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% (c) The University of Glasgow 2006
% (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
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Bag: an unordered collection with duplicates
\begin{code}
<pre><a name="line-1"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Bag</span> <span class='hs-layout'>(</span>
<a name="line-2"></a> <span class='hs-conid'>Bag</span><span class='hs-layout'>,</span> <span class='hs-comment'>-- abstract type</span>
<a name="line-3"></a>
<a name="line-4"></a> <span class='hs-varid'>emptyBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>unitBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>unionBags</span><span class='hs-layout'>,</span> <span class='hs-varid'>unionManyBags</span><span class='hs-layout'>,</span>
<a name="line-5"></a> <span class='hs-varid'>mapBag</span><span class='hs-layout'>,</span>
<a name="line-6"></a> <span class='hs-varid'>elemBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>lengthBag</span><span class='hs-layout'>,</span>
<a name="line-7"></a> <span class='hs-varid'>filterBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>partitionBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>concatBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>foldBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>foldrBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>foldlBag</span><span class='hs-layout'>,</span>
<a name="line-8"></a> <span class='hs-varid'>isEmptyBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>isSingletonBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>consBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>snocBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>anyBag</span><span class='hs-layout'>,</span>
<a name="line-9"></a> <span class='hs-varid'>listToBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>bagToList</span><span class='hs-layout'>,</span>
<a name="line-10"></a> <span class='hs-varid'>mapBagM</span><span class='hs-layout'>,</span> <span class='hs-varid'>mapAndUnzipBagM</span>
<a name="line-11"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-12"></a>
<a name="line-13"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Outputable</span>
<a name="line-14"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Util</span> <span class='hs-layout'>(</span> <span class='hs-varid'>isSingleton</span> <span class='hs-layout'>)</span>
<a name="line-15"></a>
<a name="line-16"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span> <span class='hs-layout'>(</span> <span class='hs-varid'>partition</span> <span class='hs-layout'>)</span>
</pre>\end{code}
\begin{code}
<pre><a name="line-1"></a><a name="Bag"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-2"></a> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>EmptyBag</span>
<a name="line-3"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>UnitBag</span> <span class='hs-varid'>a</span>
<a name="line-4"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>TwoBags</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- INVARIANT: neither branch is empty</span>
<a name="line-5"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>ListBag</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-comment'>-- INVARIANT: the list is non-empty</span>
<a name="line-6"></a>
<a name="line-7"></a><a name="emptyBag"></a><span class='hs-definition'>emptyBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-8"></a><span class='hs-definition'>emptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>EmptyBag</span>
<a name="line-9"></a>
<a name="line-10"></a><a name="unitBag"></a><span class='hs-definition'>unitBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-11"></a><span class='hs-definition'>unitBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>UnitBag</span>
<a name="line-12"></a>
<a name="line-13"></a><a name="lengthBag"></a><span class='hs-definition'>lengthBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span>
<a name="line-14"></a><span class='hs-definition'>lengthBag</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0</span>
<a name="line-15"></a><span class='hs-definition'>lengthBag</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-layout'>{</span><span class='hs-layout'>}</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>1</span>
<a name="line-16"></a><span class='hs-definition'>lengthBag</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lengthBag</span> <span class='hs-varid'>b1</span> <span class='hs-varop'>+</span> <span class='hs-varid'>lengthBag</span> <span class='hs-varid'>b2</span>
<a name="line-17"></a><span class='hs-definition'>lengthBag</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>length</span> <span class='hs-varid'>xs</span>
<a name="line-18"></a>
<a name="line-19"></a><a name="elemBag"></a><span class='hs-definition'>elemBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-20"></a><span class='hs-definition'>elemBag</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-21"></a><span class='hs-definition'>elemBag</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y</span>
<a name="line-22"></a><span class='hs-definition'>elemBag</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`elemBag`</span> <span class='hs-varid'>b1</span> <span class='hs-varop'>||</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`elemBag`</span> <span class='hs-varid'>b2</span>
