter.html#v:Getter">Getter</a></code>.</p><p>Since every <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> can be used for <code><a href="Control-Lens-Getter.html#v:Getting">Getting</a></code> like a
valid <code><a href="Control-Lens-Getter.html#v:Getter">Getter</a></code> it follows that it must view exactly one element in the
structure.</p><p>The <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> laws follow from this property and the desire for it to act like
a <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Traversable.html#v:Traversable">Traversable</a></code> when used as a
<code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code>.</p><p>In the examples below, <code>getter</code> and <code>setter</code> are supplied as example getters
and setters, and are not actual functions supplied by this package.</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">type</span> <a href="#t:Lens">Lens</a> s t a b = <span class="keyword">forall</span> f. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => (a -> f b) -> s -> f t</li><li class="src short"><span class="keyword">type</span> <a href="#t:Lens-39-">Lens'</a> s a = <a href="Control-Lens-Lens.html#t:Lens">Lens</a> s s a a</li><li class="src short"><span class="keyword">type</span> <a href="#t:IndexedLens">IndexedLens</a> i s t a b = <span class="keyword">forall</span> f p. (<a href="Control-Lens-Internal-Indexed.html#t:Indexable">Indexable</a> i p, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f) => p a (f b) -> s -> f t</li><li class="src short"><span class="keyword">type</span> <a href="#t:IndexedLens-39-">IndexedLens'</a> i s a = <a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a> i s s a a</li><li class="src short"><span class="keyword">type</span> <a href="#t:ALens">ALens</a> s t a b = <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="Control-Lens-Internal-Context.html#t:Pretext">Pretext</a> (->) a b) s t a b</li><li class="src short"><span class="keyword">type</span> <a href="#t:ALens-39-">ALens'</a> s a = <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a a</li><li class="src short"><span class="keyword">type</span> <a href="#t:AnIndexedLens">AnIndexedLens</a> i s t a b = <a href="Control-Lens-Type.html#t:Optical">Optical</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) (->) (<a href="Control-Lens-Internal-Context.html#t:Pretext">Pretext</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) a b) s t a b</li><li class="src short"><span class="keyword">type</span> <a href="#t:AnIndexedLens-39-">AnIndexedLens'</a> i s a = <a href="Control-Lens-Lens.html#t:AnIndexedLens">AnIndexedLens</a> i s s a a</li><li class="src short"><a href="#v:lens">lens</a> :: (s -> a) -> (s -> b -> t) -> <a href="Control-Lens-Lens.html#t:Lens">Lens</a> s t a b</li><li class="src short"><a href="#v:ilens">ilens</a> :: (s -> (i, a)) -> (s -> b -> t) -> <a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a> i s t a b</li><li class="src short"><a href="#v:iplens">iplens</a> :: (s -> a) -> (s -> b -> t) -> <a href="Control-Lens-Type.html#t:IndexPreservingLens">IndexPreservingLens</a> s t a b</li><li class="src short"><a href="#v:-37--37--126-">(%%~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f s t a b -> (a -> f b) -> s -> f t</li><li class="src short"><a href="#v:-37--37--61-">(%%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:Over">Over</a> p (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s s a b -> p a (r, b) -> m r</li><li class="src short"><a href="#v:-37--37--64--126-">(%%@~)</a> :: <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> i f s t a b -> (i -> a -> f b) -> s -> f t</li><li class="src short"><a href="#v:-37--37--64--61-">(%%@=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> i (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s s a b -> (i -> a -> (r, b)) -> m r</li><li class="src short"><a href="#v:-60--37--64--126-">(<%@~)</a> :: <a href="Control-Lens-Type.html#t:Over">Over</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> b) s t a b -> (i -> a -> b) -> s -> (b, t)</li><li class="src short"><a href="#v:-60--37--64--61-">(<%@=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> i (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> b) s s a b -> (i -> a -> b) -> m b</li><li class="src short"><a href="#v:-60--60--37--64--126-">(<<%@~)</a> :: <a href="Control-Lens-Type.html#t:Over">Over</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a b -> (i -> a -> b) -> s -> (a, t)</li><li class="src short"><a href="#v:-60--60--37--64--61-">(<<%@=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> i (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s s a b -> (i -> a -> b) -> m a</li><li class="src short"><a href="#v:-38-">(&)</a> :: a -> (a -> b) -> b</li><li class="src short"><a href="#v:-60--38--62-">(<&>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => f a -> (a -> b) -> f b</li><li class="src short"><a href="#v:-63--63-">(??)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => f (a -> b) -> a -> f b</li><li class="src short"><a href="#v:-38--126-">(&~)</a> :: s -> <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Lazy.html#t:State">State</a> s a -> s</li><li class="src short"><a href="#v:choosing">choosing</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f s t a b -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f s' t' a b -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a> s s') (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a> t t') a b</li><li class="src short"><a href="#v:chosen">chosen</a> :: <a href="Control-Lens-Type.html#t:IndexPreservingLens">IndexPreservingLens</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a> a a) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a> b b) a b</li><li class="src short"><a href="#v:alongside">alongside</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="Control-Lens-Internal-Getter.html#t:AlongsideLeft">AlongsideLeft</a> f b') s t a b -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="Control-Lens-Internal-Getter.html#t:AlongsideRight">AlongsideRight</a> f t) s' t' a' b' -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f (s, s') (t, t') (a, a') (b, b')</li><li class="src short"><a href="#v:inside">inside</a> :: <a href="file:///usr/share/doc/libghc-profunctors-doc/html/Data-Profunctor-Rep.html#t:Corepresentable">Corepresentable</a> p => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> <a href="Control-Lens-Lens.html#t:Lens">Lens</a> (p e s) (p e t) (p e a) (p e b)</li><li class="src short"><a href="#v:-60--37--126-">(<%~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> b) s t a b -> (a -> b) -> s -> (b, t)</li><li class="src short"><a href="#v:-60--43--126-">(<+~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t)</li><li class="src short"><a href="#v:-60--45--126-">(<-~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t)</li><li class="src short"><a href="#v:-60--42--126-">(<*~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t)</li><li class="src short"><a href="#v:-60--47--47--126-">(<//~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t)</li><li class="src short"><a href="#v:-60--94--126-">(<^~)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> e -> s -> (a, t)</li><li class="src short"><a href="#v:-60--94--94--126-">(<^^~)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> e -> s -> (a, t)</li><li class="src short"><a href="#v:-60--42--42--126-">(<**~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t)</li><li class="src short"><a href="#v:-60--124--124--126-">(<||~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s t <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> s -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>, t)</li><li class="src short"><a href="#v:-60--38--38--126-">(<&&~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s t <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> s -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>, t)</li><li class="src short"><a href="#v:-60--60--62--126-">(<<>~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> m => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> m) s t m m -> m -> s -> (m, t)</li><li class="src short"><a href="#v:-60--60--37--126-">(<<%~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a b -> (a -> b) -> s -> (a, t)</li><li class="src short"><a href="#v:-60--60-.-126-">(<<.~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a b -> b -> s -> (a, t)</li><li class="src short"><a href="#v:-60--60--43--126-">(<<+~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s)</li><li class="src short"><a href="#v:-60--60--45--126-">(<<-~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s)</li><li class="src short"><a href="#v:-60--60--42--126-">(<<*~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s)</li><li class="src short"><a href="#v:-60--60--47--47--126-">(<<//~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s)</li><li class="src short"><a href="#v:-60--60--94--126-">(<<^~)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> s -> (a, s)</li><li class="src short"><a href="#v:-60--60--94--94--126-">(<<^^~)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> s -> (a, s)</li><li class="src short"><a href="#v:-60--60--42--42--126-">(<<**~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s)</li><li class="src short"><a href="#v:-60--60--124--124--126-">(<<||~)</a> :: <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> s -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>, s)</li><li class="src short"><a href="#v:-60--60--38--38--126-">(<<&&~)</a> :: <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> s -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>, s)</li><li class="src short"><a href="#v:-60--60--60--62--126-">(<<<>~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> r => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s r -> r -> s -> (r, s)</li><li class="src short"><a href="#v:-60--37--61-">(<%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> b) s s a b -> (a -> b) -> m b</li><li class="src short"><a href="#v:-60--43--61-">(<+=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--45--61-">(<-=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--42--61-">(<*=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--47--47--61-">(<//=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--94--61-">(<^=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> m a</li><li class="src short"><a href="#v:-60--94--94--61-">(<^^=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> m a</li><li class="src short"><a href="#v:-60--42--42--61-">(<**=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--124--124--61-">(<||=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> m <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--38--38--61-">(<&&=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> m <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--60--62--61-">(<<>=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> r) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s r -> r -> m r</li><li class="src short"><a href="#v:-60--60--37--61-">(<<%=)</a> :: (<a href="file:///usr/share/doc/libghc-profunctors-doc/html/Data-Profunctor.html#t:Strong">Strong</a> p, <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m) => <a href="Control-Lens-Type.html#t:Over">Over</a> p (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s s a b -> p a b -> m a</li><li class="src short"><a href="#v:-60--60-.-61-">(<<.