/usr/lib/swi-prolog/doc/Manual/aggregate.html

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<h2 id="sec:aggregate"><a id="sec:A.1"><span class="sec-nr">A.1</span> <span class="sec-title">library(aggregate): 
Aggregation operators on backtrackable predicates</span></a></h2>

<p><a id="sec:aggregate"></a>

<dl class="tags">
<dt class="tag">Compatibility</dt>
<dd>
Quintus, SICStus 4. The <a class="pred" href="forall2.html#forall/2">forall/2</a> 
is a SWI-Prolog built-in and
<a class="pred" href="manipterm.html#term_variables/3">term_variables/3</a> 
is a SWI-Prolog with a <b>different definition</b>.</dd>
<dt class="mtag">To be done</dt>
<dd>
- Analysing the aggregation template and compiling a predicate for the 
list aggregation can be done at compile time. <br>
- <a class="pred" href="aggregate.html#aggregate_all/3">aggregate_all/3</a> 
can be rewritten to run in constant space using non-backtrackable 
assignment on a term.
</dd>
</dl>

<p>This library provides aggregating operators over the solutions of a 
predicate. The operations are a generalisation of the <a class="pred" href="allsolutions.html#bagof/3">bagof/3</a>, <a class="pred" href="allsolutions.html#setof/3">setof/3</a> 
and <a class="pred" href="allsolutions.html#findall/3">findall/3</a> 
built-in predicates. The defined aggregation operations are counting, 
computing the sum, minimum, maximum, a bag of solutions and a set of 
solutions. We first give a simple example, computing the country with 
the smallest area:

<pre class="code">
smallest_country(Name, Area) :-
        aggregate(min(A, N), country(N, A), min(Area, Name)).
</pre>

<p>There are four aggregation predicates (<a class="pred" href="aggregate.html#aggregate/3">aggregate/3</a>, <a class="pred" href="aggregate.html#aggregate/4">aggregate/4</a>, <a class="pred" href="aggregate.html#aggregate_all/3">aggregate_all/3</a> 
and <a class="pred" href="aggregate.html#aggregate/4">aggregate/4</a>), 
distinguished on two properties.

<dl class="latex">
<dt><b>aggregate vs. aggregate_all</b></dt>
<dd>
The aggregate predicates use <a class="pred" href="allsolutions.html#setof/3">setof/3</a> 
(<a class="pred" href="aggregate.html#aggregate/4">aggregate/4</a>) or <a class="pred" href="allsolutions.html#bagof/3">bagof/3</a> 
(<a class="pred" href="aggregate.html#aggregate/3">aggregate/3</a>), 
dealing with existential qualified variables (Var<code>^</code>Goal) and 
providing multiple solutions for the remaining free variables in Goal. 
The <a class="pred" href="aggregate.html#aggregate_all/3">aggregate_all/3</a> 
predicate uses <a class="pred" href="allsolutions.html#findall/3">findall/3</a>, 
implicitly qualifying all free variables and providing exactly one 
solution, while <a class="pred" href="aggregate.html#aggregate_all/4">aggregate_all/4</a> 
uses <a class="pred" href="builtinlist.html#sort/2">sort/2</a> over 
solutions that Discriminator (see below) generated using <a class="pred" href="allsolutions.html#findall/3">findall/3</a>.
</dd>
<dt><b>The Discriminator argument</b></dt>
<dd>
The versions with 4 arguments provide a Discriminator argument that 
allows for keeping duplicate bindings of a variable in the result. For 
example, if we wish to compute the total population of all countries, we 
do not want to lose results because two countries have the same 
population. Therefore we use:

<pre class="code">
    aggregate(sum(P), Name, country(Name, P), Total)
</pre>

<p></dd>
</dl>

<p>All aggregation predicates support the following operators below in 
Template. In addition, they allow for an arbitrary named compound term, 
where each of the arguments is a term from the list below. For example, 
the term <code>r(min(X), max(X))</code> computes both the minimum and 
maximum binding for X.

<dl class="latex">
<dt><strong>count</strong></dt>
<dd class="defbody">
Count number of solutions. Same as <code>sum(1)</code>.
</dd>
<dt><strong>sum</strong>(<var>Expr</var>)</dt>
<dd class="defbody">
Sum of <var>Expr</var> for all solutions.
</dd>
<dt><strong>min</strong>(<var>Expr</var>)</dt>
<dd class="defbody">
Minimum of <var>Expr</var> for all solutions.
</dd>
<dt><strong>min</strong>(<var>Expr, Witness</var>)</dt>
<dd class="defbody">
A term <code>min(Min, Witness)</code>, where Min is the minimal version 
of <var>Expr</var> over all solutions, and <var>Witness</var> is any 
other template applied to solutions that produced Min. If multiple 
solutions provide the same minimum, <var>Witness</var> corresponds to 
the first solution.
</dd>
<dt><strong>max</strong>(<var>Expr</var>)</dt>
<dd class="defbody">
Maximum of <var>Expr</var> for all solutions.
</dd>
<dt><strong>max</strong>(<var>Expr, Witness</var>)</dt>
<dd class="defbody">
As <code>min(Expr, Witness)</code>, but producing the maximum result.
</dd>
<dt><strong>set</strong>(<var>X</var>)</dt>
<dd class="defbody">
An ordered set with all solutions for <var>X</var>.
</dd>
<dt><strong>bag</strong>(<var>X</var>)</dt>
<dd class="defbody">
A list of all solutions for <var>X</var>.
</dd>
</dl>

