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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Control-Lens-Internal-Fold.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) 2012-2015 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>experimental</td></tr><tr><th>Portability</th><td>non-portable</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.Internal.Fold</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Monoids for folding</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc empty"> </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">newtype</span> <a href="#t:Folding">Folding</a> f a = <a href="#v:Folding">Folding</a> {<ul class="subs"><li><a href="#v:getFolding">getFolding</a> :: f a</li></ul>}</li><li class="src short"><span class="keyword">newtype</span> <a href="#t:Traversed">Traversed</a> a f = <a href="#v:Traversed">Traversed</a> {<ul class="subs"><li><a href="#v:getTraversed">getTraversed</a> :: f a</li></ul>}</li><li class="src short"><span class="keyword">newtype</span> <a href="#t:Sequenced">Sequenced</a> a m = <a href="#v:Sequenced">Sequenced</a> {<ul class="subs"><li><a href="#v:getSequenced">getSequenced</a> :: m a</li></ul>}</li><li class="src short"><span class="keyword">data</span> <a href="#t:Max">Max</a> a<ul class="subs"><li>= <a href="#v:NoMax">NoMax</a></li><li>| <a href="#v:Max">Max</a> a</li></ul></li><li class="src short"><a href="#v:getMax">getMax</a> :: <a href="Control-Lens-Internal-Fold.html#t:Max">Max</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> a</li><li class="src short"><span class="keyword">data</span> <a href="#t:Min">Min</a> a<ul class="subs"><li>= <a href="#v:NoMin">NoMin</a></li><li>| <a href="#v:Min">Min</a> a</li></ul></li><li class="src short"><a href="#v:getMin">getMin</a> :: <a href="Control-Lens-Internal-Fold.html#t:Min">Min</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> a</li><li class="src short"><span class="keyword">data</span> <a href="#t:Leftmost">Leftmost</a> a<ul class="subs"><li>= <a href="#v:LPure">LPure</a></li><li>| <a href="#v:LLeaf">LLeaf</a> a</li><li>| <a href="#v:LStep">LStep</a> (<a href="Control-Lens-Internal-Fold.html#t:Leftmost">Leftmost</a> a)</li></ul></li><li class="src short"><a href="#v:getLeftmost">getLeftmost</a> :: <a href="Control-Lens-Internal-Fold.html#t:Leftmost">Leftmost</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> a</li><li class="src short"><span class="keyword">data</span> <a href="#t:Rightmost">Rightmost</a> a<ul class="subs"><li>= <a href="#v:RPure">RPure</a></li><li>| <a href="#v:RLeaf">RLeaf</a> a</li><li>| <a href="#v:RStep">RStep</a> (<a href="Control-Lens-Internal-Fold.html#t:Rightmost">Rightmost</a> a)</li></ul></li><li class="src short"><a href="#v:getRightmost">getRightmost</a> :: <a href="Control-Lens-Internal-Fold.html#t:Rightmost">Rightmost</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> a</li><li class="src short"><span class="keyword">data</span> <a href="#t:ReifiedMonoid">ReifiedMonoid</a> a :: * -> * = <a href="#v:ReifiedMonoid">ReifiedMonoid</a> {<ul class="subs"><li><a href="#v:reifiedMappend">reifiedMappend</a> :: a -> a -> a</li><li><a href="#v:reifiedMempty">reifiedMempty</a> :: a</li></ul>}</li></ul></div><div id="interface"><h1 id="g:1">Monoids for folding</h1><div class="top"><p class="src"><span class="keyword">newtype</span> <a name="t:Folding" class="def">Folding</a> f a <a href="src/Control-Lens-Internal-Fold.html#Folding" class="link">Source</a></p><div class="doc"><p>A <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> for a <code><a href="Control-Lens-Getter.html#t:Contravariant">Contravariant</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>.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:Folding" class="def">Folding</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div class="subs fields"><p class="caption">Fields</p><dl><dt class="src"><a name="v:getFolding" class="def">getFolding</a> :: f a</dt><dd class="doc empty"> </dd></dl><div class="clear"></div></div></td></tr></table></div><div class="subs instances"><p id="control.i:Folding" class="caption collapser" onclick="toggleSection('i:Folding')">Instances</p><div id="section.i:Folding" class="show"><table><tr><td class="src clearfix"><span class="inst-left">(<a href="Control-Lens-Getter.html#t:Contravariant">Contravariant</a> f, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a> f) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> (<a href="Control-Lens-Internal-Fold.html#t:Folding">Folding</a> f a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-56" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(<a href="Control-Lens-Getter.html#t:Contravariant">Contravariant</a> f, <a href="file:///usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Apply.html#t:Apply">Apply</a> f) => <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Control-Lens-Internal-Fold.html#t:Folding">Folding</a> f a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-52" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">newtype</span> <a name="t:Traversed" class="def">Traversed</a> a f <a href="src/Control-Lens-Internal-Fold.html#Traversed" class="link">Source</a></p><div class="doc"><p>Used internally by <code><a href="Control-Lens-Traversal.html#v:traverseOf_">traverseOf_</a></code> and the like.