=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s s a b -> b -> m a</li><li class="src short"><a href="#v:-60--60--43--61-">(<<+=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--60--45--61-">(<<-=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--60--42--61-">(<<*=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--60--47--47--61-">(<<//=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--60--94--61-">(<<^=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> m a</li><li class="src short"><a href="#v:-60--60--94--94--61-">(<<^^=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> m a</li><li class="src short"><a href="#v:-60--60--42--42--61-">(<<**=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a</li><li class="src short"><a href="#v:-60--60--124--124--61-">(<<||=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> m <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--60--38--38--61-">(<<&&=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> m <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:-60--60--60--62--61-">(<<<>=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> r) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s r -> r -> m r</li><li class="src short"><a href="#v:-60--60--126-">(<<~)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> m b -> m b</li><li class="src short"><a href="#v:cloneLens">cloneLens</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> <a href="Control-Lens-Lens.html#t:Lens">Lens</a> s t a b</li><li class="src short"><a href="#v:cloneIndexPreservingLens">cloneIndexPreservingLens</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> <a href="Control-Lens-Type.html#t:IndexPreservingLens">IndexPreservingLens</a> s t a b</li><li class="src short"><a href="#v:cloneIndexedLens">cloneIndexedLens</a> :: <a href="Control-Lens-Lens.html#t:AnIndexedLens">AnIndexedLens</a> i s t a b -> <a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a> i s t a b</li><li class="src short"><a href="#v:overA">overA</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Arrow.html#t:Arrow">Arrow</a> ar => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="Control-Lens-Lens.html#t:Context">Context</a> a b) s t a b -> ar a b -> ar s t</li><li class="src short"><a href="#v:storing">storing</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> b -> s -> t</li><li class="src short"><a href="#v:-94--35-">(^#)</a> :: s -> <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> a</li><li class="src short"><a href="#v:-35--126-">(#~)</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> b -> s -> t</li><li class="src short"><a href="#v:-35--37--126-">(#%~)</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> (a -> b) -> s -> t</li><li class="src short"><a href="#v:-35--37--37--126-">(#%%~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> (a -> f b) -> s -> f t</li><li class="src short"><a href="#v:-60--35--126-">(<#~)</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> b -> s -> (b, t)</li><li class="src short"><a href="#v:-60--35--37--126-">(<#%~)</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> (a -> b) -> s -> (b, t)</li><li class="src short"><a href="#v:-35--61-">(#=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> b -> m ()</li><li class="src short"><a href="#v:-35--37--61-">(#%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> (a -> b) -> m ()</li><li class="src short"><a href="#v:-35--37--37--61-">(#%%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> (a -> (r, b)) -> m r</li><li class="src short"><a href="#v:-60--35--61-">(<#=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> b -> m b</li><li class="src short"><a href="#v:-60--35--37--61-">(<#%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> (a -> b) -> m b</li><li class="src short"><a href="#v:devoid">devoid</a> :: <a href="Control-Lens-Type.html#t:Over">Over</a> p f <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Void.html#t:Void">Void</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Void.html#t:Void">Void</a> a b</li><li class="src short"><a href="#v:united">united</a> :: <a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a> a ()</li><li class="src short"><span class="keyword">data</span> <a href="#t:Context">Context</a> a b t = <a href="#v:Context">Context</a> (b -> t) a</li><li class="src short"><span class="keyword">type</span> <a href="#t:Context-39-">Context'</a> a = <a href="Control-Lens-Lens.html#t:Context">Context</a> a a</li><li class="src short"><a href="#v:locus">locus</a> :: <a href="Control-Lens-Internal-Context.html#t:IndexedComonadStore">IndexedComonadStore</a> p => <a href="Control-Lens-Lens.html#t:Lens">Lens</a> (p a c s) (p b c s) a b</li><li class="src short"><a href="#v:fusing">fusing</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/libghc-kan-extensions-doc/html/Data-Functor-Yoneda.html#t:Yoneda">Yoneda</a> f) s t a b -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f s t a b</li></ul></div><div id="interface"><h1 id="g:1">Lenses</h1><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:Lens" class="def">Lens</a> s t a b = <span class="keyword">forall</span> f. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => (a -> f b) -> s -> f t <a href="src/Control-Lens-Type.html#Lens" class="link">Source</a></p><div class="doc"><p>A <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> is actually a lens family as described in
<a href="http://comonad.com/reader/2012/mirrored-lenses/">http://comonad.com/reader/2012/mirrored-lenses/</a>.</p><p>With great power comes great responsibility and a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> is subject to the
three common sense <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> laws:</p><p>1) You get back what you put in:</p><pre><code><a href="Control-Lens-Getter.html#v:view">view</a></code> l (<code><a href="Control-Lens-Setter.html#v:set">set</a></code> l v s) ≡ v
</pre><p>2) Putting back what you got doesn't change anything:</p><pre><code><a href="Control-Lens-Setter.html#v:set">set</a></code> l (<code><a href="Control-Lens-Getter.html#v:view">view</a></code> l s) s ≡ s
</pre><p>3) Setting twice is the same as setting once:</p><pre><code><a href="Control-Lens-Setter.html#v:set">set</a></code> l v' (<code><a href="Control-Lens-Setter.html#v:set">set</a></code> l v s) ≡ <code><a href="Control-Lens-Setter.html#v:set">set</a></code> l v' s
</pre><p>These laws are strong enough that the 4 type parameters of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> cannot
vary fully independently. For more on how they interact, read the "Why is
it a Lens Family?" section of
<a href="http://comonad.com/reader/2012/mirrored-lenses/">http://comonad.com/reader/2012/mirrored-lenses/</a>.</p><p>There are some emergent properties of these laws:</p><p>1) <code><code><a href="Control-Lens-Setter.html#v:set">set</a></code> l s</code> must be injective for every <code>s</code> This is a consequence of law #1</p><p>2) <code><code><a href="Control-Lens-Setter.html#v:set">set</a></code> l</code> must be surjective, because of law #2, which indicates that it is possible to obtain any <code>v</code> from some <code>s</code> such that <code><code><a href="Control-Lens-Setter.html#v:set">set</a></code> s v = s</code></p><p>3) Given just the first two laws you can prove a weaker form of law #3 where the values <code>v</code> that you are setting match:</p><pre><code><a href="Control-Lens-Setter.html#v:set">set</a></code> l v (<code><a href="Control-Lens-Setter.html#v:set">set</a></code> l v s) ≡ <code><a href="Control-Lens-Setter.html#v:set">set</a></code> l v s
</pre><p>Every <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> can be used directly as a <code><a href="Control-Lens-Setter.html#v:Setter">Setter</a></code> or <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code>.</p><p>You can also use a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> for <code><a href="Control-Lens-Getter.html#v:Getting">Getting</a></code> as if it were a
<code><a href="Control-Lens-Type.html#t:Fold">Fold</a></code> or <code><a href="Control-Lens-Type.html#t:Getter">Getter</a></code>.</p><p>Since every <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> is a valid <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code>, the
<code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code> laws are required of any <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> you create:</p><pre>l <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#v:pure">pure</a></code> ≡ <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#v:pure">pure</a></code>
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:fmap">fmap</a></code> (l f) <code>.</code> l g ≡ <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Compose.html#v:getCompose">getCompose</a></code> <code>.</code> l (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/transformers-0.4.2.0/Data-Functor-Compose.html#v:Compose">Compose</a></code> <code>.</code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:fmap">fmap</a></code> f <code>.</code> g)
</pre><pre>type <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b = forall f. <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> f => <code><a href="Control-Lens-Type.html#t:LensLike">LensLike</a></code> f s t a b
</pre></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:Lens-39-" class="def">Lens'</a> s a = <a href="Control-Lens-Lens.html#t:Lens">Lens</a> s s a a <a href="src/Control-Lens-Type.html#Lens%27" class="link">Source</a></p><div class="doc"><pre>type <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> = <code><a href="Control-Lens-Type.html#t:Simple">Simple</a></code> <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code>
</pre></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:IndexedLens" class="def">IndexedLens</a> i s t a b = <span class="keyword">forall</span> f p. (<a href="Control-Lens-Internal-Indexed.html#t:Indexable">Indexable</a> i p, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f) => p a (f b) -> s -> f t <a href="src/Control-Lens-Type.html#IndexedLens" class="link">Source</a></p><div class="doc"><p>Every <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> is a valid <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and a valid <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code>.</p></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:IndexedLens-39-" class="def">IndexedLens'</a> i s a = <a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a> i s s a a <a href="src/Control-Lens-Type.html#IndexedLens%27" class="link">Source</a></p><div class="doc"><pre>type <code><a href="Control-Lens-Lens.html#t:IndexedLens-39-">IndexedLens'</a></code> i = <code><a href="Control-Lens-Type.html#t:Simple">Simple</a></code> (<code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> i)
</pre></div></div><h2 id="g:2">Concrete Lenses</h2><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:ALens" class="def">ALens</a> s t a b = <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="Control-Lens-Internal-Context.html#t:Pretext">Pretext</a> (->) a b) s t a b <a href="src/Control-Lens-Lens.html#ALens" class="link">Source</a></p><div class="doc"><p>When you see this as an argument to a function, it expects a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code>.</p><p>This type can also be used when you need to store a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> in a container,
since it is rank-1. You can turn them back into a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> with <code><a href="Control-Lens-Lens.html#v:cloneLens">cloneLens</a></code>,
or use it directly with combinators like <code><a href="Control-Lens-Lens.html#v:storing">storing</a></code> and (<code><a href="Control-Lens-Lens.html#v:-94--35-">^#</a></code>).</p></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:ALens-39-" class="def">ALens'</a> s a = <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a a <a href="src/Control-Lens-Lens.html#ALens%27" class="link">Source</a></p><div class="doc"><pre>type <code><a href="Control-Lens-Lens.html#t:ALens-39-">ALens'</a></code> = <code><a href="Control-Lens-Type.html#t:Simple">Simple</a></code> <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>
</pre></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:AnIndexedLens" class="def">AnIndexedLens</a> i s t a b = <a href="Control-Lens-Type.html#t:Optical">Optical</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) (->) (<a href="Control-Lens-Internal-Context.html#t:Pretext">Pretext</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) a b) s t a b <a href="src/Control-Lens-Lens.html#AnIndexedLens" class="link">Source</a></p><div class="doc"><p>When you see this as an argument to a function, it expects an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code></p></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:AnIndexedLens-39-" class="def">AnIndexedLens'</a> i s a = <a href="Control-Lens-Lens.html#t:AnIndexedLens">AnIndexedLens</a> i s s a a <a href="src/Control-Lens-Lens.html#AnIndexedLens%27" class="link">Source</a></p><div class="doc"><pre>type <code><a href="Control-Lens-Lens.html#t:AnIndexedLens-39-">AnIndexedLens'</a></code> = <code><a href="Control-Lens-Type.html#t:Simple">Simple</a></code> (<code><a href="Control-Lens-Lens.html#t:AnIndexedLens">AnIndexedLens</a></code> i)
</pre></div></div><h1 id="g:3">Combinators</h1><div class="top"><p class="src"><a name="v:lens" class="def">lens</a> :: (s -> a) -> (s -> b -> t) -> <a href="Control-Lens-Lens.html#t:Lens">Lens</a> s t a b <a href="src/Control-Lens-Lens.html#lens" class="link">Source</a></p><div class="doc"><p>Build a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> from a getter and a setter.</p><pre><code><a href="Control-Lens-Lens.html#v:lens">lens</a></code> :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>s ^. lens getter setter
</code></strong>getter s
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>s & lens getter setter .~ b
</code></strong>setter s b
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>s & lens getter setter %~ f
</code></strong>setter s (f (getter s))
</pre><pre><code><a href="Control-Lens-Lens.html#v:lens">lens</a></code> :: (s -> a) -> (s -> a -> s) -> <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a
</pre></div></div><div class="top"><p class="src"><a name="v:ilens" class="def">ilens</a> :: (s -> (i, a)) -> (s -> b -> t) -> <a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a> i s t a b <a href="src/Control-Lens-Lens.html#ilens" class="link">Source</a></p><div class="doc"><p>Build an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> from a <code><a href="Control-Lens-Getter.html#v:Getter">Getter</a></code> and