<a name="line-23"></a><span class='hs-definition'>elemBag</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>any</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-varid'>ys</span>
<a name="line-24"></a>
<a name="line-25"></a><a name="unionManyBags"></a><span class='hs-definition'>unionManyBags</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-26"></a><span class='hs-definition'>unionManyBags</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span> <span class='hs-varid'>unionBags</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-varid'>xs</span>
<a name="line-27"></a>
<a name="line-28"></a><span class='hs-comment'>-- This one is a bit stricter! The bag will get completely evaluated.</span>
<a name="line-29"></a>
<a name="line-30"></a><a name="unionBags"></a><span class='hs-definition'>unionBags</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-31"></a><span class='hs-definition'>unionBags</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-32"></a><span class='hs-definition'>unionBags</span> <span class='hs-varid'>b</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-33"></a><span class='hs-definition'>unionBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span>
<a name="line-34"></a>
<a name="line-35"></a><a name="consBag"></a><span class='hs-definition'>consBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-36"></a><a name="snocBag"></a><span class='hs-definition'>snocBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-37"></a>
<a name="line-38"></a><span class='hs-definition'>consBag</span> <span class='hs-varid'>elt</span> <span class='hs-varid'>bag</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>unitBag</span> <span class='hs-varid'>elt</span><span class='hs-layout'>)</span> <span class='hs-varop'>`unionBags`</span> <span class='hs-varid'>bag</span>
<a name="line-39"></a><span class='hs-definition'>snocBag</span> <span class='hs-varid'>bag</span> <span class='hs-varid'>elt</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bag</span> <span class='hs-varop'>`unionBags`</span> <span class='hs-layout'>(</span><span class='hs-varid'>unitBag</span> <span class='hs-varid'>elt</span><span class='hs-layout'>)</span>
<a name="line-40"></a>
<a name="line-41"></a><a name="isEmptyBag"></a><span class='hs-definition'>isEmptyBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-42"></a><span class='hs-definition'>isEmptyBag</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-43"></a><span class='hs-definition'>isEmptyBag</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span> <span class='hs-comment'>-- NB invariants</span>
<a name="line-44"></a>
<a name="line-45"></a><a name="isSingletonBag"></a><span class='hs-definition'>isSingletonBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-46"></a><span class='hs-definition'>isSingletonBag</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-47"></a><span class='hs-definition'>isSingletonBag</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-48"></a><span class='hs-definition'>isSingletonBag</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span> <span class='hs-comment'>-- Neither is empty</span>
<a name="line-49"></a><span class='hs-definition'>isSingletonBag</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>isSingleton</span> <span class='hs-varid'>xs</span>
<a name="line-50"></a>
<a name="line-51"></a><a name="filterBag"></a><span class='hs-definition'>filterBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-52"></a><span class='hs-definition'>filterBag</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>EmptyBag</span>
<a name="line-53"></a><span class='hs-definition'>filterBag</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>b</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>val</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>val</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>else</span> <span class='hs-conid'>EmptyBag</span>
<a name="line-54"></a><span class='hs-definition'>filterBag</span> <span class='hs-varid'>pred</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sat1</span> <span class='hs-varop'>`unionBags`</span> <span class='hs-varid'>sat2</span>
<a name="line-55"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>sat1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>filterBag</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>b1</span>
<a name="line-56"></a> <span class='hs-varid'>sat2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>filterBag</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>b2</span>
<a name="line-57"></a><span class='hs-definition'>filterBag</span> <span class='hs-varid'>pred</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>vs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>listToBag</span> <span class='hs-layout'>(</span><span class='hs-varid'>filter</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>vs</span><span class='hs-layout'>)</span>
<a name="line-58"></a>
<a name="line-59"></a><a name="anyBag"></a><span class='hs-definition'>anyBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-60"></a><span class='hs-definition'>anyBag</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-61"></a><span class='hs-definition'>anyBag</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>p</span> <span class='hs-varid'>v</span>
