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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Control-Lens-Level.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-4.15.4: Lenses, Folds and Traversals</p></div><div id="content"><div id="module-header"><table class="info"><tr><th valign="top">Copyright</th><td>(C) 2012-16 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.Level</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>This module provides combinators for breadth-first searching within
arbitrary traversals.</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">data</span> <a href="#t:Level">Level</a> i a</li><li class="src short"><a href="#v:levels">levels</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> f => <a href="Control-Lens-Traversal.html#t:Traversing">Traversing</a> (->) f s t a b -> <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> f s t (<a href="Control-Lens-Level.html#t:Level">Level</a> () a) (<a href="Control-Lens-Level.html#t:Level">Level</a> () b)</li><li class="src short"><a href="#v:ilevels">ilevels</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> f => <a href="Control-Lens-Traversal.html#t:Traversing">Traversing</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) f s t a b -> <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> f s t (<a href="Control-Lens-Level.html#t:Level">Level</a> i a) (<a href="Control-Lens-Level.html#t:Level">Level</a> j b)</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">data</span> <a id="t:Level" class="def">Level</a> i a <a href="src/Control-Lens-Internal-Level.html#Level" class="link">Source</a> <a href="#t:Level" class="selflink">#</a></p><div class="doc"><p>This data type represents a path-compressed copy of one level of a source
data structure. We can safely use path-compression because we know the depth
of the tree.</p><p>Path compression is performed by viewing a <code><a href="Control-Lens-Level.html#t:Level">Level</a></code> as a PATRICIA trie of the
paths into the structure to leaves at a given depth, similar in many ways
to a <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/containers-0.5.7.1/Data-IntMap.html#v:IntMap">IntMap</a></code>, but unlike a regular PATRICIA trie we do not need
to store the mask bits merely the depth of the fork.</p><p>One invariant of this structure is that underneath a <code><a href="Control-Lens-Internal-Level.html#v:Two">Two</a></code> node you will not
find any <code><a href="Control-Lens-Internal-Level.html#v:Zero">Zero</a></code> nodes, so <code><a href="Control-Lens-Internal-Level.html#v:Zero">Zero</a></code> can only occur at the root.</p></div><div class="subs instances"><p id="control.i:Level" class="caption collapser" onclick="toggleSection('i:Level')">Instances</p><div id="section.i:Level" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:TraversableWithIndex:1" class="instance expander" onclick="toggleSection('i:id:Level:TraversableWithIndex:1')"></span> <a href="Control-Lens-Indexed.html#t:TraversableWithIndex">TraversableWithIndex</a> i (<a href="Control-Lens-Level.html#t:Level">Level</a> i)</span> <a href="src/Control-Lens-Indexed.html#line-757" class="link">Source</a> <a href="#t:TraversableWithIndex" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:TraversableWithIndex:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:itraverse">itraverse</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> f => (i -> a -> f b) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> f (<a href="Control-Lens-Level.html#t:Level">Level</a> i b) <a href="src/Control-Lens-Indexed.html#itraverse" class="link">Source</a> <a href="#v:itraverse" class="selflink">#</a></p><p class="src"><a href="#v:itraversed">itraversed</a> :: (<a href="Control-Lens-Internal-Indexed.html#t:Indexable">Indexable</a> i p, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> f) => p a (f b) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> f (<a href="Control-Lens-Level.html#t:Level">Level</a> i b) <a href="src/Control-Lens-Indexed.html#itraversed" class="link">Source</a> <a href="#v:itraversed" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:FoldableWithIndex:2" class="instance expander" onclick="toggleSection('i:id:Level:FoldableWithIndex:2')"></span> <a href="Control-Lens-Indexed.html#t:FoldableWithIndex">FoldableWithIndex</a> i (<a href="Control-Lens-Level.html#t:Level">Level</a> i)</span> <a href="src/Control-Lens-Indexed.html#line-750" class="link">Source</a> <a href="#t:FoldableWithIndex" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:FoldableWithIndex:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:ifoldMap">ifoldMap</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Monoid.html#t:Monoid">Monoid</a> m => (i -> a -> m) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> m <a href="src/Control-Lens-Indexed.html#ifoldMap" class="link">Source</a> <a href="#v:ifoldMap" class="selflink">#</a></p><p class="src"><a href="#v:ifolded">ifolded</a> :: (<a