a <code><a href="Control-Lens-Setter.html#v:Setter">Setter</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:iplens" class="def">iplens</a> :: (s -> a) -> (s -> b -> t) -> <a href="Control-Lens-Type.html#t:IndexPreservingLens">IndexPreservingLens</a> s t a b <a href="src/Control-Lens-Lens.html#iplens" class="link">Source</a></p><div class="doc"><p>Build an index-preserving <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> from a <code><a href="Control-Lens-Getter.html#v:Getter">Getter</a></code> and a
<code><a href="Control-Lens-Setter.html#v:Setter">Setter</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:-37--37--126-" class="def">(%%~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f s t a b -> (a -> f b) -> s -> f t <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%25%25~" class="link">Source</a></p><div class="doc"><p>(<code><a href="Control-Lens-Lens.html#v:-37--37--126-">%%~</a></code>) can be used in one of two scenarios:</p><p>When applied to a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code>, it can edit the target of the <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> in a
structure, extracting a functorial result.</p><p>When applied to a <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code>, it can edit the
targets of the traversals, extracting an applicative summary of its
actions.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>[66,97,116,109,97,110] & each %%~ \a -> ("na", chr a)
</code></strong>("nananananana","Batman")
</pre><p>For all that the definition of this combinator is just:</p><pre>(<code><a href="Control-Lens-Lens.html#v:-37--37--126-">%%~</a></code>) ≡ <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:id">id</a></code>
</pre><p>It may be beneficial to think about it as if it had these even more
restricted types, however:</p><pre>(<code><a href="Control-Lens-Lens.html#v:-37--37--126-">%%~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> f => <code><a href="Control-Lens-Iso.html#v:Iso">Iso</a></code> s t a b -> (a -> f b) -> s -> f t
(<code><a href="Control-Lens-Lens.html#v:-37--37--126-">%%~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> f => <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b -> (a -> f b) -> s -> f t
(<code><a href="Control-Lens-Lens.html#v:-37--37--126-">%%~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> f => <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> s t a b -> (a -> f b) -> s -> f t
</pre><p>When applied to a <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code>, it can edit the
targets of the traversals, extracting a supplemental monoidal summary
of its actions, by choosing <code>f = ((,) m)</code></p><pre>(<code><a href="Control-Lens-Lens.html#v:-37--37--126-">%%~</a></code>) :: <code><a href="Control-Lens-Iso.html#v:Iso">Iso</a></code> s t a b -> (a -> (r, b)) -> s -> (r, t)
(<code><a href="Control-Lens-Lens.html#v:-37--37--126-">%%~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b -> (a -> (r, b)) -> s -> (r, t)
(<code><a href="Control-Lens-Lens.html#v:-37--37--126-">%%~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> m => <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> s t a b -> (a -> (m, b)) -> s -> (m, t)
</pre></div></div><div class="top"><p class="src"><a name="v:-37--37--61-" class="def">(%%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:Over">Over</a> p (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s s a b -> p a (r, b) -> m r <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%25%25%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> in the current state returning some extra
information of type <code>r</code> or modify all targets of a
<code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> in the current state, extracting extra
information of type <code>r</code> and return a monoidal summary of the changes.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>runState (_1 %%= \x -> (f x, g x)) (a,b)
</code></strong>(f a,(g a,b))
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-37--37--61-">%%=</a></code>) ≡ (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#v:state">state</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:.">.</a></code>)
</pre><p>It may be useful to think of (<code><a href="Control-Lens-Lens.html#v:-37--37--61-">%%=</a></code>), instead, as having either of the
following more restricted type signatures:</p><pre>(<code><a href="Control-Lens-Lens.html#v:-37--37--61-">%%=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Iso.html#v:Iso">Iso</a></code> s s a b -> (a -> (r, b)) -> m r
(<code><a href="Control-Lens-Lens.html#v:-37--37--61-">%%=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s s a b -> (a -> (r, b)) -> m r
(<code><a href="Control-Lens-Lens.html#v:-37--37--61-">%%=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> r) => <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> s s a b -> (a -> (r, b)) -> m r
</pre></div></div><div class="top"><p class="src"><a name="v:-37--37--64--126-" class="def">(%%@~)</a> :: <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> i f s t a b -> (i -> a -> f b) -> s -> f t <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%25%25%40~" class="link">Source</a></p><div class="doc"><p>Adjust the target of an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> returning a supplementary result, or
adjust all of the targets of an <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> and return a monoidal summary
of the supplementary results and the answer.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-37--37--64--126-">%%@~</a></code>) ≡ <code><a href="Control-Lens-Indexed.html#v:withIndex">withIndex</a></code>
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-37--37--64--126-">%%@~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> f => <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> i s t a b -> (i -> a -> f b) -> s -> f t
(<code><a href="Control-Lens-Lens.html#v:-37--37--64--126-">%%@~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> f => <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> i s t a b -> (i -> a -> f b) -> s -> f t
</pre><p>In particular, it is often useful to think of this function as having one of these even more
restricted type signatures:</p><pre>(<code><a href="Control-Lens-Lens.html#v:-37--37--64--126-">%%@~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)
(<code><a href="Control-Lens-Lens.html#v:-37--37--64--126-">%%@~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> r => <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)
</pre></div></div><div class="top"><p class="src"><a name="v:-37--37--64--61-" class="def">(%%@=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> i (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s s a b -> (i -> a -> (r, b)) -> m r <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%25%25%40%3D" class="link">Source</a></p><div class="doc"><p>Adjust the target of an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> returning a supplementary result, or
adjust all of the targets of an <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> within the current state, and
return a monoidal summary of the supplementary results.</p><pre>l <code><a href="Control-Lens-Lens.html#v:-37--37--64--61-">%%@=</a></code> f ≡ <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#v:state">state</a></code> (l <code><a href="Control-Lens-Lens.html#v:-37--37--64--126-">%%@~</a></code> f)
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-37--37--64--61-">%%@=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> i s s a b -> (i -> a -> (r, b)) -> s -> m r
(<code><a href="Control-Lens-Lens.html#v:-37--37--64--61-">%%@=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> r) => <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> i s s a b -> (i -> a -> (r, b)) -> s -> m r
</pre></div></div><div class="top"><p class="src"><a name="v:-60--37--64--126-" class="def">(<%@~)</a> :: <a href="Control-Lens-Type.html#t:Over">Over</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> b) s t a b -> (i -> a -> b) -> s -> (b, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%25%40~" class="link">Source</a></p><div class="doc"><p>Adjust the target of an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> returning the intermediate result, or
adjust all of the targets of an <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> and return a monoidal summary
along with the answer.</p><pre>l <code><a href="Control-Lens-Lens.html#v:-60--37--126-"><%~</a></code> f ≡ l <code><a href="Control-Lens-Lens.html#v:-60--37--64--126-"><%@~</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:const">const</a></code> f
</pre><p>When you do not need access to the index then (<code><a href="Control-Lens-Lens.html#v:-60--37--126-"><%~</a></code>) is more liberal in what it can accept.</p><p>If you do not need the intermediate result, you can use (<code><a href="Control-Lens-Setter.html#v:-37--64--126-">%@~</a></code>) or even (<code><a href="Control-Lens-Setter.html#v:-37--126-">%~</a></code>).</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--37--64--126-"><%@~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> i s t a b -> (i -> a -> b) -> s -> (b, t)
(<code><a href="Control-Lens-Lens.html#v:-60--37--64--126-"><%@~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> b => <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> i s t a b -> (i -> a -> b) -> s -> (b, t)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--37--64--61-" class="def">(<%@=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> i (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> b) s s a b -> (i -> a -> b) -> m b <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%25%40%3D" class="link">Source</a></p><div class="doc"><p>Adjust the target of an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> returning the intermediate result, or
adjust all of the targets of an <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> within the current state, and
return a monoidal summary of the intermediate results.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--37--64--61-"><%@=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> i s s a b -> (i -> a -> b) -> m b
(<code><a href="Control-Lens-Lens.html#v:-60--37--64--61-"><%@=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> b) => <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> i s s a b -> (i -> a -> b) -> m b
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--37--64--126-" class="def">(<<%@~)</a> :: <a href="Control-Lens-Type.html#t:Over">Over</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a b -> (i -> a -> b) -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%25%40~" class="link">Source</a></p><div class="doc"><p>Adjust the target of an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> returning the old value, or
adjust all of the targets of an <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> and return a monoidal summary
of the old values along with the answer.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--37--64--126-"><<%@~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> i s t a b -> (i -> a -> b) -> s -> (a, t)
(<code><a href="Control-Lens-Lens.html#v:-60--60--37--64--126-"><<%@~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> a => <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> i s t a b -> (i -> a -> b) -> s -> (a, t)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--37--64--61-" class="def">(<<%@=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> i (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s s a b -> (i -> a -> b) -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%25%40%3D" class="link">Source</a></p><div class="doc"><p>Adjust the target of an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> returning the old value, or
adjust all of the targets of an <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> within the current state, and
return a monoidal summary of the old values.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--37--64--61-"><<%@=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> i s s a b -> (i -> a -> b) -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--37--64--61-"><<%@=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> b) => <code><a href="Control-Lens-Traversal.html#v:IndexedTraversal">IndexedTraversal</a></code> i s s a b -> (i -> a -> b) -> m a
</pre></div></div><h2 id="g:4">General Purpose Combinators</h2><div class="top"><p class="src"><a name="v:-38-" class="def">(&)</a> :: a -> (a -> b) -> b <span class="fixity">infixl 1</span><span class="rightedge"></span></p><div class="doc"><p><code><a href="Control-Lens-Lens.html#v:-38-">&</a></code> is a reverse application operator. This provides notational
convenience. Its precedence is one higher than that of the forward
