inter

OPL keyword for intersections of sets.

Purpose

OPL keyword to construct set expressions.

context
Model files (.mod)

Syntax

BinaryExpression: Expression "==" Expression
                | Expression "!=" Expression
                | Expression "<=" Expression
                | Expression "<" Expression
                | Expression ">=" Expression
                | Expression ">" Expression
                | Expression "+" Expression
                | Expression "-" Expression
                | Expression "*" Expression
                | Expression "/" Expression
                | Expression "div" Expression
                | Expression "%" Expression
                | Expression "mod" Expression
                | Expression "in" Expression
                | Expression "not in" Expression
                | Expression "inter" Expression
                | Expression "union" Expression
                | Expression "diff" Expression
                | Expression "symdiff" Expression
                | Expression "^" Expression
                | Expression "&&" Expression
                | Expression "||" Expression
                | Expression "=>" Expression


AggregateExpression: "sum" '(' Qualifiers ')' Expression
                   | "min" '(' Qualifiers ')' Expression
                   | "max" '(' Qualifiers ')' Expression
                   | "prod" '(' Qualifiers ')' Expression
                   | "or" '(' Qualifiers ')' Expression
                   | "and" '(' Qualifiers ')' Expression
                   | "union" '(' Qualifiers ')' Expression
                   | "inter" '(' Qualifiers ')' Expression
                   | AllExpression

Description

Set data can be initialized by set expressions. These expressions are constructed from previously defined sets and the set operations union, inter, diff, and symdiff.

Two forms:

In the BinaryExpression form, the keyword inter goes through the first set and checks for each element whether that element is in the second set and, if it is, keeps it.
In the AggregateExpression form, the keyword inter allows you to express an intersection using an aggregate expression.

Examples

Binary

These code lines initialize i to {1}, u to {1,2,3,4,5}, d to {2,3}, and sd to {2,3,4,5}.


{int} s1 = {1,2,3}; 
{int} s2 = {1,4,5}; 
{int} i = s1 inter s2; 
{int} u = s1 union s2; 
{int} d = s1 diff s2; 
{int} sd = s1 symdiff s2;

Aggregate

This code line initializes rInter to {2}.


{int} i[1..3] = [ {1, 2}, {2, 3}, {2, 5} ]; 
{int} rInter = inter( x in 1..3 ) i[x];

This is true if the result is an ordered set. If you apply the property sorted or reversed to the resulting set, the result is affected accordingly.