href="Control-Lens-Internal-Indexed.html#t:Indexable">Indexable</a> i p, <a href="Control-Lens-Getter.html#t:Contravariant">Contravariant</a> f, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> f) => p a (f a) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> f (<a href="Control-Lens-Level.html#t:Level">Level</a> i a) <a href="src/Control-Lens-Indexed.html#ifolded" class="link">Source</a> <a href="#v:ifolded" class="selflink">#</a></p><p class="src"><a href="#v:ifoldr">ifoldr</a> :: (i -> a -> b -> b) -> b -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> b <a href="src/Control-Lens-Indexed.html#ifoldr" class="link">Source</a> <a href="#v:ifoldr" class="selflink">#</a></p><p class="src"><a href="#v:ifoldl">ifoldl</a> :: (i -> b -> a -> b) -> b -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> b <a href="src/Control-Lens-Indexed.html#ifoldl" class="link">Source</a> <a href="#v:ifoldl" class="selflink">#</a></p><p class="src"><a href="#v:ifoldr-39-">ifoldr'</a> :: (i -> a -> b -> b) -> b -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> b <a href="src/Control-Lens-Indexed.html#ifoldr%27" class="link">Source</a> <a href="#v:ifoldr-39-" class="selflink">#</a></p><p class="src"><a href="#v:ifoldl-39-">ifoldl'</a> :: (i -> b -> a -> b) -> b -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> b <a href="src/Control-Lens-Indexed.html#ifoldl%27" class="link">Source</a> <a href="#v:ifoldl-39-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:FunctorWithIndex:3" class="instance expander" onclick="toggleSection('i:id:Level:FunctorWithIndex:3')"></span> <a href="Control-Lens-Indexed.html#t:FunctorWithIndex">FunctorWithIndex</a> i (<a href="Control-Lens-Level.html#t:Level">Level</a> i)</span> <a href="src/Control-Lens-Indexed.html#line-743" class="link">Source</a> <a href="#t:FunctorWithIndex" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:FunctorWithIndex:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:imap">imap</a> :: (i -> a -> b) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i b <a href="src/Control-Lens-Indexed.html#imap" class="link">Source</a> <a href="#v:imap" class="selflink">#</a></p><p class="src"><a href="#v:imapped">imapped</a> :: (<a href="Control-Lens-Internal-Indexed.html#t:Indexable">Indexable</a> i p, <a href="Control-Lens-Internal-Setter.html#t:Settable">Settable</a> f) => p a (f b) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> f (<a href="Control-Lens-Level.html#t:Level">Level</a> i b) <a href="src/Control-Lens-Indexed.html#imapped" class="link">Source</a> <a href="#v:imapped" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:Functor:4" class="instance expander" onclick="toggleSection('i:id:Level:Functor:4')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Functor.html#t:Functor">Functor</a> (<a href="Control-Lens-Level.html#t:Level">Level</a> i)</span> <a href="src/Control-Lens-Internal-Level.html#line-74" class="link">Source</a> <a href="#t:Level" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:Functor:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:fmap">fmap</a> :: (a -> b) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i b <a href="#v:fmap" class="selflink">#</a></p><p class="src"><a href="#v:-60--36-">(<$)</a> :: a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i b -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a <a href="#v:-60--36-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:Foldable:5" class="instance expander" onclick="toggleSection('i:id:Level:Foldable:5')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Foldable.html#t:Foldable">Foldable</a> (<a href="Control-Lens-Level.html#t:Level">Level</a> i)</span> <a href="src/Control-Lens-Internal-Level.html#line-81" class="link">Source</a> <a href="#t:Level" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:Foldable:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:fold">fold</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Monoid.html#t:Monoid">Monoid</a> m => <a href="Control-Lens-Level.html#t:Level">Level</a> i m -> m <a href="#v:fold" class="selflink">#</a></p><p class="src"><a href="#v:foldMap">foldMap</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Monoid.html#t:Monoid">Monoid</a> m => (a -> m) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> m <a href="#v:foldMap" class="selflink">#</a></p><p class="src"><a href="#v:foldr">foldr</a> :: (a -> b -> b) -> b -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> b <a href="#v:foldr" class="selflink">#</a></p><p class="src"><a href="#v:foldr-39-">foldr'</a> :: (a -> b -> b) -> b -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> b <a href="#v:foldr-39-" class="selflink">#</a></p><p class="src"><a href="#v:foldl">foldl</a> :: (b -> a -> b) -> b -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> b <a href="#v:foldl" class="selflink">#</a></p><p class="src"><a href="#v:foldl-39-">foldl'</a> :: (b -> a -> b) -> b -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> b <a href="#v:foldl-39-" class="selflink">#</a></p><p