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<pre><a name="line-1"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-2"></a><span class='hs-comment'>-- |</span>
<a name="line-3"></a><span class='hs-comment'>-- Module : Data.Tree</span>
<a name="line-4"></a><span class='hs-comment'>-- Copyright : (c) The University of Glasgow 2002</span>
<a name="line-5"></a><span class='hs-comment'>-- License : BSD-style (see the file libraries/base/LICENSE)</span>
<a name="line-6"></a><span class='hs-comment'>-- </span>
<a name="line-7"></a><span class='hs-comment'>-- Maintainer : libraries@haskell.org</span>
<a name="line-8"></a><span class='hs-comment'>-- Stability : experimental</span>
<a name="line-9"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-10"></a><span class='hs-comment'>--</span>
<a name="line-11"></a><span class='hs-comment'>-- Multi-way trees (/aka/ rose trees) and forests.</span>
<a name="line-12"></a><span class='hs-comment'>--</span>
<a name="line-13"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-14"></a>
<a name="line-15"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Tree</span><span class='hs-layout'>(</span>
<a name="line-16"></a> <span class='hs-conid'>Tree</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>Forest</span><span class='hs-layout'>,</span>
<a name="line-17"></a> <span class='hs-comment'>-- * Two-dimensional drawing</span>
<a name="line-18"></a> <span class='hs-varid'>drawTree</span><span class='hs-layout'>,</span> <span class='hs-varid'>drawForest</span><span class='hs-layout'>,</span>
<a name="line-19"></a> <span class='hs-comment'>-- * Extraction</span>
<a name="line-20"></a> <span class='hs-varid'>flatten</span><span class='hs-layout'>,</span> <span class='hs-varid'>levels</span><span class='hs-layout'>,</span>
<a name="line-21"></a> <span class='hs-comment'>-- * Building trees</span>
<a name="line-22"></a> <span class='hs-varid'>unfoldTree</span><span class='hs-layout'>,</span> <span class='hs-varid'>unfoldForest</span><span class='hs-layout'>,</span>
<a name="line-23"></a> <span class='hs-varid'>unfoldTreeM</span><span class='hs-layout'>,</span> <span class='hs-varid'>unfoldForestM</span><span class='hs-layout'>,</span>
<a name="line-24"></a> <span class='hs-varid'>unfoldTreeM_BF</span><span class='hs-layout'>,</span> <span class='hs-varid'>unfoldForestM_BF</span><span class='hs-layout'>,</span>
<a name="line-25"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-26"></a>
<a name="line-27"></a><span class='hs-cpp'>#ifdef __HADDOCK__</span>
<a name="line-28"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Prelude</span>
<a name="line-29"></a><span class='hs-cpp'>#endif</span>
<a name="line-30"></a>
<a name="line-31"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'><$></span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-32"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<a name="line-33"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-34"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Sequence</span> <span class='hs-layout'>(</span><span class='hs-conid'>Seq</span><span class='hs-layout'>,</span> <span class='hs-varid'>empty</span><span class='hs-layout'>,</span> <span class='hs-varid'>singleton</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'><|</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>|></span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>fromList</span><span class='hs-layout'>,</span>
<a name="line-35"></a> <span class='hs-conid'>ViewL</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>ViewR</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>viewl</span><span class='hs-layout'>,</span> <span class='hs-varid'>viewr</span><span class='hs-layout'>)</span>
<a name="line-36"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Foldable</span><span class='hs-layout'>(</span><span class='hs-varid'>foldMap</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>toList</span><span class='hs-layout'>)</span>
<a name="line-37"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Traversable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Traversable</span><span class='hs-layout'>(</span><span class='hs-varid'>traverse</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-38"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Typeable</span>
<a name="line-39"></a>
<a name="line-40"></a><span class='hs-cpp'>#ifdef __GLASGOW_HASKELL__</span>
<a name="line-41"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Data</span> <span class='hs-layout'>(</span><span class='hs-conid'>Data</span><span class='hs-layout'>)</span>
<a name="line-42"></a><span class='hs-cpp'>#endif</span>
<a name="line-43"></a>
<a name="line-44"></a><a name="Tree"></a><span class='hs-comment'>-- | Multi-way trees, also known as /rose trees/.</span>
<a name="line-45"></a><a name="Tree"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Node</span> <span class='hs-layout'>{</span>