application operator <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:-36-">$</a></code>, which allows <code><a href="Control-Lens-Lens.html#v:-38-">&</a></code> to be nested in <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:-36-">$</a></code>.</p><p><em>Since: 4.8.0.0</em></p></div></div><div class="top"><p class="src"><a name="v:-60--38--62-" class="def">(<&>)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => f a -> (a -> b) -> f b <span class="fixity">infixl 1</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%26%3E" class="link">Source</a></p><div class="doc"><p>Infix flipped <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:fmap">fmap</a></code>.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--38--62-"><&></a></code>) = <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:flip">flip</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:fmap">fmap</a></code>
</pre></div></div><div class="top"><p class="src"><a name="v:-63--63-" class="def">(??)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => f (a -> b) -> a -> f b <span class="fixity">infixl 1</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3F%3F" class="link">Source</a></p><div class="doc"><p>This is convenient to <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:flip">flip</a></code> argument order of composite functions defined as:</p><pre>fab ?? a = fmap ($ a) fab
</pre><p>For the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> instance <code>f = ((->) r)</code> you can reason about this function as if the definition was <code>(<code><a href="Control-Lens-Lens.html#v:-63--63-">??</a></code>) ≡ <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:flip">flip</a></code></code>:</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(h ?? x) a
</code></strong>h a x
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>execState ?? [] $ modify (1:)
</code></strong>[1]
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>over _2 ?? ("hello","world") $ length
</code></strong>("hello",5)
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>over ?? length ?? ("hello","world") $ _2
</code></strong>("hello",5)
</pre></div></div><div class="top"><p class="src"><a name="v:-38--126-" class="def">(&~)</a> :: s -> <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Lazy.html#t:State">State</a> s a -> s <span class="fixity">infixl 1</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%26~" class="link">Source</a></p><div class="doc"><p>This can be used to chain lens operations using <code>op=</code> syntax
rather than <code>op~</code> syntax for simple non-type-changing cases.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(10,20) & _1 .~ 30 & _2 .~ 40
</code></strong>(30,40)
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(10,20) &~ do _1 .= 30; _2 .= 40
</code></strong>(30,40)
</pre><p>This does not support type-changing assignment, <em>e.g.</em></p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(10,20) & _1 .~ "hello"
</code></strong>("hello",20)
</pre></div></div><h1 id="g:5">Lateral Composition</h1><div class="top"><p class="src"><a name="v:choosing" class="def">choosing</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f s t a b -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f s' t' a b -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a> s s') (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a> t t') a b <a href="src/Control-Lens-Lens.html#choosing" class="link">Source</a></p><div class="doc"><p>Merge two lenses, getters, setters, folds or traversals.</p><pre><code><a href="Control-Lens-Lens.html#v:chosen">chosen</a></code> ≡ <code><a href="Control-Lens-Lens.html#v:choosing">choosing</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:id">id</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:id">id</a></code>
</pre><pre><code><a href="Control-Lens-Lens.html#v:choosing">choosing</a></code> :: <code><a href="Control-Lens-Getter.html#v:Getter">Getter</a></code> s a -> <code><a href="Control-Lens-Getter.html#v:Getter">Getter</a></code> s' a -> <code><a href="Control-Lens-Getter.html#v:Getter">Getter</a></code> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a></code> s s') a
<code><a href="Control-Lens-Lens.html#v:choosing">choosing</a></code> :: <code><a href="Control-Lens-Fold.html#v:Fold">Fold</a></code> s a -> <code><a href="Control-Lens-Fold.html#v:Fold">Fold</a></code> s' a -> <code><a href="Control-Lens-Fold.html#v:Fold">Fold</a></code> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a></code> s s') a
<code><a href="Control-Lens-Lens.html#v:choosing">choosing</a></code> :: <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s' a -> <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a></code> s s') a
<code><a href="Control-Lens-Lens.html#v:choosing">choosing</a></code> :: <code><a href="Control-Lens-Traversal.html#v:Traversal-39-">Traversal'</a></code> s a -> <code><a href="Control-Lens-Traversal.html#v:Traversal-39-">Traversal'</a></code> s' a -> <code><a href="Control-Lens-Traversal.html#v:Traversal-39-">Traversal'</a></code> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a></code> s s') a
<code><a href="Control-Lens-Lens.html#v:choosing">choosing</a></code> :: <code><a href="Control-Lens-Setter.html#v:Setter-39-">Setter'</a></code> s a -> <code><a href="Control-Lens-Setter.html#v:Setter-39-">Setter'</a></code> s' a -> <code><a href="Control-Lens-Setter.html#v:Setter-39-">Setter'</a></code> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a></code> s s') a
</pre></div></div><div class="top"><p class="src"><a name="v:chosen" class="def">chosen</a> :: <a href="Control-Lens-Type.html#t:IndexPreservingLens">IndexPreservingLens</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a> a a) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a> b b) a b <a href="src/Control-Lens-Lens.html#chosen" class="link">Source</a></p><div class="doc"><p>This is a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> that updates either side of an <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a></code>, where both sides have the same type.</p><pre><code><a href="Control-Lens-Lens.html#v:chosen">chosen</a></code> ≡ <code><a href="Control-Lens-Lens.html#v:choosing">choosing</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:id">id</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Function.html#v:id">id</a></code>
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>Left a^.chosen
</code></strong>a
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>Right a^.chosen
</code></strong>a
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>Right "hello"^.chosen
</code></strong>"hello"
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>Right a & chosen *~ b
</code></strong>Right (a * b)
</pre><pre><code><a href="Control-Lens-Lens.html#v:chosen">chosen</a></code> :: <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a></code> a a) (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#t:Either">Either</a></code> b b) a b
<code><a href="Control-Lens-Lens.html#v:chosen">chosen</a></code> f (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#v:Left">Left</a></code> a) = <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#v:Left">Left</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:-60--36--62-"><$></a></code> f a
<code><a href="Control-Lens-Lens.html#v:chosen">chosen</a></code> f (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#v:Right">Right</a></code> a) = <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Either.html#v:Right">Right</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:-60--36--62-"><$></a></code> f a
</pre></div></div><div class="top"><p class="src"><a name="v:alongside" class="def">alongside</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="Control-Lens-Internal-Getter.html#t:AlongsideLeft">AlongsideLeft</a> f b') s t a b -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="Control-Lens-Internal-Getter.html#t:AlongsideRight">AlongsideRight</a> f t) s' t' a' b' -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f (s, s') (t, t') (a, a') (b, b') <a href="src/Control-Lens-Lens.html#alongside" class="link">Source</a></p><div class="doc"><p><code><a href="Control-Lens-Lens.html#v:alongside">alongside</a></code> makes a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> from two other lenses or a <code><a href="Control-Lens-Type.html#t:Getter">Getter</a></code> from two other getters
by executing them on their respective halves of a product.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(Left a, Right b)^.alongside chosen chosen
</code></strong>(a,b)
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(Left a, Right b) & alongside chosen chosen .~ (c,d)
</code></strong>(Left c,Right d)
</pre><pre><code><a href="Control-Lens-Lens.html#v:alongside">alongside</a></code> :: <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b -> <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s' t' a' b' -> <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> (s,s') (t,t') (a,a') (b,b')
<code><a href="Control-Lens-Lens.html#v:alongside">alongside</a></code> :: <code><a href="Control-Lens-Type.html#t:Getter">Getter</a></code> s t a b -> <code><a href="Control-Lens-Type.html#t:Getter">Getter</a></code> s' t' a' b' -> <code><a href="Control-Lens-Type.html#t:Getter">Getter</a></code> (s,s') (t,t') (a,a') (b,b')
</pre></div></div><div class="top"><p class="src"><a name="v:inside" class="def">inside</a> :: <a href="file:///usr/share/doc/libghc-profunctors-doc/html/Data-Profunctor-Rep.html#t:Corepresentable">Corepresentable</a> p => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> <a href="Control-Lens-Lens.html#t:Lens">Lens</a> (p e s) (p e t) (p e a) (p e b) <a href="src/Control-Lens-Lens.html#inside" class="link">Source</a></p><div class="doc"><p>Lift a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> so it can run under a function (or other corepresentable profunctor).</p><pre><code><a href="Control-Lens-Lens.html#v:inside">inside</a></code> :: <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b -> <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> (e -> s) (e -> t) (e -> a) (e -> b)
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(\x -> (x-1,x+1)) ^. inside _1 $ 5
</code></strong>4
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>runState (modify (1:) >> modify (2:)) ^. (inside _2) $ []
</code></strong>[2,1]
</pre></div></div><h1 id="g:6">Setting Functionally with Passthrough</h1><div class="top"><p class="src"><a name="v:-60--37--126-" class="def">(<%~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> b) s t a b -> (a -> b) -> s -> (b, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%25~" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the result.</p><p>When you do not need the result of the addition, (<code><a href="Control-Lens-Setter.html#v:-37--126-">%~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--37--126-"><%~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b -> (a -> b) -> s -> (b, t)
(<code><a href="Control-Lens-Lens.html#v:-60--37--126-"><%~</a></code>) :: <code><a href="Control-Lens-Iso.html#v:Iso">Iso</a></code> s t a b -> (a -> b) -> s -> (b, t)
(<code><a href="Control-Lens-Lens.html#v:-60--37--126-"><%~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> b => <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> s t a b -> (a -> b) -> s -> (b, t)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--43--126-" class="def">(<+~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%2B~" class="link">Source</a></p><div class="doc"><p>Increment the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the result.</p><p>When you do not need the result of the addition, (<code><a href="Control-Lens-Setter.html#v:-43--126-">+~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--43--126-"><+~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--43--126-"><+~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--45--126-" class="def">(<-~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C-~" class="link">Source</a></p><div class="doc"><p>Decrement the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the result.</p><p>When you do not need the result of the subtraction, (<code><a href="Control-Lens-Setter.html#v:-45--126-">-~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--45--126-"><-~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--45--126-"><-~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--42--126-" class="def">(<*~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%2A~" class="link">Source</a></p><div class="doc"><p>Multiply the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the result.</p><p>When you do not need the result of the multiplication, (<code><a href="Control-Lens-Setter.html#v:-42--126-">*~</a></code>) is more
flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--42--126-"><*~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--42--126-"><*~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--47--47--126-" class="def">(<//~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%2F%2F~" class="link">Source</a></p><div class="doc"><p>Divide the target of a fractionally valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the result.</p><p>When you do not need the result of the division, (<code><a href="Control-Lens-Setter.html#v:-47--47--126-">//~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--47--47--126-"><//~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--47--47--126-"><//~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--94--126-" class="def">(<^~)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> e -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%5E~" class="link">Source</a></p><div class="doc"><p>Raise the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> to a non-negative
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> power and return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-94--126-">^~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--94--126-"><^~</a></code>) :: (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> e -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--94--126-"><^~</a></code>) :: (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> e -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--94--94--126-" class="def">(<^^~)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> e -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%5E%5E~" class="link">Source</a></p><div class="doc"><p>Raise the target of a fractionally valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> to an <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> power
and return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-94--94--126-">^^~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--94--94--126-"><^^~</a></code>) :: (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> e -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--94--94--126-"><^^~</a></code>) :: (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> e -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--42--42--126-" class="def">(<**~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a a -> a -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%2A%2A~" class="link">Source</a></p><div class="doc"><p>Raise the target of a floating-point valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> to an arbitrary power
and return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-42--42--126-">**~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--42--42--126-"><**~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a></code> a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--42--42--126-"><**~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a></code> a => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--124--124--126-" class="def">(<||~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s t <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> s -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%7C%7C~" class="link">Source</a></p><div class="doc"><p>Logically <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#v:-124--124-">||</a></code> a Boolean valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-124--124--126-">||~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--124--124--126-"><||~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> s -> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>, s)
(<code><a href="Control-Lens-Lens.html#v:-60--124--124--126-"><||~</a></code>) :: <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> s -> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--38--38--126-" class="def">(<&&~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s t <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> s -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%26%26~" class="link">Source</a></p><div class="doc"><p>Logically <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#v:-38--38-">&&</a></code> a Boolean valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-38--38--126-">&&~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--38--38--126-"><&&~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> s -> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>, s)
(<code><a href="Control-Lens-Lens.html#v:-60--38--38--126-"><&&~</a></code>) :: <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> s -> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--62--126-" class="def">(<<>~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> m => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> m) s t m m -> m -> s -> (m, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%3E~" class="link">Source</a></p><div class="doc"><p><code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#v:mappend">mappend</a></code> a monoidal value onto the end of the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and
return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-60--62--126-"><>~</a></code>) is more flexible.</p></div></div><div class="top"><p class="src"><a name="v:-60--60--37--126-" class="def">(<<%~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a b -> (a -> b) -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%25~" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code>, but return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-37--126-">%~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--37--126-"><<%~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b -> (a -> b) -> s -> (a, t)
(<code><a href="Control-Lens-Lens.html#v:-60--60--37--126-"><<%~</a></code>) :: <code><a href="Control-Lens-Iso.html#v:Iso">Iso</a></code> s t a b -> (a -> b) -> s -> (a, t)
(<code><a href="Control-Lens-Lens.html#v:-60--60--37--126-"><<%~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> a => <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> s t a b -> (a -> b) -> s -> (a, t)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60-.-126-" class="def">(<<.~)</a> :: <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s t a b -> b -> s -> (a, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C.~" class="link">Source</a></p><div class="doc"><p>Replace the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code>, but return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:.-126-">.~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60-.-126-"><<.~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b -> b -> s -> (a, t)
(<code><a href="Control-Lens-Lens.html#v:-60--60-.-126-"><<.~</a></code>) :: <code><a href="Control-Lens-Iso.html#v:Iso">Iso</a></code> s t a b -> b -> s -> (a, t)
(<code><a href="Control-Lens-Lens.html#v:-60--60-.-126-"><<.~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> a => <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> s t a b -> b -> s -> (a, t)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--43--126-" class="def">(<<+~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%2B~" class="link">Source</a></p><div class="doc"><p>Increment the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-43--126-">+~</a></code>) is more flexible.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(a,b) & _1 <<+~ c
</code></strong>(a,(a + c,b))
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(a,b) & _2 <<+~ c
</code></strong>(b,(a,b + c))
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--43--126-"><<+~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--43--126-"><<+~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--45--126-" class="def">(<<-~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C-~" class="link">Source</a></p><div class="doc"><p>Decrement the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-45--126-">-~</a></code>) is more flexible.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(a,b) & _1 <<-~ c
</code></strong>(a,(a - c,b))
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(a,b) & _2 <<-~ c
</code></strong>(b,(a,b - c))
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--45--126-"><<-~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--45--126-"><<-~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--42--126-" class="def">(<<*~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%2A~" class="link">Source</a></p><div class="doc"><p>Multiply the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-45--126-">-~</a></code>) is more flexible.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(a,b) & _1 <<*~ c
</code></strong>(a,(a * c,b))
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(a,b) & _2 <<*~ c
</code></strong>(b,(a,b * c))
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--42--126-"><<*~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--42--126-"><<*~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--47--47--126-" class="def">(<<//~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%2F%2F~" class="link">Source</a></p><div class="doc"><p>Divide the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-47--47--126-">//~</a></code>) is more flexible.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(a,b) & _1 <<//~ c
</code></strong>(a,(a / c,b))
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>("Hawaii",10) & _2 <<//~ 2
</code></strong>(10.0,("Hawaii",5.0))
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--47--47--126-"><<//~</a></code>) :: Fractional a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--47--47--126-"><<//~</a></code>) :: Fractional a => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--94--126-" class="def">(<<^~)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> s -> (a, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%5E~" class="link">Source</a></p><div class="doc"><p>Raise the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> to a non-negative power and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-94--126-">^~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--94--126-"><<^~</a></code>) :: (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> e -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--94--126-"><<^~</a></code>) :: (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> e -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--94--94--126-" class="def">(<<^^~)</a> :: (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> s -> (a, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%5E%5E~" class="link">Source</a></p><div class="doc"><p>Raise the target of a fractionally valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> to an integral power and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-94--94--126-">^^~</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--94--94--126-"><<^^~</a></code>) :: (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> e -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--94--94--126-"><<^^~</a></code>) :: (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> e -> S -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--42--42--126-" class="def">(<<**~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> s -> (a, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%2A%2A~" class="link">Source</a></p><div class="doc"><p>Raise the target of a floating-point valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> to an arbitrary power and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-42--42--126-">**~</a></code>) is more flexible.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(a,b) & _1 <<**~ c
</code></strong>(a,(a**c,b))
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(a,b) & _2 <<**~ c
</code></strong>(b,(a,b**c))
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--42--42--126-"><<**~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a></code> a => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> s -> (a, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--42--42--126-"><<**~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a></code> a => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> s -> (a, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--124--124--126-" class="def">(<<||~)</a> :: <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> s -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%7C%7C~" class="link">Source</a></p><div class="doc"><p>Logically <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#v:-124--124-">||</a></code> the target of a <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>-valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-124--124--126-">||~</a></code>) is more flexible.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(False,6) & _1 <<||~ True
</code></strong>(False,(True,6))
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>("hello",True) & _2 <<||~ False
</code></strong>(True,("hello",True))
