Local Binding vs. Default Binding

In this article we will compare two ways of defining index binding: local binding and default binding.

Assume there are two sets:

Set s_RootSet {
    Index: i_rs;
}

and

Set s_SubSet {
    Index: i_ss;
}

Let’s compare the expressions ( i in MySubSet ) and ( i \| i in MySubSet ).

When you use (i in MySubSet), AIMMS will handle i as an index in s_Subset. We say i is used as local binding in this case.

When you write (i \| i in MySubSet), AIMMS will still consider i as an index of its original set s_RootSet. We say i is used as default binding in this case.

In general, using local binding and default binding doesn’t make a difference, but when element ordering is used, such as, ord(i), i+1 and i–1, it will have an impact. For instance, the following statement:

Parameter1(i in MySubSet) := ord(i);

is the same as

Parameter1(i | i in MySubSet) := ord(i,MySubSet );

while

Parameter1(i | i in MySubSet) := ord(i);

is the same as

Parameter1(i | i in MySubSet) := ord(i,RootSet );

So there is a difference between the two only if you use certain functions that are relative to the set. A complete explanation can be found in the section “Index Binding” of AIMMS Language Reference.