<a name="line-46"></a> <span class='hs-varid'>rootLabel</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-comment'>-- ^ label value</span>
<a name="line-47"></a> <span class='hs-varid'>subForest</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Forest</span> <span class='hs-varid'>a</span> <span class='hs-comment'>-- ^ zero or more child trees</span>
<a name="line-48"></a> <span class='hs-layout'>}</span>
<a name="line-49"></a><span class='hs-cpp'>#ifndef __HADDOCK__</span>
<a name="line-50"></a><span class='hs-cpp'># ifdef __GLASGOW_HASKELL__</span>
<a name="line-51"></a> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span><span class='hs-layout'>,</span> <span class='hs-conid'>Read</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span><span class='hs-layout'>,</span> <span class='hs-conid'>Data</span><span class='hs-layout'>)</span>
<a name="line-52"></a><span class='hs-cpp'># else</span>
<a name="line-53"></a> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span><span class='hs-layout'>,</span> <span class='hs-conid'>Read</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span><span class='hs-layout'>)</span>
<a name="line-54"></a><span class='hs-cpp'># endif</span>
<a name="line-55"></a><span class='hs-cpp'>#else /* __HADDOCK__ (which can't figure these out by itself) */</span>
<a name="line-56"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Eq</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-57"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Read</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Read</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-58"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-59"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Data</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Data</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-60"></a><span class='hs-cpp'>#endif</span>
<a name="line-61"></a><a name="Forest"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Forest</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-62"></a>
<a name="line-63"></a><span class='hs-cpp'>#include "Typeable.h"</span>
<a name="line-64"></a><span class='hs-conid'>INSTANCE_TYPEABLE1</span><span class='hs-layout'>(</span><span class='hs-conid'>Tree</span><span class='hs-layout'>,</span><span class='hs-varid'>treeTc</span><span class='hs-layout'>,</span><span class='hs-str'>"Tree"</span><span class='hs-layout'>)</span>
<a name="line-65"></a>
<a name="line-66"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-conid'>Tree</span> <span class='hs-keyword'>where</span>
<a name="line-67"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>x</span> <span class='hs-varid'>ts</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Node</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>ts</span><span class='hs-layout'>)</span>
<a name="line-68"></a>
<a name="line-69"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-conid'>Tree</span> <span class='hs-keyword'>where</span>
<a name="line-70"></a> <span class='hs-varid'>pure</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Node</span> <span class='hs-varid'>x</span> <span class='hs-conid'>[]</span>
<a name="line-71"></a> <span class='hs-conid'>Node</span> <span class='hs-varid'>f</span> <span class='hs-varid'>tfs</span> <span class='hs-varop'><*></span> <span class='hs-varid'>tx</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>x</span> <span class='hs-varid'>txs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-72"></a> <span class='hs-conid'>Node</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'><$></span><span class='hs-layout'>)</span> <span class='hs-varid'>txs</span> <span class='hs-varop'>++</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varop'><*></span> <span class='hs-varid'>tx</span><span class='hs-layout'>)</span> <span class='hs-varid'>tfs</span><span class='hs-layout'>)</span>
<a name="line-73"></a>
<a name="line-74"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monad</span> <span class='hs-conid'>Tree</span> <span class='hs-keyword'>where</span>
<a name="line-75"></a> <span class='hs-varid'>return</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Node</span> <span class='hs-varid'>x</span> <span class='hs-conid'>[]</span>
<a name="line-76"></a> <span class='hs-conid'>Node</span> <span class='hs-varid'>x</span> <span class='hs-varid'>ts</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Node</span> <span class='hs-varid'>x'</span> <span class='hs-layout'>(</span><span class='hs-varid'>ts'</span> <span class='hs-varop'>++</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varop'>>>=</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>ts</span><span class='hs-layout'>)</span>
<a name="line-77"></a> <span class='hs-keyword'>where</span> <span class='hs-conid'>Node</span> <span class='hs-varid'>x'</span> <span class='hs-varid'>ts'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span>
<a name="line-78"></a>