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--124--124--126-"><<||~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> s -> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--124--124--126-"><<||~</a></code>) :: <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> s -> (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--38--38--126-" class="def">(<<&&~)</a> :: <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> s -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%26%26~" class="link">Source</a></p><div class="doc"><p>Logically <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#v:-38--38-">&&</a></code> the target of a <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>-valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-38--38--126-">&&~</a></code>) is more flexible.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(False,6) & _1 <<&&~ True
</code></strong>(False,(False,6))
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>("hello",True) & _2 <<&&~ False
</code></strong>(True,("hello",False))
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--38--38--126-"><<&&~</a></code>) :: <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s Bool -> Bool -> s -> (Bool, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--38--38--126-"><<&&~</a></code>) :: <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s Bool -> Bool -> s -> (Bool, s)
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--60--62--126-" class="def">(<<<>~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> r => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s r -> r -> s -> (r, s) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%3C%3E~" class="link">Source</a></p><div class="doc"><p>Modify the target of a monoidally valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> by <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#v:mappend">mappend</a></code>ing a new value and return the old value.</p><p>When you do not need the old value, (<code><a href="Control-Lens-Setter.html#v:-60--62--126-"><>~</a></code>) is more flexible.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>(Sum a,b) & _1 <<<>~ Sum c
</code></strong>(Sum {getSum = a},(Sum {getSum = a + c},b))
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>_2 <<<>~ ", 007" $ ("James", "Bond")
</code></strong>("Bond",("James","Bond, 007"))
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--60--62--126-"><<<>~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> r => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s r -> r -> s -> (r, s)
(<code><a href="Control-Lens-Lens.html#v:-60--60--60--62--126-"><<<>~</a></code>) :: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> r => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s r -> r -> s -> (r, s)
</pre></div></div><h1 id="g:7">Setting State with Passthrough</h1><div class="top"><p class="src"><a name="v:-60--37--61-" class="def">(<%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> b) s s a b -> (a -> b) -> m b <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%25%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by a user supplied
function and return the result.</p><p>When applied to a <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code>, it this will return a monoidal summary of all of the intermediate
results.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-37--61-">%=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--37--61-"><%=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> (a -> a) -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--37--61-"><%=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> (a -> a) -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--37--61-"><%=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> a) => <code><a href="Control-Lens-Traversal.html#v:Traversal-39-">Traversal'</a></code> s a -> (a -> a) -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--43--61-" class="def">(<+=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%2B%3D" class="link">Source</a></p><div class="doc"><p>Add to the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state
and return the result.</p><p>When you do not need the result of the addition, (<code><a href="Control-Lens-Setter.html#v:-43--61-">+=</a></code>) is more
flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--43--61-"><+=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--43--61-"><+=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--45--61-" class="def">(<-=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C-%3D" class="link">Source</a></p><div class="doc"><p>Subtract from the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s
state and return the result.</p><p>When you do not need the result of the subtraction, (<code><a href="Control-Lens-Setter.html#v:-45--61-">-=</a></code>) is more
flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--45--61-"><-=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--45--61-"><-=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--42--61-" class="def">(<*=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%2A%3D" class="link">Source</a></p><div class="doc"><p>Multiply the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s
state and return the result.</p><p>When you do not need the result of the multiplication, (<code><a href="Control-Lens-Setter.html#v:-42--61-">*=</a></code>) is more
flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--42--61-"><*=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--42--61-"><*=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--47--47--61-" class="def">(<//=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%2F%2F%3D" class="link">Source</a></p><div class="doc"><p>Divide the target of a fractionally valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state
and return the result.</p><p>When you do not need the result of the division, (<code><a href="Control-Lens-Setter.html#v:-47--47--61-">//=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--47--47--61-"><//=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--47--47--61-"><//=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a) => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--94--61-" class="def">(<^=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%5E%3D" class="link">Source</a></p><div class="doc"><p>Raise the target of a numerically valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state
to a non-negative <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> power and return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-94--61-">^=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--94--61-"><^=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> e -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--94--61-"><^=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> e -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--94--94--61-" class="def">(<^^=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%5E%5E%3D" class="link">Source</a></p><div class="doc"><p>Raise the target of a fractionally valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state
to an <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> power and return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-94--94--61-">^^=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--94--94--61-"><^^=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> b, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> e -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--94--94--61-"><^^=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> b, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> e -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--42--42--61-" class="def">(<**=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%2A%2A%3D" class="link">Source</a></p><div class="doc"><p>Raise the target of a floating-point valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s
state to an arbitrary power and return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-42--42--61-">**=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--42--42--61-"><**=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--42--42--61-"><**=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a></code> a) => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--124--124--61-" class="def">(<||=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> m <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%7C%7C%3D" class="link">Source</a></p><div class="doc"><p>Logically <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#v:-124--124-">||</a></code> a Boolean valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state and return
the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-124--124--61-">||=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--124--124--61-"><||=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> m <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>
(<code><a href="Control-Lens-Lens.html#v:-60--124--124--61-"><||=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> m <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>
</pre></div></div><div class="top"><p class="src"><a name="v:-60--38--38--61-" class="def">(<&&=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> m <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%26%26%3D" class="link">Source</a></p><div class="doc"><p>Logically <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#v:-38--38-">&&</a></code> a Boolean valued <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state and return
the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-38--38--61-">&&=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--38--38--61-"><&&=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> m <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>
(<code><a href="Control-Lens-Lens.html#v:-60--38--38--61-"><&&=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> m <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--62--61-" class="def">(<<>=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> r) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s r -> r -> m r <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%3E%3D" class="link">Source</a></p><div class="doc"><p><code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#v:mappend">mappend</a></code> a monoidal value onto the end of the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into
your <code>Monad'</code>s state and return the result.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-60--62--61-"><>=</a></code>) is more flexible.</p></div></div><div class="top"><p class="src"><a name="v:-60--60--37--61-" class="def">(<<%=)</a> :: (<a href="file:///usr/share/doc/libghc-profunctors-doc/html/Data-Profunctor.html#t:Strong">Strong</a> p, <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m) => <a href="Control-Lens-Type.html#t:Over">Over</a> p (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s s a b -> p a b -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%25%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by a user supplied
function and return the <em>old</em> value that was replaced.</p><p>When applied to a <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code>, it this will return a monoidal summary of all of the old values
present.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-37--61-">%=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--37--61-"><<%=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> (a -> a) -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--37--61-"><<%=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> (a -> a) -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--37--61-"><<%=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> a) => <code><a href="Control-Lens-Traversal.html#v:Traversal-39-">Traversal'</a></code> s a -> (a -> a) -> m a
</pre><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--37--61-"><<%=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Type.html#t:LensLike">LensLike</a></code> ((,)a) s s a b -> (a -> b) -> m a</pre></div></div><div class="top"><p class="src"><a name="v:-60--60-.-61-" class="def">(<<.=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s s a b -> b -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C.%3D" class="link">Source</a></p><div class="doc"><p>Replace the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state with a user supplied
value and return the <em>old</em> value that was replaced.</p><p>When applied to a <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code>, it this will return a monoidal summary of all of the old values
present.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:.-61-">.=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60-.-61-"><<.=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60-.-61-"><<.=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Iso.html#v:Iso-39-">Iso'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60-.-61-"><<.=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> t) => <code><a href="Control-Lens-Traversal.html#v:Traversal-39-">Traversal'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--43--61-" class="def">(<<+=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%2B%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by adding a value
