(r3) LogicInAMPL < OpsRes

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---+<a name="top"></a> Logic in AMPL

<ol>
<li><a href="#relational">Relational Operators</a>
<li><a href="#logical">Logical Expressions</a>
<li><a href="#binary">Binary Parameters</a>
<li><a href="#operators">Logical Operators</a>
<li><a href="#conditional">Conditional Expressions</a>
<li><a href="#structure">Conditional Structures</a>
</ol>

---++<a name="relational"></a> Relational Operators

Relational operators are used to compare two expressions. They are most commonly used in [[ConstraintsInAMPL][constraints]], but not exclusively. The relational operators are:
| *Expression* | *Meaning* |
| <tt>&lt;</tt> | Less than |
| <tt>&lt;=</tt> | Less than or equal to |
| <tt>&gt;</tt> | Greater than |
| <tt>&gt;=</tt> | Greater than or equal to |
| <tt>&gt;=</tt> | Equal to |
| <tt>&lt;&gt;</tt> | Not equal to |

[[#top][Return to top]]

---++<a name="logical"></a> Logical Expressions

Logical expressions are expressions that will evaluate to either true or false. Logical expressions are
usually defined in terms of the <a href="#relational">relational operators:
<pre>
Lower[r] <= sum {i in INGREDIENTS} Contributes[r, i] * Amount[i]
</pre>

<pre>
sum {s in SURFBOARDS} Recipe[m, s] * Production[s] <= Supply[m];
</pre>

However, there are some special logical expressions in AMPL for use with [[SetsInAMPL][sets]]:
   1 =&lt;e&gt; in &lt;SET&gt;= is _true_ if =&lt;e&gt;= is a member of =&lt;SET&gt;=;
   1 {\tt &lt;e&gt; not in &lt;SET&gt;} is _false_ if =&lt;e&gt;= is a member of =&lt;SET&gt;=;
   1 =exists {&lt;e&gt; in &lt;SET&gt;} &lt;expression&gt;= is _true_ if some =&lt;e&gt;= in =&lt;SET&gt;= has =&lt;expression&gt;= being true;
   1 =forall {&lt;e&gt; in &lt;SET&gt;} &lt;expression&gt;= is _true_ if all =&lt;e&gt;= in =&lt;SET&gt;= have =&lt;expression&gt;= being true;
   1 =&lt;SUBSET&gt; within &lt;SET&gt;= is _true_ if all the elements in =&lt;SUBSET&gt;= are in =&lt;SET&gt;=;
   1 =&lt;SUBSET&gt; not within &lt;SET&gt;= is _true_ if some element in =&lt;SUBSET&gt;= is _not_ in =&lt;SET&gt;=.

Logical expressions can be built up from other logical expressions, [[#binary][binary parameters]] and [[#operators][logical operators]].

[[#top][Return to top]]

---++<a name="binary"></a> Binary Parameters

In AMPL we can create <i>binary</i> parameters by using the {\tt binary} keyword in the parameter declaration:
<p>\begin{verbatim}
param stillSearching binary;
\end{verbatim}<p>
Binary parameters are used in a similar way to boolean variables (in Matlab, C, etc) and logical variables (Fortran). If a binary parameter has the value 0 this is equivalent to false, and 1 is equivalent to true. Binary parameters can be used with <a href="#conditional">conditional expressions</a> to hold a true/false result from a <a href="#logical">logical expression</a>:
<p>\begin{verbatim}
param isGreater binary;

let isGreater := if 4 > 5 then 1 else 0; # isGreater = 0 (false)
let isGreater := if 6 > 5 then 1; # else 0 is the default, isGreater = 1 (true)
\end{verbatim}<p>
so the syntax is
<p>\begin{verbatim}
\end{verbatim}
or as the condition in a <a href="#condition">conditional statement</a> or <a href="#structure">conditional structure</a>. They are very useful for building complex conditional statements or structures:
<p>\begin{verbatim}
Some example from depth first searching or column generation
\end{verbatim}<p>
and controlling <a href="Loops in AMPL">loops</a>.

<a name="operators"><h3>Logical Operators</h3></a>

<\tt not} {\tt and} {\tt or}

<a name="conditional"><h3>Conditional Expressions</h3></a>

A conditional expression is very much like the IF function in Excel:
param ifvalue := if <some logical expression> then
                   <a value>
                [else
                   <another value>];
 
If the logical expression is true then ifvalue will be set to <a value>, otherwise it is set to 0 (by default) or, if the else part of the expression is present, <another value>. Note that if the else keyword is present, then no ; needs to be included after <a value>.

<a name="structure"><h3>Conditional Structures</h3></a>

A conditional structure is the same as the classical if-then-else statement in programming languages like MATLAB, Fortran, Visual Basic and C++:
if <logical expression> then
  <a statement>;
[else
  <another statement>;]
Note here that even if the else keyword is present you need to end <a statement> with ;. If you want to include more than one statement within the conditional structures you can use { and } to enclose your statements.
if <logical expression> then
{
  <some statements>
}
[else
{
  <some other statements>
}]
 

-- Main.TWikiAdminGroup - 18 Mar 2008
Topic revision: r3 - 2008-03-18 - TWikiAdminUser
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