<a name="line-79"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Traversable</span> <span class='hs-conid'>Tree</span> <span class='hs-keyword'>where</span>
<a name="line-80"></a> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>x</span> <span class='hs-varid'>ts</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Node</span> <span class='hs-varop'><$></span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varop'><*></span> <span class='hs-varid'>traverse</span> <span class='hs-layout'>(</span><span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>ts</span>
<a name="line-81"></a>
<a name="line-82"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Foldable</span> <span class='hs-conid'>Tree</span> <span class='hs-keyword'>where</span>
<a name="line-83"></a> <span class='hs-varid'>foldMap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>x</span> <span class='hs-varid'>ts</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>foldMap</span> <span class='hs-layout'>(</span><span class='hs-varid'>foldMap</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>ts</span>
<a name="line-84"></a>
<a name="line-85"></a><a name="drawTree"></a><span class='hs-comment'>-- | Neat 2-dimensional drawing of a tree.</span>
<a name="line-86"></a><span class='hs-definition'>drawTree</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Tree</span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>String</span>
<a name="line-87"></a><span class='hs-definition'>drawTree</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unlines</span> <span class='hs-varop'>.</span> <span class='hs-varid'>draw</span>
<a name="line-88"></a>
<a name="line-89"></a><a name="drawForest"></a><span class='hs-comment'>-- | Neat 2-dimensional drawing of a forest.</span>
<a name="line-90"></a><span class='hs-definition'>drawForest</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Forest</span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>String</span>
<a name="line-91"></a><span class='hs-definition'>drawForest</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unlines</span> <span class='hs-varop'>.</span> <span class='hs-varid'>map</span> <span class='hs-varid'>drawTree</span>
<a name="line-92"></a>
<a name="line-93"></a><a name="draw"></a><span class='hs-definition'>draw</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Tree</span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>String</span><span class='hs-keyglyph'>]</span>
<a name="line-94"></a><span class='hs-definition'>draw</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>x</span> <span class='hs-varid'>ts0</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>drawSubTrees</span> <span class='hs-varid'>ts0</span>
<a name="line-95"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>drawSubTrees</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-96"></a> <span class='hs-varid'>drawSubTrees</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>t</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>=</span>
<a name="line-97"></a> <span class='hs-str'>"|"</span> <span class='hs-conop'>:</span> <span class='hs-varid'>shift</span> <span class='hs-str'>"`- "</span> <span class='hs-str'>" "</span> <span class='hs-layout'>(</span><span class='hs-varid'>draw</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<a name="line-98"></a> <span class='hs-varid'>drawSubTrees</span> <span class='hs-layout'>(</span><span class='hs-varid'>t</span><span class='hs-conop'>:</span><span class='hs-varid'>ts</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-99"></a> <span class='hs-str'>"|"</span> <span class='hs-conop'>:</span> <span class='hs-varid'>shift</span> <span class='hs-str'>"+- "</span> <span class='hs-str'>"| "</span> <span class='hs-layout'>(</span><span class='hs-varid'>draw</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-varop'>++</span> <span class='hs-varid'>drawSubTrees</span> <span class='hs-varid'>ts</span>
<a name="line-100"></a>
<a name="line-101"></a> <span class='hs-varid'>shift</span> <span class='hs-varid'>first</span> <span class='hs-varid'>other</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>zipWith</span> <span class='hs-layout'>(</span><span class='hs-varop'>++</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>first</span> <span class='hs-conop'>:</span> <span class='hs-varid'>repeat</span> <span class='hs-varid'>other</span><span class='hs-layout'>)</span>
<a name="line-102"></a>
<a name="line-103"></a><a name="flatten"></a><span class='hs-comment'>-- | The elements of a tree in pre-order.</span>
<a name="line-104"></a><span class='hs-definition'>flatten</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-105"></a><span class='hs-definition'>flatten</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>squish</span> <span class='hs-varid'>t</span> <span class='hs-conid'>[]</span>