<a name="line-62"></a><span class='hs-definition'>anyBag</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>anyBag</span> <span class='hs-varid'>p</span> <span class='hs-varid'>b1</span> <span class='hs-varop'>||</span> <span class='hs-varid'>anyBag</span> <span class='hs-varid'>p</span> <span class='hs-varid'>b2</span>
<a name="line-63"></a><span class='hs-definition'>anyBag</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>any</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span>
<a name="line-64"></a>
<a name="line-65"></a><a name="concatBag"></a><span class='hs-definition'>concatBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bag</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-66"></a><span class='hs-definition'>concatBag</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>EmptyBag</span>
<a name="line-67"></a><span class='hs-definition'>concatBag</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-68"></a><span class='hs-definition'>concatBag</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>concatBag</span> <span class='hs-varid'>b1</span> <span class='hs-varop'>`unionBags`</span> <span class='hs-varid'>concatBag</span> <span class='hs-varid'>b2</span>
<a name="line-69"></a><span class='hs-definition'>concatBag</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unionManyBags</span> <span class='hs-varid'>bs</span>
<a name="line-70"></a>
<a name="line-71"></a><a name="partitionBag"></a><span class='hs-definition'>partitionBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-comment'>{- Satisfy predictate -}</span><span class='hs-layout'>,</span>
<a name="line-72"></a> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-comment'>{- Don't -}</span><span class='hs-layout'>)</span>
<a name="line-73"></a><span class='hs-definition'>partitionBag</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>EmptyBag</span><span class='hs-layout'>,</span> <span class='hs-conid'>EmptyBag</span><span class='hs-layout'>)</span>
<a name="line-74"></a><span class='hs-definition'>partitionBag</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>b</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>val</span><span class='hs-layout'>)</span>
<a name="line-75"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>val</span> <span class='hs-keyword'>then</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>EmptyBag</span><span class='hs-layout'>)</span> <span class='hs-keyword'>else</span> <span class='hs-layout'>(</span><span class='hs-conid'>EmptyBag</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-76"></a><span class='hs-definition'>partitionBag</span> <span class='hs-varid'>pred</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span>
<a name="line-77"></a> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>sat1</span> <span class='hs-varop'>`unionBags`</span> <span class='hs-varid'>sat2</span><span class='hs-layout'>,</span> <span class='hs-varid'>fail1</span> <span class='hs-varop'>`unionBags`</span> <span class='hs-varid'>fail2</span><span class='hs-layout'>)</span>
<a name="line-78"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>sat1</span><span class='hs-layout'>,</span> <span class='hs-varid'>fail1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>partitionBag</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>b1</span>
<a name="line-79"></a> <span class='hs-layout'>(</span><span class='hs-varid'>sat2</span><span class='hs-layout'>,</span> <span class='hs-varid'>fail2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>partitionBag</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>b2</span>
<a name="line-80"></a><span class='hs-definition'>partitionBag</span> <span class='hs-varid'>pred</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>vs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>listToBag</span> <span class='hs-varid'>sats</span><span class='hs-layout'>,</span> <span class='hs-varid'>listToBag</span> <span class='hs-varid'>fails</span><span class='hs-layout'>)</span>
<a name="line-81"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>sats</span><span class='hs-layout'>,</span> <span class='hs-varid'>fails</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>partition</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>vs</span>
<a name="line-82"></a>
<a name="line-83"></a>
<a name="line-84"></a><a name="foldBag"></a><span class='hs-definition'>foldBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- Replace TwoBags with this; should be associative</span>
<a name="line-85"></a> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- Replace UnitBag with this</span>
<a name="line-86"></a> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-comment'>-- Replace EmptyBag with this</span>
<a name="line-87"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-88"></a> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span>
<a name="line-89"></a>
<a name="line-90"></a><span class='hs-comment'>{- Standard definition
<a name="line-91"></a>foldBag t u e EmptyBag = e
<a name="line-92"></a>foldBag t u e (UnitBag x) = u x
<a name="line-93"></a>foldBag t u e (TwoBags b1 b2) = (foldBag t u e b1) `t` (foldBag t u e b2)
<a name="line-94"></a>foldBag t u e (ListBag xs) = foldr (t.u) e xs
<a name="line-95"></a>-}</span>
<a name="line-96"></a>
<a name="line-97"></a><span class='hs-comment'>-- More tail-recursive definition, exploiting associativity of "t"</span>