</p><p>The argument <code>a</code> of the result should not be used!</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:Traversed" class="def">Traversed</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div class="subs fields"><p class="caption">Fields</p><dl><dt class="src"><a name="v:getTraversed" class="def">getTraversed</a> :: f a</dt><dd class="doc empty"> </dd></dl><div class="clear"></div></div></td></tr></table></div><div class="subs instances"><p id="control.i:Traversed" class="caption collapser" onclick="toggleSection('i:Traversed')">Instances</p><div id="section.i:Traversed" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a> f => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> (<a href="Control-Lens-Internal-Fold.html#t:Traversed">Traversed</a> a f)</span> <a href="src/Control-Lens-Internal-Fold.html#line-75" 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/libghc-semigroupoids-doc/html/Data-Functor-Apply.html#t:Apply">Apply</a> f => <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Control-Lens-Internal-Fold.html#t:Traversed">Traversed</a> a f)</span> <a href="src/Control-Lens-Internal-Fold.html#line-71" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">newtype</span> <a name="t:Sequenced" class="def">Sequenced</a> a m <a href="src/Control-Lens-Internal-Fold.html#Sequenced" class="link">Source</a></p><div class="doc"><p>Used internally by <code><a href="Control-Lens-Traversal.html#v:mapM_">mapM_</a></code> and the like.</p><p>The argument <code>a</code> of the result should not be used!</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:Sequenced" class="def">Sequenced</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div class="subs fields"><p class="caption">Fields</p><dl><dt class="src"><a name="v:getSequenced" class="def">getSequenced</a> :: m a</dt><dd class="doc empty"> </dd></dl><div class="clear"></div></div></td></tr></table></div><div class="subs instances"><p id="control.i:Sequenced" class="caption collapser" onclick="toggleSection('i:Sequenced')">Instances</p><div id="section.i:Sequenced" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Monad.html#t:Monad">Monad</a> m => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> (<a href="Control-Lens-Internal-Fold.html#t:Sequenced">Sequenced</a> a m)</span> <a href="src/Control-Lens-Internal-Fold.html#line-94" 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/libghc-semigroupoids-doc/html/Data-Functor-Apply.html#t:Apply">Apply</a> m => <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Control-Lens-Internal-Fold.html#t:Sequenced">Sequenced</a> a m)</span> <a href="src/Control-Lens-Internal-Fold.html#line-90" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Max" class="def">Max</a> a <a href="src/Control-Lens-Internal-Fold.html#Max" class="link">Source</a></p><div class="doc"><p>Used for <code><a href="Control-Lens-Fold.html#v:maximumOf">maximumOf</a></code>.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:NoMax" class="def">NoMax</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a name="v:Max" class="def">Max</a> a</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Max" class="caption collapser" onclick="toggleSection('i:Max')">Instances</p><div id="section.i:Max" class="show"><table><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-Ord.html#t:Ord">Ord</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> (<a href="Control-Lens-Internal-Fold.html#t:Max">Max</a> a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-140" 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-Ord.html#t:Ord">Ord</a> a => <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Control-Lens-Internal-Fold.html#t:Max">Max</a> a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-134" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:getMax" class="def">getMax</a> :: <a href="Control-Lens-Internal-Fold.html#t:Max">Max</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> a <a href="src/Control-Lens-Internal-Fold.html#getMax" class="link">Source</a></p><div class="doc"><p>Obtain the maximum.</p></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Min" class="def">Min</a> a <a href="src/Control-Lens-Internal-Fold.html#Min" class="link">Source</a></p><div class="doc"><p>Used for <code><a href="Control-Lens-Fold.html#v:minimumOf">minimumOf</a></code>.