<a name="line-106"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>squish</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>x</span> <span class='hs-varid'>ts</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-conid'>Prelude</span><span class='hs-varop'>.</span><span class='hs-varid'>foldr</span> <span class='hs-varid'>squish</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ts</span>
<a name="line-107"></a>
<a name="line-108"></a><a name="levels"></a><span class='hs-comment'>-- | Lists of nodes at each level of the tree.</span>
<a name="line-109"></a><span class='hs-definition'>levels</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span>
<a name="line-110"></a><span class='hs-definition'>levels</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>rootLabel</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-111"></a> <span class='hs-varid'>takeWhile</span> <span class='hs-layout'>(</span><span class='hs-varid'>not</span> <span class='hs-varop'>.</span> <span class='hs-varid'>null</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-112"></a> <span class='hs-varid'>iterate</span> <span class='hs-layout'>(</span><span class='hs-varid'>concatMap</span> <span class='hs-varid'>subForest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>t</span><span class='hs-keyglyph'>]</span>
<a name="line-113"></a>
<a name="line-114"></a><a name="unfoldTree"></a><span class='hs-comment'>-- | Build a tree from a seed value</span>
<a name="line-115"></a><span class='hs-definition'>unfoldTree</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span>
<a name="line-116"></a><span class='hs-definition'>unfoldTree</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>in</span> <span class='hs-conid'>Node</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-varid'>unfoldForest</span> <span class='hs-varid'>f</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span>
<a name="line-117"></a>
<a name="line-118"></a><a name="unfoldForest"></a><span class='hs-comment'>-- | Build a forest from a list of seed values</span>
<a name="line-119"></a><span class='hs-definition'>unfoldForest</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Forest</span> <span class='hs-varid'>a</span>
<a name="line-120"></a><span class='hs-definition'>unfoldForest</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>unfoldTree</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-121"></a>
<a name="line-122"></a><a name="unfoldTreeM"></a><span class='hs-comment'>-- | Monadic tree builder, in depth-first order</span>
<a name="line-123"></a><span class='hs-definition'>unfoldTreeM</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-124"></a><span class='hs-definition'>unfoldTreeM</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-125"></a> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span>
<a name="line-126"></a> <span class='hs-varid'>ts</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>unfoldForestM</span> <span class='hs-varid'>f</span> <span class='hs-varid'>bs</span>
<a name="line-127"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>a</span> <span class='hs-varid'>ts</span><span class='hs-layout'>)</span>
<a name="line-128"></a>
<a name="line-129"></a><span class='hs-comment'>-- | Monadic forest builder, in depth-first order</span>
<a name="line-130"></a><span class='hs-cpp'>#ifndef __NHC__</span>
<a name="line-131"></a><a name="unfoldForestM"></a><span class='hs-definition'>unfoldForestM</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Forest</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-132"></a><span class='hs-cpp'>#endif</span>
<a name="line-133"></a><span class='hs-definition'>unfoldForestM</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Prelude</span><span class='hs-varop'>.</span><span class='hs-varid'>mapM</span> <span class='hs-layout'>(</span><span class='hs-varid'>unfoldTreeM</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-134"></a>
<a name="line-135"></a><a name="unfoldTreeM_BF"></a><span class='hs-comment'>-- | Monadic tree builder, in breadth-first order,</span>
<a name="line-136"></a><span class='hs-comment'>-- using an algorithm adapted from</span>
<a name="line-137"></a><span class='hs-comment'>-- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,</span>
<a name="line-138"></a><span class='hs-comment'>-- by Chris Okasaki, /ICFP'00/.</span>
<a name="line-139"></a><span class='hs-definition'>unfoldTreeM_BF</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-140"></a><span class='hs-definition'>unfoldTreeM_BF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftM</span> <span class='hs-varid'>getElement</span> <span class='hs-varop'>$</span> <span class='hs-varid'>unfoldForestQ</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>singleton</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-141"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>getElement</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>viewl</span> <span class='hs-varid'>xs</span> <span class='hs-keyword'>of</span>
