148 lines
15 KiB
Markdown
148 lines
15 KiB
Markdown
---
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layout: default
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title: "Maps"
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parent: Composite
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ancestor: Funcons-beta
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---
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[Funcons-beta] : [Maps.cbs]
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-----------------------------
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### Maps
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<div class="highlighter-rouge"><pre class="highlight"><code>[
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<i class="keyword">Type</i> <span class="name"><a href="#Name_maps">maps</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_map">map</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_map-elements">map-elements</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_map-lookup">map-lookup</a></span> <i class="keyword">Alias</i> <span class="name"><a href="#Name_lookup">lookup</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_map-domain">map-domain</a></span> <i class="keyword">Alias</i> <span class="name"><a href="#Name_dom">dom</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_map-override">map-override</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_map-unite">map-unite</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_map-delete">map-delete</a></span>
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]</code></pre></div>
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Meta-variables</i>
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<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>
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<span id="PartVariable_T?"><i class="var">T<sup class="sup">?</sup></i></span> <: <span class="name"><a href="../../Value-Types/index.html#Name_values">values</a></span><sup class="sup">?</sup></code></pre></div>
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Type</i>
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<span class="name"><span id="Name_maps">maps</span></span>(<span id="Variable82_GT"><i class="var">GT</i></span>, <span id="Variable89_T?"><i class="var">T<sup class="sup">?</sup></i></span>)</code></pre></div>
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<code><span class="name"><a href="#Name_maps">maps</a></span>(<i class="var">GT</i>, <i class="var">T<sup class="sup">?</sup></i>)</code> is the type of possibly-empty finite maps from values of
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type <code><i class="var">GT</i></code> to optional values of type <code><i class="var">T<sup class="sup">?</sup></i></code>.
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
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<span class="name"><span id="Name_map">map</span></span>(_:(<span class="name"><a href="../Tuples/index.html#Name_tuples">tuples</a></span>(<span id="Variable171_GT"><i class="var">GT</i></span>, <span id="Variable177_T?"><i class="var">T<sup class="sup">?</sup></i></span>))<sup class="sup">*</sup>) : =>(<span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable206_GT"><i class="var">GT</i></span>, <span id="Variable212_T?"><i class="var">T<sup class="sup">?</sup></i></span>))<sup class="sup">?</sup></code></pre></div>
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<code><span class="name"><a href="#Name_map">map</a></span>(<span class="name"><a href="../Tuples/index.html#Name_tuple">tuple</a></span>(<i class="var">K<sub class="sub">1</sub></i>, <i class="var">V<sub class="sub">1</sub><sup class="sup">?</sup></i>), ..., <span class="name"><a href="../Tuples/index.html#Name_tuple">tuple</a></span>(<i class="var">Kn</i>, <i class="var">Vn<sup class="sup">?</sup></i>))</code> constructs a map from
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<code><i class="var">K<sub class="sub">1</sub></i></code> to <code><i class="var">V<sub class="sub">1</sub><sup class="sup">?</sup></i></code>, ..., <code><i class="var">Kn</i></code> to <code><i class="var">Vn<sup class="sup">?</sup></i></code>, provided that <code><i class="var">K<sub class="sub">1</sub></i></code>, ..., <code><i class="var">Kn</i></code>
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are distinct, otherwise the result is <code>( )</code>.
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Note that <code><span class="name"><a href="#Name_map">map</a></span>(...)</code> is not a constructor operation.
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The built-in notation <code>{<i class="var">K<sub class="sub">1</sub></i>|-><i class="var">V<sub class="sub">1</sub><sup class="sup">?</sup></i>, ..., <i class="var">Kn</i>|-><i class="var">Vn<sup class="sup">?</sup></i>}</code> is equivalent to
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<code><span class="name"><a href="#Name_map">map</a></span>(<span class="name"><a href="../Tuples/index.html#Name_tuple">tuple</a></span>(<i class="var">K<sub class="sub">1</sub></i>, <i class="var">V<sub class="sub">1</sub><sup class="sup">?</sup></i>), ..., <span class="name"><a href="../Tuples/index.html#Name_tuple">tuple</a></span>(<i class="var">Kn</i>, <i class="var">Vn<sup class="sup">?</sup></i>))</code>. Note however that in general,
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maps cannot be identified with sets of tuples, since the values <code><i class="var">Vi<sup class="sup">?</sup></i></code> are
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not restricted to <code><span class="name"><a href="../../Value-Types/index.html#Name_ground-values">ground-values</a></span></code>.