class="src"><a href="#v:foldr1">foldr1</a> :: (a -> a -> a) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> a <a href="#v:foldr1" class="selflink">#</a></p><p class="src"><a href="#v:foldl1">foldl1</a> :: (a -> a -> a) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> a <a href="#v:foldl1" class="selflink">#</a></p><p class="src"><a href="#v:toList">toList</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> [a] <a href="#v:toList" class="selflink">#</a></p><p class="src"><a href="#v:null">null</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:null" class="selflink">#</a></p><p class="src"><a href="#v:length">length</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> <a href="#v:length" class="selflink">#</a></p><p class="src"><a href="#v:elem">elem</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a => a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:elem" class="selflink">#</a></p><p class="src"><a href="#v:maximum">maximum</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> a <a href="#v:maximum" class="selflink">#</a></p><p class="src"><a href="#v:minimum">minimum</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a => <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> a <a href="#v:minimum" class="selflink">#</a></p><p class="src"><a href="#v:sum">sum</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> a <a href="#v:sum" class="selflink">#</a></p><p class="src"><a href="#v:product">product</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Num">Num</a> a => <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> a <a href="#v:product" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:Traversable:6" class="instance expander" onclick="toggleSection('i:id:Level:Traversable:6')"></span> <a href="Control-Lens-Traversal.html#t:Traversable">Traversable</a> (<a href="Control-Lens-Level.html#t:Level">Level</a> i)</span> <a href="src/Control-Lens-Internal-Level.html#line-88" class="link">Source</a> <a href="#t:Level" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:Traversable:6" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:traverse">traverse</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> f => (a -> f b) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> f (<a href="Control-Lens-Level.html#t:Level">Level</a> i b) <a href="#v:traverse" class="selflink">#</a></p><p class="src"><a href="#v:sequenceA">sequenceA</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> f => <a href="Control-Lens-Level.html#t:Level">Level</a> i (f a) -> f (<a href="Control-Lens-Level.html#t:Level">Level</a> i a) <a href="#v:sequenceA" class="selflink">#</a></p><p class="src"><a href="#v:mapM">mapM</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Monad.html#t:Monad">Monad</a> m => (a -> m b) -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> m (<a href="Control-Lens-Level.html#t:Level">Level</a> i b) <a href="#v:mapM" class="selflink">#</a></p><p class="src"><a href="#v:sequence">sequence</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Monad.html#t:Monad">Monad</a> m => <a href="Control-Lens-Level.html#t:Level">Level</a> i (m a) -> m (<a href="Control-Lens-Level.html#t:Level">Level</a> i a) <a href="#v:sequence" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:Eq:7" class="instance expander" onclick="toggleSection('i:id:Level:Eq:7')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> i) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Control-Lens-Level.html#t:Level">Level</a> i a)</span> <a href="src/Control-Lens-Internal-Level.html#line-59" class="link">Source</a> <a href="#t:Level" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:Eq:7" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-61--61-" class="selflink">#</a></p><p class="src"><a href="#v:-47--61-">(/=)</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-47--61-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:Ord:8" class="instance expander" onclick="toggleSection('i:id:Level:Ord:8')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> i) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Control-Lens-Level.html#t:Level">Level</a> i a)</span> <a href="src/Control-Lens-Internal-Level.html#line-59" class="link">Source</a> <a href="#t:Level" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:Ord:8" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:compare">compare</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Ord.html#t:Ordering">Ordering</a> <a href="#v:compare" class="selflink">#</a></p><p class="src"><a href="#v:-60-">(<)</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60-" class="selflink">#</a></p><p class="src"><a href="#v:-60--61-">(<=)</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-60--61-" class="selflink">#</a></p><p class="src"><a href="#v:-62-">(>)</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62-" class="selflink">#</a></p><p class="src"><a href="#v:-62--61-">(>=)</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-62--61-" class="selflink">#</a></p><p