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:NoMin" class="def">NoMin</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a name="v:Min" class="def">Min</a> a</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Min" class="caption collapser" onclick="toggleSection('i:Min')">Instances</p><div id="section.i:Min" class="show"><table><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-Ord.html#t:Ord">Ord</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> (<a href="Control-Lens-Internal-Fold.html#t:Min">Min</a> a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-113" 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-Ord.html#t:Ord">Ord</a> a => <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Control-Lens-Internal-Fold.html#t:Min">Min</a> a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-107" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:getMin" class="def">getMin</a> :: <a href="Control-Lens-Internal-Fold.html#t:Min">Min</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> a <a href="src/Control-Lens-Internal-Fold.html#getMin" class="link">Source</a></p><div class="doc"><p>Obtain the minimum.</p></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Leftmost" class="def">Leftmost</a> a <a href="src/Control-Lens-Internal-Fold.html#Leftmost" class="link">Source</a></p><div class="doc"><p>Used for <code><a href="Control-Lens-Fold.html#v:preview">preview</a></code>.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:LPure" class="def">LPure</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a name="v:LLeaf" class="def">LLeaf</a> a</td><td class="doc empty"> </td></tr><tr><td class="src"><a name="v:LStep" class="def">LStep</a> (<a href="Control-Lens-Internal-Fold.html#t:Leftmost">Leftmost</a> a)</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Leftmost" class="caption collapser" onclick="toggleSection('i:Leftmost')">Instances</p><div id="section.i:Leftmost" class="show"><table><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-Monoid.html#t:Monoid">Monoid</a> (<a href="Control-Lens-Internal-Fold.html#t:Leftmost">Leftmost</a> a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-165" 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/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Control-Lens-Internal-Fold.html#t:Leftmost">Leftmost</a> a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-161" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:getLeftmost" class="def">getLeftmost</a> :: <a href="Control-Lens-Internal-Fold.html#t:Leftmost">Leftmost</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> a <a href="src/Control-Lens-Internal-Fold.html#getLeftmost" class="link">Source</a></p><div class="doc"><p>Extract the <code><a href="Control-Lens-Internal-Fold.html#t:Leftmost">Leftmost</a></code> element. This will fairly eagerly determine that it can return <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#v:Just">Just</a></code>
the moment it sees any element at all.</p></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Rightmost" class="def">Rightmost</a> a <a href="src/Control-Lens-Internal-Fold.html#Rightmost" class="link">Source</a></p><div class="doc"><p>Used for <code><a href="Control-Lens-Fold.html#v:lastOf">lastOf</a></code>.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:RPure" class="def">RPure</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a name="v:RLeaf" class="def">RLeaf</a> a</td><td class="doc empty"> </td></tr><tr><td class="src"><a name="v:RStep" class="def">RStep</a> (<a href="Control-Lens-Internal-Fold.html#t:Rightmost">Rightmost</a> a)</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Rightmost" class="caption collapser" onclick="toggleSection('i:Rightmost')">Instances</p><div id="section.i:Rightmost" class="show"><table><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-Monoid.html#t:Monoid">Monoid</a> (<a href="Control-Lens-Internal-Fold.html#t:Rightmost">Rightmost</a> a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-194" 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/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Control-Lens-Internal-Fold.html#t:Rightmost">Rightmost</a> a)</span> <a href="src/Control-Lens-Internal-Fold.html#line-190" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:getRightmost" class="def">getRightmost</a> :: <a href="Control-Lens-Internal-Fold.html#t:Rightmost">Rightmost</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> a <a href="src/Control-Lens-Internal-Fold.html#getRightmost" class="link">Source</a></p><div class="doc"><p>Extract the <code><a href="Control-Lens-Internal-Fold.html#t:Rightmost">Rightmost</a></code> element. This will fairly eagerly determine that it can return <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#v:Just">Just</a></code>
the moment it sees any element at all.</p></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:ReifiedMonoid" class="def">ReifiedMonoid</a> a :: * -> *</p><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:ReifiedMonoid" class="def">ReifiedMonoid</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div class="subs fields"><p class="caption">Fields</p><dl><dt class="src"><a name="v:reifiedMappend" class="def">reifiedMappend</a> :: a -> a -> a</dt><dd class="doc empty"> </dd><dt class="src"><a name="v:reifiedMempty" class="def">reifiedMempty</a> :: a</dt><dd class="doc empty"> </dd></dl><div class="clear"></div></div></td></tr></table></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>
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