Specification of Reactive Hardware/Software Systems - Electronic ...

248 Data Part of POOSL
We define a set of variables states 5 ranging over ¡ ¥¡ ¡ ¡ as follows:
£
£
¡ ¦ ¡ ¦£ ¡ proc¦ ¦£ Dom(¡ (NDObj finite¦
¦£ Dom(¡ £
proc¦ ¦ ¢¨¥¡ ¡ ¡ ¡
£ ¡ ¦£ ¡ ¥¡
) (IVar DObj) ) is
Here, we use to indicate that a variables state is a partial function. ) denotes the
domain of function . We will denote elements of NDObj by and elements
of set IVar DObj by .
Later in Chapter 9 we will see that every data expression or data statement is executed
within the context of a single process object. Such a process has instance variables, which
refer to data objects known to that process object. A variables state ¡ ¡ stores the
values of all these instance variables as well as of those of all non-primitive data objects
(indirectly) known to the process. Domain element proc is an identifier of the process
itself. The other domain elements refer to the non-primitive data objects.
We define a function MaxId which retrieves the greatest object identifier contained in a
variables state. MaxId is needed to describe the creation of data objects. If a state does
not contain any object identifiers, the function returns 0. Let ¡¢¡ . Then
Max £
n ¡
¢ n ¡ Dom(¡ )¦ if Dom(¡ ¤ NDObj) ¡
) MaxId(¡ ¥ 0 if Dom(¡ ¤ NDObj) ¤
¡ ¤ Here NDObj denotes ¡ function restricted to set NDObj.
Next, we define a set Stack of local variable stacks, with typical elements s¥¡ ¡ ¡ ,
Stack ( £
(LVar ¦£ DObj)) (NDObj (LVar ¦£ DObj))
proc¦
A stack is a (possibly empty) list of stack elements. An element of a stack denotes
a local variables environment. Such an element consists of two components. The first
component denotes the owner of the environment, which is either the involved process
object or some non-primitive data object. The second component stores the values of
the local variables of the owner. The first component of the top of a stack denotes the
object which is currently executing one of its methods. Note that the bottom (left-side)
elements of each stack are owned by the involved process object, whereas the top (right-
side) elements are owned by non-primitive data-objects. We e¥¡ ¡ ¡ let range over the £
set
of local variables environments ¦ (NDObj
range over ¦£ Lvar DObj.
proc¦ ) (LVar ¦£ DObj). We further let ¤ ¥¡ ¡ ¡
We shall need the following operations upon stacks: For stack elements
and stack
e1 ¥¡ ¡ ¡ ¥ en ¥ e ¡ ((NDObj ¦
e1 ¥¡ ¡ ¡ ¥ en ¡ Stack
5 See also Paragraph 6.6.3.4
£
proc¦ ) (LVar ¦£ DObj))
¤