class="src"><a href="#v:max">max</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a <a href="#v:max" class="selflink">#</a></p><p class="src"><a href="#v:min">min</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a <a href="#v:min" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:Read:9" class="instance expander" onclick="toggleSection('i:id:Level:Read:9')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Read.html#t:Read">Read</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Read.html#t:Read">Read</a> i) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Read.html#t:Read">Read</a> (<a href="Control-Lens-Level.html#t:Level">Level</a> i a)</span> <a href="src/Control-Lens-Internal-Level.html#line-59" class="link">Source</a> <a href="#t:Level" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:Read:9" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:readsPrec">readsPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> (<a href="Control-Lens-Level.html#t:Level">Level</a> i a) <a href="#v:readsPrec" class="selflink">#</a></p><p class="src"><a href="#v:readList">readList</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> [<a href="Control-Lens-Level.html#t:Level">Level</a> i a] <a href="#v:readList" class="selflink">#</a></p><p class="src"><a href="#v:readPrec">readPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> (<a href="Control-Lens-Level.html#t:Level">Level</a> i a) <a href="#v:readPrec" class="selflink">#</a></p><p class="src"><a href="#v:readListPrec">readListPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> [<a href="Control-Lens-Level.html#t:Level">Level</a> i a] <a href="#v:readListPrec" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Level:Show:10" class="instance expander" onclick="toggleSection('i:id:Level:Show:10')"></span> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Show.html#t:Show">Show</a> a, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Show.html#t:Show">Show</a> i) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Show.html#t:Show">Show</a> (<a href="Control-Lens-Level.html#t:Level">Level</a> i a)</span> <a href="src/Control-Lens-Internal-Level.html#line-59" class="link">Source</a> <a href="#t:Level" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Level:Show:10" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:showsPrec">showsPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showsPrec" class="selflink">#</a></p><p class="src"><a href="#v:show">show</a> :: <a href="Control-Lens-Level.html#t:Level">Level</a> i a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-String.html#t:String">String</a> <a href="#v:show" class="selflink">#</a></p><p class="src"><a href="#v:showList">showList</a> :: [<a href="Control-Lens-Level.html#t:Level">Level</a> i a] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showList" class="selflink">#</a></p></div></div></td></tr></table></div></div></div><div class="top"><p class="src"><a id="v:levels" class="def">levels</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> f => <a href="Control-Lens-Traversal.html#t:Traversing">Traversing</a> (->) f s t a b -> <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> f s t (<a href="Control-Lens-Level.html#t:Level">Level</a> () a) (<a href="Control-Lens-Level.html#t:Level">Level</a> () b) <a href="src/Control-Lens-Level.html#levels" class="link">Source</a> <a href="#v:levels" class="selflink">#</a></p><div class="doc"><p>This provides a breadth-first <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code> or <code><a href="Control-Lens-Type.html#t:Fold">Fold</a></code> of the individual
<code><a href="Control-Lens-Level.html#v:levels">levels</a></code> of any other <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code> or <code><a href="Control-Lens-Type.html#t:Fold">Fold</a></code> via iterative deepening
depth-first search. The levels are returned to you in a compressed format.</p><p>This can permit us to extract the <code><a href="Control-Lens-Level.html#v:levels">levels</a></code> directly:</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>["hello","world"]^..levels (traverse.traverse)
</code></strong>[Zero,Zero,One () 'h',Two 0 (One () 'e') (One () 'w'),Two 0 (One () 'l') (One () 'o'),Two 0 (One () 'l') (One () 'r'),Two 0 (One () 'o') (One () 'l'),One () 'd']
</pre><p>But we can also traverse them in turn:</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>["hello","world"]^..levels (traverse.traverse).traverse
</code></strong>"hewlolrold"
</pre><p>We can use this to traverse to a fixed depth in the tree of (<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#v:-60--42--62-"><*></a></code>) used in the <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code>:</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>["hello","world"] & taking 4 (levels (traverse.traverse)).traverse %~ toUpper
</code></strong>["HEllo","World"]
</pre><p>Or we can use it to traverse the first <code>n</code> elements in found in that <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code> regardless of the depth