<a name="line-98"></a><span class='hs-definition'>foldBag</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>e</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>e</span>
<a name="line-99"></a><span class='hs-definition'>foldBag</span> <span class='hs-varid'>t</span> <span class='hs-varid'>u</span> <span class='hs-varid'>e</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>u</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`t`</span> <span class='hs-varid'>e</span>
<a name="line-100"></a><span class='hs-definition'>foldBag</span> <span class='hs-varid'>t</span> <span class='hs-varid'>u</span> <span class='hs-varid'>e</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldBag</span> <span class='hs-varid'>t</span> <span class='hs-varid'>u</span> <span class='hs-layout'>(</span><span class='hs-varid'>foldBag</span> <span class='hs-varid'>t</span> <span class='hs-varid'>u</span> <span class='hs-varid'>e</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-varid'>b1</span>
<a name="line-101"></a><span class='hs-definition'>foldBag</span> <span class='hs-varid'>t</span> <span class='hs-varid'>u</span> <span class='hs-varid'>e</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span> <span class='hs-layout'>(</span><span class='hs-varid'>t</span><span class='hs-varop'>.</span><span class='hs-varid'>u</span><span class='hs-layout'>)</span> <span class='hs-varid'>e</span> <span class='hs-varid'>xs</span>
<a name="line-102"></a>
<a name="line-103"></a><a name="foldrBag"></a><span class='hs-definition'>foldrBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span>
<a name="line-104"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-105"></a> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span>
<a name="line-106"></a>
<a name="line-107"></a><span class='hs-definition'>foldrBag</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>z</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>z</span>
<a name="line-108"></a><span class='hs-definition'>foldrBag</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k</span> <span class='hs-varid'>x</span> <span class='hs-varid'>z</span>
<a name="line-109"></a><span class='hs-definition'>foldrBag</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldrBag</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-varid'>foldrBag</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-varid'>b1</span>
<a name="line-110"></a><span class='hs-definition'>foldrBag</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-varid'>xs</span>
<a name="line-111"></a>
<a name="line-112"></a><a name="foldlBag"></a><span class='hs-definition'>foldlBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span>
<a name="line-113"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-114"></a> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span>
<a name="line-115"></a>
<a name="line-116"></a><span class='hs-definition'>foldlBag</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>z</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>z</span>
<a name="line-117"></a><span class='hs-definition'>foldlBag</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-varid'>x</span>
<a name="line-118"></a><span class='hs-definition'>foldlBag</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldlBag</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-varid'>foldlBag</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-varid'>b1</span><span class='hs-layout'>)</span> <span class='hs-varid'>b2</span>
<a name="line-119"></a><span class='hs-definition'>foldlBag</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldl</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-varid'>xs</span>
<a name="line-120"></a>
<a name="line-121"></a>
<a name="line-122"></a><a name="mapBag"></a><span class='hs-definition'>mapBag</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>b</span>
<a name="line-123"></a><span class='hs-definition'>mapBag</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>EmptyBag</span>
<a name="line-124"></a><span class='hs-definition'>mapBag</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>UnitBag</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-125"></a><span class='hs-definition'>mapBag</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>TwoBags</span> <span class='hs-layout'>(</span><span class='hs-varid'>mapBag</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>mapBag</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span>
<a name="line-126"></a><span class='hs-definition'>mapBag</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ListBag</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-127"></a>
<a name="line-128"></a><a name="mapBagM"></a><span class='hs-definition'>mapBagM</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'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bag</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-129"></a><span class='hs-definition'>mapBagM</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-conid'>EmptyBag</span>
<a name="line-130"></a><span class='hs-definition'>mapBagM</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span>
<a name="line-131"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span>
<a name="line-132"></a><span class='hs-definition'>mapBagM</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>r1</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>mapBagM</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b1</span>
