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Introductory remark about order
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HeikoTheissen committed Jun 30, 2023
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Expand Up @@ -2750,7 +2750,7 @@ <h2 id="56-functions-on-aggregated-entities"><a name="FunctionsonAggregatedEntit
<hr />
<h1 id="6-hierarchical-transformations"><a name="HierarchicalTransformations" href="#HierarchicalTransformations">6 Hierarchical Transformations</a></h1>
<p>The transformations and the <code>rolluprecursive</code> operator defined in this section are called hierarchical, because they make use of a recursive hierarchy and are defined in terms of hierarchy functions introduced in the previous section.</p>
<p>With the exceptions of <code>traverse</code> and <code>rolluprecursive</code> whose fourth parameter ends with <code>traverse</code>, the hierarchical transformations do not define an order on the output set. An order can be reinstated by a subsequent <code>orderby</code> or <code>traverse</code> transformation or a <code>$orderby</code>.</p>
<p>The transformations <code>ancestors</code> and <code>descendants</code> do not define an order on the output set. An order can be imposed by a subsequent <code>orderby</code> or <code>traverse</code> transformation or a <code>$orderby</code>. The output set of <code>traverse</code> is in preorder order post order, and grouping with <code>rolluprecursive</code> orders its output set in analogy with <a href="#SimpleGrouping">simple grouping</a>.</p>
<p>The algorithmic descriptions of the transformations make use of a <em>union</em> of collections, this is defined as an unordered collection containing the items from all these collections and from which duplicates have been removed.</p>
<p>The notation <span class="math inline">\(u[t]\)</span> is used to denote the value of a property <span class="math inline">\(t\)</span>, possibly preceded by a type-cast segment, in an instance <span class="math inline">\(u\)</span>. It is also used to denote the value of a single-valued data aggregation path <span class="math inline">\(t\)</span>, evaluated relative to <span class="math inline">\(u\)</span>. The value of a collection-valued <a href="#DataAggregationPath">data aggregation path</a> is denoted in the <a href="#EvaluationofDataAggregationPaths"><span class="math inline">\(\Gamma\)</span> notation</a> by <span class="math inline">\(γ(u,t)\)</span>.</p>
<p>The notations introduced here are used throughout the following subsections.</p>
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Expand Up @@ -2672,7 +2672,7 @@ Example 59: assume the product is an implicit input for a function bound to a co

The transformations and the `rolluprecursive` operator defined in this section are called hierarchical, because they make use of a recursive hierarchy and are defined in terms of hierarchy functions introduced in the previous section.

With the exceptions of `traverse` and `rolluprecursive` whose fourth parameter ends with `traverse`, the hierarchical transformations do not define an order on the output set. An order can be reinstated by a subsequent `orderby` or `traverse` transformation or a `$orderby`.
The transformations `ancestors` and `descendants` do not define an order on the output set. An order can be imposed by a subsequent `orderby` or `traverse` transformation or a `$orderby`. The output set of `traverse` is in preorder order post order, and grouping with `rolluprecursive` orders its output set in analogy with [simple grouping](#SimpleGrouping).

The algorithmic descriptions of the transformations make use of a _union_ of collections, this is defined as an unordered collection containing the items from all these collections and from which duplicates have been removed.

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The transformations and the `rolluprecursive` operator defined in this section are called hierarchical, because they make use of a recursive hierarchy and are defined in terms of hierarchy functions introduced in the previous section.

With the exceptions of `traverse` and `rolluprecursive` whose fourth parameter ends with `traverse`, the hierarchical transformations do not define an order on the output set. An order can be reinstated by a subsequent `orderby` or `traverse` transformation or a `$orderby`.
The transformations `ancestors` and `descendants` do not define an order on the output set. An order can be imposed by a subsequent `orderby` or `traverse` transformation or a `$orderby`. The output set of `traverse` is in preorder order post order, and grouping with `rolluprecursive` orders its output set in analogy with [simple grouping](#SimpleGrouping).

The algorithmic descriptions of the transformations make use of a _union_ of collections, this is defined as an unordered collection containing the items from all these collections and from which duplicates have been removed.

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