at which they were found.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>["hello","world"] & taking 4 (levels (traverse.traverse).traverse) %~ toUpper
</code></strong>["HELlo","World"]
</pre><p>The resulting <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code> of the <code><a href="Control-Lens-Level.html#v:levels">levels</a></code> which is indexed by the depth of each <code><a href="Control-Lens-Level.html#t:Level">Level</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>["dog","cat"]^@..levels (traverse.traverse) <. traverse
</code></strong>[(2,'d'),(3,'o'),(3,'c'),(4,'g'),(4,'a'),(5,'t')]
</pre><pre><code><a href="Control-Lens-Level.html#v:levels">levels</a></code> :: <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code> s t a b -> <code><a href="Control-Lens-Type.html#t:IndexedTraversal">IndexedTraversal</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a></code> s t (<code><a href="Control-Lens-Level.html#t:Level">Level</a></code> () a) (<code><a href="Control-Lens-Level.html#t:Level">Level</a></code> () b)
<code><a href="Control-Lens-Level.html#v:levels">levels</a></code> :: <code><a href="Control-Lens-Type.html#t:Fold">Fold</a></code> s a -> <code><a href="Control-Lens-Type.html#t:IndexedFold">IndexedFold</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a></code> s (<code><a href="Control-Lens-Level.html#t:Level">Level</a></code> () a)
</pre><p><em>Note:</em> Internally this is implemented by using an illegal <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a></code>, as it extracts information
in an order that violates the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a></code> laws.</p></div></div><div class="top"><p class="src"><a id="v:ilevels" class="def">ilevels</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> f => <a href="Control-Lens-Traversal.html#t:Traversing">Traversing</a> (<a href="Control-Lens-Internal-Indexed.html#t:Indexed">Indexed</a> i) f s t a b -> <a href="Control-Lens-Type.html#t:IndexedLensLike">IndexedLensLike</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> f s t (<a href="Control-Lens-Level.html#t:Level">Level</a> i a) (<a href="Control-Lens-Level.html#t:Level">Level</a> j b) <a href="src/Control-Lens-Level.html#ilevels" class="link">Source</a> <a href="#v:ilevels" class="selflink">#</a></p><div class="doc"><p>This provides a breadth-first <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code> or <code><a href="Control-Lens-Type.html#t:Fold">Fold</a></code> of the individual
levels of any other <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code> or <code><a href="Control-Lens-Type.html#t:Fold">Fold</a></code> via iterative deepening depth-first
search. The levels are returned to you in a compressed format.</p><p>This is similar to <code><a href="Control-Lens-Level.html#v:levels">levels</a></code>, but retains the index of the original <code><a href="Control-Lens-Type.html#t:IndexedTraversal">IndexedTraversal</a></code>, so you can
access it when traversing the levels later on.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>["dog","cat"]^@..ilevels (traversed<.>traversed).itraversed
</code></strong>[((0,0),'d'),((0,1),'o'),((1,0),'c'),((0,2),'g'),((1,1),'a'),((1,2),'t')]
</pre><p>The resulting <code><a href="Control-Lens-Type.html#t:Traversal">Traversal</a></code> of the levels which is indexed by the depth of each <code><a href="Control-Lens-Level.html#t:Level">Level</a></code>.</p><pre class="screen"><code class="prompt">>>> </code><strong class="userinput"><code>["dog","cat"]^@..ilevels (traversed<.>traversed)<.>itraversed
</code></strong>[((2,(0,0)),'d'),((3,(0,1)),'o'),((3,(1,0)),'c'),((4,(0,2)),'g'),((4,(1,1)),'a'),((5,(1,2)),'t')]
</pre><pre><code><a href="Control-Lens-Level.html#v:ilevels">ilevels</a></code> :: <code><a href="Control-Lens-Type.html#t:IndexedTraversal">IndexedTraversal</a></code> i s t a b -> <code><a href="Control-Lens-Type.html#t:IndexedTraversal">IndexedTraversal</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a></code> s t (<code><a href="Control-Lens-Level.html#t:Level">Level</a></code> i a) (<code><a href="Control-Lens-Level.html#t:Level">Level</a></code> i b)
<code><a href="Control-Lens-Level.html#v:ilevels">ilevels</a></code> :: <code><a href="Control-Lens-Type.html#t:IndexedFold">IndexedFold</a></code> i s a -> <code><a href="Control-Lens-Type.html#t:IndexedFold">IndexedFold</a></code> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a></code> s (<code><a href="Control-Lens-Level.html#t:Level">Level</a></code> i a)
</pre><p><em>Note:</em> Internally this is implemented by using an illegal <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a></code>, as it extracts information
in an order that violates the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a></code> laws.</p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.17.3</p></div></body></html>
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