2.3.1 A list of (indexed) expressions

A list of expressions is normally written as follows:

zi = xi - yi  forall i ∈ I

This notation is very common. It says that the equations zi = xi - yi has to be repeated as many times as I has elements. However, this notation could be transformed into the general indexed notation by using the list operator as follows:

 .
∧
  i∈I (zi = xi - yi)

The index operator is the . -operator. The meaning of this operator is to list all indexed expressions. In this case, the indexed expression is normally an equation or an assignment, hence the “side effect” of this operator is to assign a list of values. Of course, in a mathematical text the first notation is preferred, because it is so common. However, this example shows that it can really be seen as an indexed notation. This fact will be important in the context of modeling languages later on, because we can use the same syntax to specify a list of expressions. To express it, we only need to use the list operator instead of any other index operator, as for instance the sigma operator.