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+---
+layout: default
+title: "Multisets"
+parent: Composite
+ancestor: Funcons-beta
+
+---
+
+[Funcons-beta] : [Multisets.cbs]
+-----------------------------
+
+### Multisets (bags)
+
+<div class="highlighter-rouge"><pre class="highlight"><code>[
+  <i class="keyword">Type</i>   <span class="name"><a href="#Name_multisets">multisets</a></span>
+  <i class="keyword">Funcon</i> <span class="name"><a href="#Name_multiset">multiset</a></span>
+  <i class="keyword">Funcon</i> <span class="name"><a href="#Name_multiset-elements">multiset-elements</a></span>
+  <i class="keyword">Funcon</i> <span class="name"><a href="#Name_multiset-occurrences">multiset-occurrences</a></span>
+  <i class="keyword">Funcon</i> <span class="name"><a href="#Name_multiset-insert">multiset-insert</a></span>
+  <i class="keyword">Funcon</i> <span class="name"><a href="#Name_multiset-delete">multiset-delete</a></span>
+  <i class="keyword">Funcon</i> <span class="name"><a href="#Name_is-submultiset">is-submultiset</a></span>
+]</code></pre></div>
+
+
+
+<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Meta-variables</i>
+  <span id="PartVariable_GT"><i class="var">GT</i></span> <: <span class="name"><a href="../../Value-Types/index.html#Name_ground-values">ground-values</a></span></code></pre></div>
+
+
+
+<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Type</i>
+  <span class="name"><span id="Name_multisets">multisets</span></span>(<span id="Variable56_GT"><i class="var">GT</i></span>)</code></pre></div>
+
+  <code><span class="name"><a href="#Name_multisets">multisets</a></span>(<i class="var">GT</i>)</code> is the type of possibly-empty finite multisets of elements
+  of <code><i class="var">GT</i></code>. 
+
+
+
+<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
+  <span class="name"><span id="Name_multiset">multiset</span></span>(_:(<span id="Variable115_GT"><i class="var">GT</i></span>)<sup class="sup">*</sup>) : =><span class="name"><a href="#Name_multisets">multisets</a></span>(<span id="Variable137_GT"><i class="var">GT</i></span>)</code></pre></div>
+
+  Note that <code><span class="name"><a href="#Name_multiset">multiset</a></span>(...)</code> is not a constructor operation. The order of
+  argument values is ignored, but duplicates are significant, e.g., 
+  <code><span class="name"><a href="#Name_multiset">multiset</a></span>(1, 2, 2)</code> is equivalent to <code><span class="name"><a href="#Name_multiset">multiset</a></span>(2, 1, 2)</code>, but not to
+  <code><span class="name"><a href="#Name_multiset">multiset</a></span>(1, 2)</code> or <code><span class="name"><a href="#Name_multiset">multiset</a></span>(2, 1)</code>.
+
+
+
+<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i> 
+  <span class="name"><span id="Name_multiset-elements">multiset-elements</span></span>(_:<span class="name"><a href="#Name_multisets">multisets</a></span>(<span id="Variable267_GT"><i class="var">GT</i></span>)) : =>(<span id="Variable287_GT"><i class="var">GT</i></span>)<sup class="sup">*</sup></code></pre></div>
+
+  For each multiset <code><i class="var">MS</i></code>, the sequence of values <code><i class="var">V<sup class="sup">*</sup></i></code> returned by 
+  <code><span class="name"><a href="#Name_multiset-elements">multiset-elements</a></span>(<i class="var">MS</i>)</code> contains each element of <code><i class="var">MS</i></code> the same number of times
+  as <code><i class="var">MS</i></code> does.
+  The order of the values in <code><i class="var">V<sup class="sup">*</sup></i></code> is unspecified, and may vary between multisets.
+
+<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Assert</i>
+  <span class="name"><a href="#Name_multiset">multiset</a></span>(<span class="name"><a href="#Name_multiset-elements">multiset-elements</a></span>(<i class="var">S</i>)) == <i class="var">S</i></code></pre></div>
+
+
+
+<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
+  <span class="name"><span id="Name_multiset-occurrences">multiset-occurrences</span></span>(_:<span id="Variable426_GT"><i class="var">GT</i></span>, _:<span class="name"><a href="#Name_multisets">multisets</a></span>(<span id="Variable438_GT"><i class="var">GT</i></span>)) : =><span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span></code></pre></div>
+
+  <code><span class="name"><a href="#Name_multiset-occurrences">multiset-occurrences</a></span>(<i class="var">GV</i>, <i class="var">MS</i>)</code> returns the number of occurrences of <code><i class="var">GV</i></code>
+  in <code><i class="var">MS</i></code>. 
+
+
+
+<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
+  <span class="name"><span id="Name_multiset-insert">multiset-insert</span></span>(_:<span id="Variable527_GT"><i class="var">GT</i></span>, _:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>, _:<span class="name"><a href="#Name_multisets">multisets</a></span>(<span id="Variable547_GT"><i class="var">GT</i></span>)) : =><span class="name"><a href="#Name_multisets">multisets</a></span>(<span id="Variable570_GT"><i class="var">GT</i></span>)</code></pre></div>
+
+  <code><span class="name"><a href="#Name_multiset-insert">multiset-insert</a></span>(<i class="var">GV</i>, <i class="var">N</i>, <i class="var">MS</i>)</code> returns the multiset that differs from <code><i class="var">MS</i></code> 
+  by containing <code><i class="var">N</i></code> more copies of <code><i class="var">GV</i></code>.
+
+
+
+<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
+  <span class="name"><span id="Name_multiset-delete">multiset-delete</span></span>(_:<span class="name"><a href="#Name_multisets">multisets</a></span>(<span id="Variable667_GT"><i class="var">GT</i></span>), _:<span id="Variable684_GT"><i class="var">GT</i></span>, _:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : =><span class="name"><a href="#Name_multisets">multisets</a></span>(<span id="Variable709_GT"><i class="var">GT</i></span>)</code></pre></div>
+
+ <code><span class="name"><a href="#Name_multiset-delete">multiset-delete</a></span>(<i class="var">MS</i>, <i class="var">GV</i>, <i class="var">N</i>)</code> removes <code><i class="var">N</i></code> copies of <code><i class="var">V</i></code> from the multiset <code><i class="var">MS</i></code>,
+ or all copies of <code><i class="var">GV</i></code> if there are fewer than <code><i class="var">N</i></code> in <code><i class="var">MS</i></code>.
+
+
+
+<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
+  <span class="name"><span id="Name_is-submultiset">is-submultiset</span></span>(_:<span class="name"><a href="#Name_multisets">multisets</a></span>(<span id="Variable845_GT"><i class="var">GT</i></span>), _:<span class="name"><a href="#Name_multisets">multisets</a></span>(<span id="Variable863_GT"><i class="var">GT</i></span>)) : =><span class="name"><a href="../../Primitive/Booleans/index.html#Name_booleans">booleans</a></span></code></pre></div>
+
+  <code><span class="name"><a href="#Name_is-submultiset">is-submultiset</a></span>(<i class="var">MS<sub class="sub">1</sub></i>, <i class="var">MS<sub class="sub">2</sub></i>)</code> tests whether every element of <code><i class="var">MS<sub class="sub">1</sub></i></code> has equal or
+  fewer occurrences in <code><i class="var">MS<sub class="sub">1</sub></i></code> than in <code><i class="var">MS<sub class="sub">2</sub></i></code>. 
+
+
+
+____
+
+From the [PLanCompS Project] | [CBS-beta issues...] | [Suggest an improvement...]
+
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