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When <code><i class="var">T<sup class="sup">?</sup></i> <: <span class="name"><a href="../../Value-Types/index.html#Name_types">types</a></span></code>, <code><span class="name"><a href="#Name_maps">maps</a></span>(<i class="var">GT</i>, <i class="var">T<sup class="sup">?</sup></i>) <: <span class="name"><a href="../../Value-Types/index.html#Name_types">types</a></span></code>. The type <code><i class="var">MT</i>:<span class="name"><a href="#Name_maps">maps</a></span>(<i class="var">GT</i>, <i class="var">T<sup class="sup">?</sup></i>)</code>
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represents the set of value-maps <code><i class="var">MV</i>:<span class="name"><a href="#Name_maps">maps</a></span>(<i class="var">GT</i>, <span class="name"><a href="../../Value-Types/index.html#Name_values">values</a></span><sup class="sup">?</sup>)</code> such that
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<code><span class="name"><a href="#Name_dom">dom</a></span>(<i class="var">MV</i>)</code> is a subset of <code><span class="name"><a href="#Name_dom">dom</a></span>(<i class="var">MT</i>)</code> and for all <code><i class="var">K</i></code> in <code><span class="name"><a href="#Name_dom">dom</a></span>(<i class="var">MV</i>)</code>,
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<code><span class="name"><a href="#Name_map-lookup">map-lookup</a></span>(<i class="var">MV</i>, <i class="var">K</i>) : <span class="name"><a href="#Name_map-lookup">map-lookup</a></span>(<i class="var">MT</i>, <i class="var">K</i>)</code>.
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
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<span class="name"><span id="Name_map-elements">map-elements</span></span>(_:<span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable766_GT"><i class="var">GT</i></span>, <span id="Variable772_T?"><i class="var">T<sup class="sup">?</sup></i></span>)) : =>(<span class="name"><a href="../Tuples/index.html#Name_tuples">tuples</a></span>(<span id="Variable794_GT"><i class="var">GT</i></span>, <span id="Variable800_T?"><i class="var">T<sup class="sup">?</sup></i></span>))<sup class="sup">*</sup></code></pre></div>
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The sequence of tuples <code>(<span class="name"><a href="../Tuples/index.html#Name_tuple">tuple</a></span>(<i class="var">K<sub class="sub">1</sub></i>, <i class="var">V<sub class="sub">1</sub><sup class="sup">?</sup></i>), ..., <span class="name"><a href="../Tuples/index.html#Name_tuple">tuple</a></span>(<i class="var">Kn</i>, <i class="var">Vn<sup class="sup">?</sup></i>))</code> given by
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<code><span class="name"><a href="#Name_map-elements">map-elements</a></span>(<i class="var">M</i>)</code> contains each mapped value <code><i class="var">Ki</i></code> just once. The order of
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the elements is unspecified, and may vary between maps.
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Assert</i>
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<span class="name"><a href="#Name_map">map</a></span>(<span class="name"><a href="#Name_map-elements">map-elements</a></span>(<i class="var">M</i>)) == <i class="var">M</i></code></pre></div>
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
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<span class="name"><span id="Name_map-lookup">map-lookup</span></span>(_:<span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable951_GT"><i class="var">GT</i></span>, <span id="Variable957_T?"><i class="var">T<sup class="sup">?</sup></i></span>), <span id="Variable972_K"><i class="var">K</i></span>:<span id="Variable976_GT"><i class="var">GT</i></span>) : =>(<span id="Variable992_T?"><i class="var">T<sup class="sup">?</sup></i></span>)<sup class="sup">?</sup>
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<i class="keyword">Alias</i>
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<span class="name"><span id="Name_lookup">lookup</span></span> = <span class="name"><a href="#Name_map-lookup">map-lookup</a></span></code></pre></div>
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<code><span class="name"><a href="#Name_map-lookup">map-lookup</a></span>(<i class="var">M</i>,<i class="var">K</i>)</code> gives the optional value to which <code><i class="var">K</i></code> is mapped by <code><i class="var">M</i></code>,
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if any, and otherwise <code>( )</code>.
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
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<span class="name"><span id="Name_map-domain">map-domain</span></span>(_:<span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable1086_GT"><i class="var">GT</i></span>, <span id="Variable1092_T?"><i class="var">T<sup class="sup">?</sup></i></span>)) : =><span class="name"><a href="../Sets/index.html#Name_sets">sets</a></span>(<span id="Variable1114_GT"><i class="var">GT</i></span>)
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<i class="keyword">Alias</i>
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<span class="name"><span id="Name_dom">dom</span></span> = <span class="name"><a href="#Name_map-domain">map-domain</a></span></code></pre></div>
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<code><span class="name"><a href="#Name_map-domain">map-domain</a></span>(<i class="var">M</i>)</code> gives the set of values mapped by <code><i class="var">M</i></code>.
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<code><span class="name"><a href="#Name_map-lookup">map-lookup</a></span>(<i class="var">M</i>, <i class="var">K</i>)</code> is always <code>( )</code> when <code><i class="var">K</i></code> is not in <code><span class="name"><a href="#Name_map-domain">map-domain</a></span>(<i class="var">M</i>)</code>.