<a name="line-142"></a> <span class='hs-varid'>x</span> <span class='hs-conop'>:<</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>x</span>
<a name="line-143"></a> <span class='hs-conid'>EmptyL</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>error</span> <span class='hs-str'>"unfoldTreeM_BF"</span>
<a name="line-144"></a>
<a name="line-145"></a><a name="unfoldForestM_BF"></a><span class='hs-comment'>-- | Monadic forest builder, in breadth-first order,</span>
<a name="line-146"></a><span class='hs-comment'>-- using an algorithm adapted from</span>
<a name="line-147"></a><span class='hs-comment'>-- /Breadth-First Numbering: Lessons from a Small Exercise in Algorithm Design/,</span>
<a name="line-148"></a><span class='hs-comment'>-- by Chris Okasaki, /ICFP'00/.</span>
<a name="line-149"></a><span class='hs-definition'>unfoldForestM_BF</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Forest</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-150"></a><span class='hs-definition'>unfoldForestM_BF</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftM</span> <span class='hs-varid'>toList</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unfoldForestQ</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fromList</span>
<a name="line-151"></a>
<a name="line-152"></a><a name="unfoldForestQ"></a><span class='hs-comment'>-- takes a sequence (queue) of seeds</span>
<a name="line-153"></a><span class='hs-comment'>-- produces a sequence (reversed queue) of trees of the same length</span>
<a name="line-154"></a><span class='hs-definition'>unfoldForestQ</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Seq</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Seq</span> <span class='hs-layout'>(</span><span class='hs-conid'>Tree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-155"></a><span class='hs-definition'>unfoldForestQ</span> <span class='hs-varid'>f</span> <span class='hs-varid'>aQ</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>viewl</span> <span class='hs-varid'>aQ</span> <span class='hs-keyword'>of</span>
<a name="line-156"></a> <span class='hs-conid'>EmptyL</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-varid'>empty</span>
<a name="line-157"></a> <span class='hs-varid'>a</span> <span class='hs-conop'>:<</span> <span class='hs-varid'>aQ'</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-158"></a> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-159"></a> <span class='hs-varid'>tQ</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>unfoldForestQ</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Prelude</span><span class='hs-varop'>.</span><span class='hs-varid'>foldl</span> <span class='hs-layout'>(</span><span class='hs-varop'>|></span><span class='hs-layout'>)</span> <span class='hs-varid'>aQ'</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span>
<a name="line-160"></a> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>tQ'</span><span class='hs-layout'>,</span> <span class='hs-varid'>ts</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>splitOnto</span> <span class='hs-conid'>[]</span> <span class='hs-keyword'>as</span> <span class='hs-varid'>tQ</span>
<a name="line-161"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>b</span> <span class='hs-varid'>ts</span> <span class='hs-varop'><|</span> <span class='hs-varid'>tQ'</span><span class='hs-layout'>)</span>
<a name="line-162"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>splitOnto</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a'</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b'</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Seq</span> <span class='hs-varid'>a'</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>Seq</span> <span class='hs-varid'>a'</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a'</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-163"></a> <span class='hs-varid'>splitOnto</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span><span class='hs-layout'>,</span> <span class='hs-keyword'>as</span><span class='hs-layout'>)</span>
<a name="line-164"></a> <span class='hs-varid'>splitOnto</span> <span class='hs-keyword'>as</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-conop'>:</span><span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>viewr</span> <span class='hs-varid'>q</span> <span class='hs-keyword'>of</span>
<a name="line-165"></a> <span class='hs-varid'>q'</span> <span class='hs-conop'>:></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>splitOnto</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-conop'>:</span><span class='hs-keyword'>as</span><span class='hs-layout'>)</span> <span class='hs-varid'>bs</span> <span class='hs-varid'>q'</span>
<a name="line-166"></a> <span class='hs-conid'>EmptyR</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>error</span> <span class='hs-str'>"unfoldForestQ"</span>
</pre></body>
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