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-43--61-">+=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--43--61-"><<+=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--43--61-"><<+=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--45--61-" class="def">(<<-=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C-%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by subtracting a value
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-45--61-">-=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--45--61-"><<-=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--45--61-"><<-=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--42--61-" class="def">(<<*=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%2A%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by multipling a value
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-42--61-">*=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--42--61-"><<*=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--42--61-"><<*=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--47--47--61-" class="def">(<<//=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%2F%2F%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Monad.html#t:Monad">Monad</a></code>s state by dividing by a value
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-47--47--61-">//=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--47--47--61-"><<//=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--47--47--61-"><<//=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--94--61-" class="def">(<<^=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%5E%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by raising it by a non-negative power
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-94--61-">^=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--94--61-"><<^=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> e -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--94--61-"><<^=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--94--94--61-" class="def">(<<^^=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a> e) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> e -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%5E%5E%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by raising it by an integral power
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-94--94--61-">^^=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--94--94--61-"><<^^=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> e -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--94--94--61-"><<^^=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> a, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Integral">Integral</a></code> e) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> e -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--42--42--61-" class="def">(<<**=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a> a) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> a) s a -> a -> m a <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%2A%2A%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by raising it by an arbitrary power
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-42--42--61-">**=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--42--42--61-"><<**=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a></code> a) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s a -> a -> m a
(<code><a href="Control-Lens-Lens.html#v:-60--60--42--42--61-"><<**=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Floating">Floating</a></code> a) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s a -> a -> m a
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--124--124--61-" class="def">(<<||=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> m <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%7C%7C%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by taking its logical <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#v:-124--124-">||</a></code> with a value
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-124--124--61-">||=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--124--124--61-"><<||=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> m <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>
(<code><a href="Control-Lens-Lens.html#v:-60--60--124--124--61-"><<||=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> m <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--38--38--61-" class="def">(<<&&=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a>) s <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> -> m <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%26%26%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by taking its logical <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#v:-38--38-">&&</a></code> with a value
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-38--38--61-">&&=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--38--38--61-"><<&&=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> m <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>
(<code><a href="Control-Lens-Lens.html#v:-60--60--38--38--61-"><<&&=</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code> -> m <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></code>
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--60--62--61-" class="def">(<<<>=)</a> :: (<a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> r) => <a href="Control-Lens-Type.html#t:LensLike-39-">LensLike'</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/ghc-prim-0.4.0.0/GHC-Tuple.html#t:-40--44--41-">(,)</a> r) s r -> r -> m r <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C%3C%3E%3D" class="link">Source</a></p><div class="doc"><p>Modify the target of a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> into your <code>Monad'</code>s state by <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#v:mappend">mappend</a></code>ing a value
and return the <em>old</em> value that was replaced.</p><p>When you do not need the result of the operation, (<code><a href="Control-Lens-Setter.html#v:-60--62--61-"><>=</a></code>) is more flexible.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--60--62--61-"><<<>=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> r) => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> s r -> r -> m r
(<code><a href="Control-Lens-Lens.html#v:-60--60--60--62--61-"><<<>=</a></code>) :: (<code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m, <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> r) => <code><a href="Control-Lens-Type.html#t:Iso-39-">Iso'</a></code> s r -> r -> m r
</pre></div></div><div class="top"><p class="src"><a name="v:-60--60--126-" class="def">(<<~)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> m b -> m b <span class="fixity">infixr 2</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%3C~" class="link">Source</a></p><div class="doc"><p>Run a monadic action, and set the target of <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> to its result.</p><pre>(<code><a href="Control-Lens-Lens.html#v:-60--60--126-"><<~</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Iso.html#v:Iso">Iso</a></code> s s a b -> m b -> m b
(<code><a href="Control-Lens-Lens.html#v:-60--60--126-"><<~</a></code>) :: <code><a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a></code> s m => <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s s a b -> m b -> m b
</pre><p>NB: This is limited to taking an actual <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> than admitting a <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> because
there are potential loss of state issues otherwise.</p></div></div><h1 id="g:8">Cloning Lenses</h1><div class="top"><p class="src"><a name="v:cloneLens" class="def">cloneLens</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> <a href="Control-Lens-Lens.html#t:Lens">Lens</a> s t a b <a href="src/Control-Lens-Lens.html#cloneLens" class="link">Source</a></p><div class="doc"><p>Cloning a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> is one way to make sure you aren't given
something weaker, such as a <code><a href="Control-Lens-Traversal.html#v:Traversal">Traversal</a></code> and can be
used as a way to pass around lenses that have to be monomorphic in <code>f</code>.</p><p>Note: This only accepts a proper <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>let example l x = set (cloneLens l) (x^.cloneLens l + 1) x in example _2 ("hello",1,"you")
</code></strong>("hello",2,"you")
</pre></div></div><div class="top"><p class="src"><a name="v:cloneIndexPreservingLens" class="def">cloneIndexPreservingLens</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> <a href="Control-Lens-Type.html#t:IndexPreservingLens">IndexPreservingLens</a> s t a b <a href="src/Control-Lens-Lens.html#cloneIndexPreservingLens" class="link">Source</a></p><div class="doc"><p>Clone a <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> as an <code>IndexedPreservingLens</code> that just passes through whatever
index is on any <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code>, <code><a href="Control-Lens-Type.html#t:IndexedFold">IndexedFold</a></code>, <code><a href="Control-Lens-Type.html#t:IndexedGetter">IndexedGetter</a></code> or <code><a href="Control-Lens-Type.html#t:IndexedTraversal">IndexedTraversal</a></code> it is composed with.</p></div></div><div class="top"><p class="src"><a name="v:cloneIndexedLens" class="def">cloneIndexedLens</a> :: <a href="Control-Lens-Lens.html#t:AnIndexedLens">AnIndexedLens</a> i s t a b -> <a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a> i s t a b <a href="src/Control-Lens-Lens.html#cloneIndexedLens" class="link">Source</a></p><div class="doc"><p>Clone an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> as an <code><a href="Control-Lens-Lens.html#t:IndexedLens">IndexedLens</a></code> with the same index.</p></div></div><h1 id="g:9">Arrow operators</h1><div class="top"><p class="src"><a name="v:overA" class="def">overA</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Arrow.html#t:Arrow">Arrow</a> ar => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="Control-Lens-Lens.html#t:Context">Context</a> a b) s t a b -> ar a b -> ar s t <a href="src/Control-Lens-Lens.html#overA" class="link">Source</a></p><div class="doc"><p><code><a href="Control-Lens-Setter.html#v:over">over</a></code> for Arrows.</p><p>Unlike <code><a href="Control-Lens-Setter.html#v:over">over</a></code>, <code><a href="Control-Lens-Lens.html#v:overA">overA</a></code> can't accept a simple
<code><a href="Control-Lens-Setter.html#v:Setter">Setter</a></code>, but requires a full lens, or close
enough.</p><pre>overA :: Arrow ar => Lens s t a b -> ar a b -> ar s t
</pre></div></div><h1 id="g:10">ALens Combinators</h1><div class="top"><p class="src"><a name="v:storing" class="def">storing</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> b -> s -> t <a href="src/Control-Lens-Lens.html#storing" class="link">Source</a></p><div class="doc"><p>A version of <code><a href="Control-Lens-Setter.html#v:set">set</a></code> that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>storing _2 "world" ("hello","there")
</code></strong>("hello","world")
</pre></div></div><div class="top"><p class="src"><a name="v:-94--35-" class="def">(^#)</a> :: s -> <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> a <span class="fixity">infixl 8</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%5E%23" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Getter.html#v:-94-.">^.</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>("hello","world")^#_2
</code></strong>"world"
</pre></div></div><div class="top"><p class="src"><a name="v:-35--126-" class="def">(#~)</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> b -> s -> t <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%23~" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Setter.html#v:.-126-">.~</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>("hello","there") & _2 #~ "world"
</code></strong>("hello","world")
</pre></div></div><div class="top"><p class="src"><a name="v:-35--37--126-" class="def">(#%~)</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> (a -> b) -> s -> t <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%23%25~" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Setter.html#v:-37--126-">%~</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>("hello","world") & _2 #%~ length
</code></strong>("hello",5)
</pre></div></div><div class="top"><p class="src"><a name="v:-35--37--37--126-" class="def">(#%%~)</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> (a -> f b) -> s -> f t <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%23%25%25~" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Lens.html#v:-37--37--126-">%%~</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
</code></strong>(5,("hello","world!"))
