LogicInAMPL < OpsRes

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

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

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---++<a name="operators"></a> Logical Operators

Logical operators are used to combine [[#logical][logical expressions]]. They are most commonly used in [[#conditional][conditional statements]], [[#structure][conditional structures]] and [[LoopingInAMPL#condition][conditional loops]]. The logical operators are =not=, =and= and =or=. They are used as shown in the table below:

| *Expression* | *Result* |
| =not &lt;expression&gt;= | True if =&lt;expression&gt;= is false, false if =&lt;expression&gt;= is true |
| =&lt;e1&gt; and &lt;e2&gt;= | True if =&lt;e1&gt;= and =&lt;e2&gt;= are both true, otherwise false |
| =&lt;e1&gt; or &lt;e2&gt;= | True if either =&lt;e1&gt;= or =&lt;e2&gt;= are true, otherwise false |

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---++<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 [[#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 =&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]].

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---++<a name="conditional"></a> Conditional Expressions

A conditional expression is very much like the =IF= function in Microsoft Excel:
<pre>
param ifvalue := if &lt;some logical expression&gt; then
                   &lt;a value&gt;
                &#91;else
                   &lt;another value&gt;&#93;;
</pre>
 
If the logical expression is true then =ifvalue= will be set to =&lt;a value&gt;=, otherwise it is set to 0 (by default) or, if the else part of the expression is present, =&lt;another value&gt;=. Note that if the =else= keyword is present, then no =;= needs to be included after =&lt;a value&gt;=.

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---++<a name="structure"></a> Conditional Structures

A conditional structure is the same as the classical _if_-_then_-_else_ statement in programming languages like MATLAB, Fortran, Visual Basic and C++:
<pre>
if &lt;logical expression&gt; then
  &lt;a statement&gt;;
&#91;else
  &lt;another statement&gt;;&#93;
</pre>

Note here that even if the =else= keyword is present you need to end =&lt;a statement&gt;= with =;=. If you want to include more than one statement within the conditional structures you can use ={= and =}= to enclose your statements:
<pre>
if &lt;logical expression&gt; then
{
  &lt;some statements&gt;
}
&#91;else
{
  &lt;some other statements&gt;
}&#93;
</pre>
 
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---++<a name="binary"></a> Binary Parameters

In AMPL we can create _binary_ parameters by using the =binary= keyword in the parameter declaration:
<pre>
param stillSearching binary;
</pre>

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 [[#conditional][conditional expressions]] to hold a true/false result from a [[#logical][logical expression]]:
<pre>
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)
</pre>
so the syntax is
<pre>
let &lt;binary parameter&gt; := if &lt;expression&gt; then 1;
</pre>

You can also set binary parameters within [[#structure][conditional structures]]
<pre>
binary &lt;binary parameter&gt;;

if &lt;expression&gt; then
  let &lt;binary parameter&gt; := 1;
else
  let &lt;binary parameter&gt; := 0;
</pre>

Binary parameters may be used in [[#logical][logical expressions]] or as the condition in a [[#condition][conditional statement]] or [[#structure][conditional structure]]. They are very useful for building complex conditional statements or structures:
<pre>
Some example from depth first searching or column generation
</pre>
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and controlling [[LoopingInAMPL#condition][conditional loops]]:
<pre>
Some example from depth first searching or column generation
</pre>
%RED%Coming soon!%ENDCOLOR%

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-- Main.TWikiAdminGroup - 18 Mar 2008
This topic: OpsRes > WebHome > AMPLGuide > AMPLSyntax > LogicInAMPL
Topic revision: r6 - 2008-04-06 - MichaelOSullivan