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
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<span class="name"><span id="Name_map-override">map-override</span></span>(_:(<span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable1247_GT"><i class="var">GT</i></span>, <span id="Variable1253_T?"><i class="var">T<sup class="sup">?</sup></i></span>))<sup class="sup">*</sup>) : =><span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable1282_GT"><i class="var">GT</i></span>,<span id="Variable1288_T?"><i class="var">T<sup class="sup">?</sup></i></span>)</code></pre></div>
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<code><span class="name"><a href="#Name_map-override">map-override</a></span>(...)</code> takes a sequence of maps. It returns the map whose
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domain is the union of their domains, and which maps each of those values
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to the same optional value as the first map in the sequence in whose domain
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it occurs
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.
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When the domains of the <code><i class="var">M<sup class="sup">*</sup></i></code> are disjoint, <code><span class="name"><a href="#Name_map-override">map-override</a></span>(<i class="var">M<sup class="sup">*</sup></i>)</code> is equivalent
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to <code><span class="name"><a href="#Name_map-unite">map-unite</a></span>(<i class="var">M<sup class="sup">*</sup></i>)</code>.
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
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<span class="name"><span id="Name_map-unite">map-unite</span></span>(_:(<span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable1389_GT"><i class="var">GT</i></span>, <span id="Variable1395_T?"><i class="var">T<sup class="sup">?</sup></i></span>))<sup class="sup">*</sup>) : =>(<span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable1424_GT"><i class="var">GT</i></span>, <span id="Variable1430_T?"><i class="var">T<sup class="sup">?</sup></i></span>))<sup class="sup">?</sup></code></pre></div>
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<code><span class="name"><a href="#Name_map-unite">map-unite</a></span>(...)</code> takes a sequence of maps. It returns the map whose
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domain is the union of their domains, and which maps each of those values
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to the same optional value as the map in the sequence in whose domain it occurs,
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provided that those domains are disjoint - otherwise the result is <code>( )</code>.
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
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<span class="name"><span id="Name_map-delete">map-delete</span></span>(_:<span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable1494_GT"><i class="var">GT</i></span>, <span id="Variable1500_T?"><i class="var">T<sup class="sup">?</sup></i></span>), _:<span class="name"><a href="../Sets/index.html#Name_sets">sets</a></span>(<span id="Variable1519_GT"><i class="var">GT</i></span>)) : =><span class="name"><a href="#Name_maps">maps</a></span>(<span id="Variable1541_GT"><i class="var">GT</i></span>, <span id="Variable1547_T?"><i class="var">T<sup class="sup">?</sup></i></span>)</code></pre></div>
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<code><span class="name"><a href="#Name_map-delete">map-delete</a></span>(<i class="var">M</i>, <i class="var">S</i>)</code> takes a map <code><i class="var">M</i></code> and a set of values <code><i class="var">S</i></code>, and returns the
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map obtained from <code><i class="var">M</i></code> by removing <code><i class="var">S</i></code> from its domain.
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Assert</i>
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<span class="name"><a href="#Name_map-domain">map-domain</a></span>(<span class="name"><a href="#Name_map-delete">map-delete</a></span>(<i class="var">M</i>, <i class="var">S</i>)) == <span class="name"><a href="../Sets/index.html#Name_set-difference">set-difference</a></span>(<span class="name"><a href="#Name_map-domain">map-domain</a></span>(<i class="var">M</i>), <i class="var">S</i>)</code></pre></div>
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____
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From the [PLanCompS Project] | [CBS-beta issues...] | [Suggest an improvement...]
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[Maps.cbs]: Maps.cbs
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"CBS SOURCE FILE"
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[Funcons-beta]: /CBS-beta/docs/Funcons-beta
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"FUNCONS-BETA"
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[Unstable-Funcons-beta]: /CBS-beta/docs/Unstable-Funcons-beta
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"UNSTABLE-FUNCONS-BETA"
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[Languages-beta]: /CBS-beta/docs/Languages-beta
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"LANGUAGES-BETA"
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[Unstable-Languages-beta]: /CBS-beta/docs/Unstable-Languages-beta
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"UNSTABLE-LANGUAGES-BETA"
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[CBS-beta]: /CBS-beta "CBS-BETA"
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[PLanCompS Project]: https://plancomps.github.io
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"PROGRAMMING LANGUAGE COMPONENTS AND SPECIFICATIONS PROJECT HOME PAGE"
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[CBS-beta issues...]: https://github.com/plancomps/CBS-beta/issues
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"CBS-BETA ISSUE REPORTS ON GITHUB"
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[Suggest an improvement...]: mailto:plancomps@gmail.com?Subject=CBS-beta%20-%20comment&Body=Re%3A%20CBS-beta%20specification%20at%20Values/Composite/Maps/Maps.cbs%0A%0AComment/Query/Issue/Suggestion%3A%0A%0A%0ASignature%3A%0A
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"GENERATE AN EMAIL TEMPLATE"
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