</pre></div></div><div class="top"><p class="src"><a name="v:-60--35--126-" class="def">(<#~)</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> b -> s -> (b, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%23~" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Setter.html#v:-60-.-126-"><.~</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>("hello","there") & _2 <#~ "world"
</code></strong>("world",("hello","world"))
</pre></div></div><div class="top"><p class="src"><a name="v:-60--35--37--126-" class="def">(<#%~)</a> :: <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s t a b -> (a -> b) -> s -> (b, t) <span class="fixity">infixr 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%23%25~" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Lens.html#v:-60--37--126-"><%~</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>("hello","world") & _2 <#%~ length
</code></strong>(5,("hello",5))
</pre></div></div><div class="top"><p class="src"><a name="v:-35--61-" class="def">(#=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> b -> m () <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%23%3D" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Setter.html#v:.-61-">.=</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:-35--37--61-" class="def">(#%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> (a -> b) -> m () <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%23%25%3D" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Setter.html#v:-37--61-">%=</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:-35--37--37--61-" class="def">(#%%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> (a -> (r, b)) -> m r <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%23%25%25%3D" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Lens.html#v:-37--37--61-">%%=</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:-60--35--61-" class="def">(<#=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> b -> m b <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%23%3D" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Setter.html#v:-60-.-61-"><.=</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:-60--35--37--61-" class="def">(<#%=)</a> :: <a href="file:///usr/share/doc/libghc-mtl-doc/html/Control-Monad-State-Class.html#t:MonadState">MonadState</a> s m => <a href="Control-Lens-Lens.html#t:ALens">ALens</a> s s a b -> (a -> b) -> m b <span class="fixity">infix 4</span><span class="rightedge"></span> <a href="src/Control-Lens-Lens.html#%3C%23%25%3D" class="link">Source</a></p><div class="doc"><p>A version of (<code><a href="Control-Lens-Lens.html#v:-60--37--61-"><%=</a></code>) that works on <code><a href="Control-Lens-Lens.html#t:ALens">ALens</a></code>.</p></div></div><h1 id="g:11">Common Lenses</h1><div class="top"><p class="src"><a name="v:devoid" class="def">devoid</a> :: <a href="Control-Lens-Type.html#t:Over">Over</a> p f <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Void.html#t:Void">Void</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Void.html#t:Void">Void</a> a b <a href="src/Control-Lens-Lens.html#devoid" class="link">Source</a></p><div class="doc"><p>There is a field for every type in the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Void.html#t:Void">Void</a></code>. Very zen.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>[] & mapped.devoid +~ 1
</code></strong>[]
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>Nothing & mapped.devoid %~ abs
</code></strong>Nothing
</pre><pre><code><a href="Control-Lens-Lens.html#v:devoid">devoid</a></code> :: <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Void.html#t:Void">Void</a></code> a
</pre></div></div><div class="top"><p class="src"><a name="v:united" class="def">united</a> :: <a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a> a () <a href="src/Control-Lens-Lens.html#united" class="link">Source</a></p><div class="doc"><p>We can always retrieve a <code>()</code> from any type.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>"hello"^.united
</code></strong>()
</pre><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>"hello" & united .~ ()
</code></strong>"hello"
</pre></div></div><h1 id="g:12">Context</h1><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Context" class="def">Context</a> a b t <a href="src/Control-Lens-Internal-Context.html#Context" class="link">Source</a></p><div class="doc"><p>The indexed store can be used to characterize a <code><a href="Control-Lens-Lens.html#v:Lens">Lens</a></code>
and is used by <code><a href="Control-Lens-Lens.html#v:clone">clone</a></code>.</p><p><code><code><a href="Control-Lens-Lens.html#t:Context">Context</a></code> a b t</code> is isomorphic to
<code>newtype <code><a href="Control-Lens-Lens.html#t:Context">Context</a></code> a b t = <code><a href="Control-Lens-Lens.html#t:Context">Context</a></code> { runContext :: forall f. <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> f => (a -> f b) -> f t }</code>,
and to <code>exists s. (s, <code><a href="Control-Lens-Lens.html#v:Lens">Lens</a></code> s t a b)</code>.</p><p>A <code><a href="Control-Lens-Lens.html#t:Context">Context</a></code> is like a <code><a href="Control-Lens-Lens.html#v:Lens">Lens</a></code> that has already been applied to a some structure.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:Context" class="def">Context</a> (b -> t) a</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Context" class="caption collapser" onclick="toggleSection('i:Context')">Instances</p><div id="section.i:Context" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="Control-Lens-Internal-Context.html#t:IndexedComonadStore">IndexedComonadStore</a> <a href="Control-Lens-Lens.html#t:Context">Context</a></span> <a href="src/Control-Lens-Internal-Context.html#line-160" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Control-Lens-Internal-Context.html#t:IndexedComonad">IndexedComonad</a> <a href="Control-Lens-Lens.html#t:Context">Context</a></span> <a href="src/Control-Lens-Internal-Context.html#line-152" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Control-Lens-Internal-Context.html#t:IndexedFunctor">IndexedFunctor</a> <a href="Control-Lens-Lens.html#t:Context">Context</a></span> <a href="src/Control-Lens-Internal-Context.html#line-148" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="Control-Lens-Internal-Context.html#t:Sellable">Sellable</a> (->) <a href="Control-Lens-Lens.html#t:Context">Context</a></span> <a href="src/Control-Lens-Internal-Context.html#line-202" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(~) * a b => <a href="file:///usr/share/doc/libghc-comonad-doc/html/Control-Comonad-Store-Class.html#t:ComonadStore">ComonadStore</a> a (<a href="Control-Lens-Lens.html#t:Context">Context</a> a b)</span> <a href="src/Control-Lens-Internal-Context.html#line-188" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> (<a href="Control-Lens-Lens.html#t:Context">Context</a> a b)</span> <a href="src/Control-Lens-Internal-Context.html#line-176" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(~) * a b => <a href="file:///usr/share/doc/libghc-comonad-doc/html/Control-Comonad.html#t:Comonad">Comonad</a> (<a href="Control-Lens-Lens.html#t:Context">Context</a> a b)</span> <a href="src/Control-Lens-Internal-Context.html#line-180" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">type</span> <a name="t:Context-39-" class="def">Context'</a> a = <a href="Control-Lens-Lens.html#t:Context">Context</a> a a <a href="src/Control-Lens-Internal-Context.html#Context%27" class="link">Source</a></p><div class="doc"><pre>type <code><a href="Control-Lens-Lens.html#t:Context-39-">Context'</a></code> a s = <code><a href="Control-Lens-Lens.html#t:Context">Context</a></code> a a s</pre></div></div><div class="top"><p class="src"><a name="v:locus" class="def">locus</a> :: <a href="Control-Lens-Internal-Context.html#t:IndexedComonadStore">IndexedComonadStore</a> p => <a href="Control-Lens-Lens.html#t:Lens">Lens</a> (p a c s) (p b c s) a b <a href="src/Control-Lens-Lens.html#locus" class="link">Source</a></p><div class="doc"><p>This <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> lets you <code>view</code> the current <code>pos</code> of any indexed
store comonad and <code>seek</code> to a new position. This reduces the API
for working these instances to a single <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code>.</p><pre><code><a href="Control-Lens-Internal-Context.html#v:ipos">ipos</a></code> w ≡ w <code><a href="Control-Lens-Getter.html#v:-94-.">^.</a></code> <code><a href="Control-Lens-Lens.html#v:locus">locus</a></code>
<code><a href="Control-Lens-Internal-Context.html#v:iseek">iseek</a></code> s w ≡ w <code><a href="Control-Lens-Lens.html#v:-38-">&</a></code> <code><a href="Control-Lens-Lens.html#v:locus">locus</a></code> <code><a href="Control-Lens-Setter.html#v:.-126-">.~</a></code> s
<code><a href="Control-Lens-Internal-Context.html#v:iseeks">iseeks</a></code> f w ≡ w <code><a href="Control-Lens-Lens.html#v:-38-">&</a></code> <code><a href="Control-Lens-Lens.html#v:locus">locus</a></code> <code><a href="Control-Lens-Setter.html#v:-37--126-">%~</a></code> f
</pre><pre><code><a href="Control-Lens-Lens.html#v:locus">locus</a></code> :: <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> (<code><a href="Control-Lens-Lens.html#t:Context-39-">Context'</a></code> a s) a
<code><a href="Control-Lens-Lens.html#v:locus">locus</a></code> :: <code><a href="Control-Lens-Internal-Indexed.html#t:Conjoined">Conjoined</a></code> p => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> (<code><a href="Control-Lens-Internal-Context.html#t:Pretext-39-">Pretext'</a></code> p a s) a
<code><a href="Control-Lens-Lens.html#v:locus">locus</a></code> :: <code><a href="Control-Lens-Internal-Indexed.html#t:Conjoined">Conjoined</a></code> p => <code><a href="Control-Lens-Lens.html#t:Lens-39-">Lens'</a></code> (<code><a href="Control-Lens-Internal-Context.html#t:PretextT-39-">PretextT'</a></code> p g a s) a
</pre></div></div><h1 id="g:13">Lens fusion</h1><div class="top"><p class="src"><a name="v:fusing" class="def">fusing</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> f => <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> (<a href="file:///usr/share/doc/libghc-kan-extensions-doc/html/Data-Functor-Yoneda.html#t:Yoneda">Yoneda</a> f) s t a b -> <a href="Control-Lens-Type.html#t:LensLike">LensLike</a> f s t a b <a href="src/Control-Lens-Lens.html#fusing" class="link">Source</a></p><div class="doc"><p>Fuse a composition of lenses using <code><a href="file:///usr/share/doc/libghc-kan-extensions-doc/html/Data-Functor-Yoneda.html#t:Yoneda">Yoneda</a></code> to provide <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:fmap">fmap</a></code> fusion.</p><p>In general, given a pair of lenses <code>foo</code> and <code>bar</code></p><pre>fusing (foo.bar) = foo.bar
</pre><p>however, <code>foo</code> and <code>bar</code> are either going to <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:fmap">fmap</a></code> internally or they are trivial.</p><p><code><a href="Control-Lens-Lens.html#v:fusing">fusing</a></code> exploits the <code><a href="file:///usr/share/doc/libghc-kan-extensions-doc/html/Data-Functor-Yoneda.html#t:Yoneda">Yoneda</a></code> lemma to merge these separate uses into a single <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:fmap">fmap</a></code>.</p><p>This is particularly effective when the choice of functor <code>f</code> is unknown at compile
time or when the <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> <code>foo.bar</code> in the above description is recursive or complex
enough to prevent inlining.</p><pre><code><a href="Control-Lens-Lens.html#v:fusing">fusing</a></code> :: <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b -> <code><a href="Control-Lens-Lens.html#t:Lens">Lens</a></code> s t a b
</pre></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.16.1</p></div></body></html>
|