# Difference: LogicInAMPL (3 vs. 4)

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 META TOPICPARENT name="AMPLSyntax"
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# Logic in AMPL

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• Logical Expressions
• Binary Parameters
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• Logical Operators
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• Logical Expressions
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• Conditional Expressions
• Conditional Structures
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• Binary Parameters
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## Relational Operators

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## Logical Operators

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

Expression Result
not <expression> True if <expression> is false, false if <expression> is true
<e1> and <e2> True if <e1> and <e2> are both true, otherwise false
<e1> or <e2> True if either <e1> or <e2> are true, otherwise false

## Logical Expressions

Logical expressions are expressions that will evaluate to either true or false. Logical expressions are

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usually defined in terms of the relational operators:
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usually defined in terms of the relational operators:

Lower[r] <= sum {i in INGREDIENTS} Contributes[r, i] * Amount[i]

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## Conditional Expressions

A conditional expression is very much like the IF function in Microsoft 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>.

## 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++:

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>
}]


## Binary Parameters

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In AMPL we can create binary parameters by using the {\tt binary} keyword in the parameter declaration:

\begin{verbatim}

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In AMPL we can create binary parameters by using the binary keyword in the parameter declaration:


param stillSearching binary;
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\end{verbatim}

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 expressions to hold a true/false result from a logical expression:

\begin{verbatim}

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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 expressions to hold a true/false result from a logical expression:



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)

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\end{verbatim}

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so the syntax is
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\begin{verbatim} \end{verbatim} or as the condition in a conditional statement or conditional structure. They are very useful for building complex conditional statements or structures:

\begin{verbatim} Some example from depth first searching or column generation \end{verbatim}

and controlling loops.

### Logical Operators

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

### Conditional Expressions

A conditional expression is very much like the IF function in Excel: param ifvalue := if then [else ];

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let <binary parameter> := if <expression> then 1;


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If the logical expression is true then ifvalue will be set to , otherwise it is set to 0 (by default) or, if the else part of the expression is present, . Note that if the else keyword is present, then no ; needs to be included after .
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You can also set binary parameters within conditional structures
binary <binary parameter>;



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### Conditional Structures

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if <expression> then let <binary parameter> := 1; else let <binary parameter> := 0;

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A conditional structure is the same as the classical if-then-else statement in programming languages like MATLAB, Fortran, Visual Basic and C++: if then ; [else ;] Note here that even if the else keyword is present you need to end with ;. If you want to include more than one statement within the conditional structures you can use { and } to enclose your statements. if then { } [else { }]
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Binary parameters may be used in logical expressions or as the condition in a conditional statement or conditional structure. They are very useful for building complex conditional statements or structures:
Some example from depth first searching or column generation

and controlling conditional loops:
Some example from depth first searching or column generation


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