<p><b>Acknowledgements</b>

<p><i>The development of this library was sponsored by SecuritEase, <a class="url" href="http://www.securitease.com">http://www.securitease.com</a></i>

<dl class="latex">
<dt class="pubdef"><span class="pred-tag">[nondet]</span><a id="aggregate/3"><strong>aggregate</strong>(<var>+Template, 
:Goal, -Result</var>)</a></dt>
<dd class="defbody">
Aggregate bindings in <var>Goal</var> according to <var>Template</var>. 
The <a class="pred" href="aggregate.html#aggregate/3">aggregate/3</a> 
version performs <a class="pred" href="allsolutions.html#bagof/3">bagof/3</a> 
on <var>Goal</var>.</dd>
<dt class="pubdef"><span class="pred-tag">[nondet]</span><a id="aggregate/4"><strong>aggregate</strong>(<var>+Template, 
+Discriminator, :Goal, -Result</var>)</a></dt>
<dd class="defbody">
Aggregate bindings in <var>Goal</var> according to <var>Template</var>. 
The <a class="pred" href="aggregate.html#aggregate/4">aggregate/4</a> 
version performs <a class="pred" href="allsolutions.html#setof/3">setof/3</a> 
on <var>Goal</var>.</dd>
<dt class="pubdef"><span class="pred-tag">[semidet]</span><a id="aggregate_all/3"><strong>aggregate_all</strong>(<var>+Template, 
:Goal, -Result</var>)</a></dt>
<dd class="defbody">
Aggregate bindings in <var>Goal</var> according to <var>Template</var>. 
The
<a class="pred" href="aggregate.html#aggregate_all/3">aggregate_all/3</a> 
version performs <a class="pred" href="allsolutions.html#findall/3">findall/3</a> 
on <var>Goal</var>.</dd>
<dt class="pubdef"><span class="pred-tag">[semidet]</span><a id="aggregate_all/4"><strong>aggregate_all</strong>(<var>+Template, 
+Discriminator, :Goal, -Result</var>)</a></dt>
<dd class="defbody">
Aggregate bindings in <var>Goal</var> according to <var>Template</var>. 
The
<a class="pred" href="aggregate.html#aggregate_all/4">aggregate_all/4</a> 
version performs <a class="pred" href="allsolutions.html#findall/3">findall/3</a> 
followed by <a class="pred" href="builtinlist.html#sort/2">sort/2</a> on
<var>Goal</var>.</dd>
<dt class="pubdef"><a id="foreach/2"><strong>foreach</strong>(<var>:Generator, 
:Goal</var>)</a></dt>
<dd class="defbody">
True if conjunction of results is true. Unlike <a class="pred" href="forall2.html#forall/2">forall/2</a>, 
which runs a failure-driven loop that proves <var>Goal</var> for each 
solution of
<var>Generator</var>, <a class="pred" href="aggregate.html#foreach/2">foreach/2</a> 
creates a conjunction. Each member of the conjunction is a copy of <var>Goal</var>, 
where the variables it shares with <var>Generator</var> are filled with 
the values from the corresponding solution.

<p>The implementation executes <a class="pred" href="forall2.html#forall/2">forall/2</a> 
if <var>Goal</var> does not contain any variables that are not shared 
with <var>Generator</var>.

<p>Here is an example:

<pre class="code">
?- foreach(between(1,4,X), dif(X,Y)), Y = 5.
Y = 5.
?- foreach(between(1,4,X), dif(X,Y)), Y = 3.
false.
</pre>

<dl class="tags">
<dt class="tag">bug</dt>
<dd>
<var>Goal</var> is copied repeatedly, which may cause problems if 
attributed variables are involved.
</dd>
</dl>

</dd>
<dt class="pubdef"><span class="pred-tag">[det]</span><a id="free_variables/4"><strong>free_variables</strong>(<var>:Generator, 
+Template, +VarList0, -VarList</var>)</a></dt>
<dd class="defbody">
Find free variables in bagof/setof template. In order to handle 
variables properly, we have to find all the universally quantified 
variables in the <var>Generator</var>. All variables as yet unbound are 
universally quantified, unless

<p>
<ol class="latex">
<li>they occur in the template
<li>they are bound by X<code>^</code>P, <a class="pred" href="allsolutions.html#setof/3">setof/3</a>, 
or <a class="pred" href="allsolutions.html#bagof/3">bagof/3</a>
</ol>

<p><code>free_variables(Generator, Template, OldList, NewList)</code> 
finds this set using OldList as an accumulator.

<dl class="tags">
<dt class="mtag">author</dt>
<dd>
- Richard O'Keefe <br>
- Jan Wielemaker (made some SWI-Prolog enhancements)
</dd>
<dt class="tag">license</dt>
<dd>
Public domain (from DEC10 library).</dd>
<dt class="mtag">To be done</dt>
<dd>
- Distinguish between control-structures and data terms. <br>
- Exploit our built-in <a class="pred" href="manipterm.html#term_variables/2">term_variables/2</a> 
at some places?
</dd>
</dl>

</dd>
<dt class="multidef"><span class="pred-tag">[semidet,multifile]</span><a id="sandbox:safe_meta/2"><span class="module">sandbox</span>:<strong>safe_meta</strong>(<var>+Goal, 
-Called</var>)</a></dt>
<dd class="defbody">
Declare the aggregate meta-calls safe. This cannot be proven due to the 
manipulations of the argument <var>Goal</var>.
</dd>
</dl>

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swi-prolog-nox 6.6.4-2ubuntu1 / usr / lib / swi-prolog / doc / Manual / aggregate.html