<a name="line-133"></a> <span class='hs-varid'>r2</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>mapBagM</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b2</span>
<a name="line-134"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>r1</span> <span class='hs-varid'>r2</span><span class='hs-layout'>)</span>
<a name="line-135"></a><span class='hs-definition'>mapBagM</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>rs</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>mapM</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span>
<a name="line-136"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>rs</span><span class='hs-layout'>)</span>
<a name="line-137"></a>
<a name="line-138"></a><a name="mapAndUnzipBagM"></a><span class='hs-definition'>mapAndUnzipBagM</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'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bag</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bag</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-139"></a><span class='hs-definition'>mapAndUnzipBagM</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>EmptyBag</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-conid'>EmptyBag</span><span class='hs-layout'>,</span> <span class='hs-conid'>EmptyBag</span><span class='hs-layout'>)</span>
<a name="line-140"></a><span class='hs-definition'>mapAndUnzipBagM</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-layout'>(</span><span class='hs-varid'>r</span><span class='hs-layout'>,</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span>
<a name="line-141"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-conid'>UnitBag</span> <span class='hs-varid'>r</span><span class='hs-layout'>,</span> <span class='hs-conid'>UnitBag</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-142"></a><span class='hs-definition'>mapAndUnzipBagM</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-layout'>(</span><span class='hs-varid'>r1</span><span class='hs-layout'>,</span><span class='hs-varid'>s1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>mapAndUnzipBagM</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b1</span>
<a name="line-143"></a> <span class='hs-layout'>(</span><span class='hs-varid'>r2</span><span class='hs-layout'>,</span><span class='hs-varid'>s2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>mapAndUnzipBagM</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b2</span>
<a name="line-144"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoBags</span> <span class='hs-varid'>r1</span> <span class='hs-varid'>r2</span><span class='hs-layout'>,</span> <span class='hs-conid'>TwoBags</span> <span class='hs-varid'>s1</span> <span class='hs-varid'>s2</span><span class='hs-layout'>)</span>
<a name="line-145"></a><span class='hs-definition'>mapAndUnzipBagM</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>ts</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>mapM</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span>
<a name="line-146"></a> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>rs</span><span class='hs-layout'>,</span><span class='hs-varid'>ss</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unzip</span> <span class='hs-varid'>ts</span>
<a name="line-147"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-conid'>ListBag</span> <span class='hs-varid'>rs</span><span class='hs-layout'>,</span> <span class='hs-conid'>ListBag</span> <span class='hs-varid'>ss</span><span class='hs-layout'>)</span>
<a name="line-148"></a>
<a name="line-149"></a><a name="listToBag"></a><span class='hs-definition'>listToBag</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-conid'>Bag</span> <span class='hs-varid'>a</span>
<a name="line-150"></a><span class='hs-definition'>listToBag</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>EmptyBag</span>
<a name="line-151"></a><span class='hs-definition'>listToBag</span> <span class='hs-varid'>vs</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ListBag</span> <span class='hs-varid'>vs</span>
<a name="line-152"></a>
<a name="line-153"></a><a name="bagToList"></a><span class='hs-definition'>bagToList</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bag</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-154"></a><span class='hs-definition'>bagToList</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldrBag</span> <span class='hs-layout'>(</span><span class='hs-conop'>:</span><span class='hs-layout'>)</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>b</span>
</pre>\end{code}
\begin{code}
<pre><a name="line-1"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Outputable</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Outputable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bag</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-2"></a> <span class='hs-varid'>ppr</span> <span class='hs-varid'>bag</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>braces</span> <span class='hs-layout'>(</span><span class='hs-varid'>pprWithCommas</span> <span class='hs-varid'>ppr</span> <span class='hs-layout'>(</span><span class='hs-varid'>bagToList</span> <span class='hs-varid'>bag</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
</pre>\end{code}
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