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

272 Process Part of POOSL
We let Env denote the set of all process environments and let it range over env¥¡ ¡ ¡ . Env
is defined as
Env PStack Type
Here, and Type are as defined in Subsection 8.5.2. PStack denotes the set of process
stacks which is a subset of Stack as defined in Subsection 8.5.2. PStack ranges over ps¥¡ ¡ ¡
and is defined as
PStack ( £
Env will be used to denote the set of all lists of process environments. It ranges over
envs¥¡ ¡ ¡ . Further, we will write envs1 envs2 for the concatenation of lists envs1 and envs2,
and we write
proc¦ (LVar ¦£ DObj))
for the empty list.
We will now define the set Conf p of process configurations. Conf p ¥ BSpecifications e Env
Systems p Systems is inductively defined by means of the following inference rules:
(1) Cp
¡ ¡ ¥ Er)¥ ¥ (E1 Sys ¥¡ p ¡ Conf ¥ Sys p
if there exists a process class Cp ¡ ¡ ¥ yr y1 in Sys ¥¡ p and if no Ei contains variables or
self .
The condition is derived from context condition (15’) given in Section 9.4.
(2) Cc
¡ ¡ ¥ Er)¥ ¥ (E1 Sys ¥¡ p ¡ Conf ¥ Sys p
if there exists a cluster class Cc ¡ ¡ ¥ Pr P1 in Sys ¥¡ p and if no Ei contains variables or
self .
The condition is again derived from context condition (15’) given in Section 9.4.
(3)
S § p£ e
Cp
¡£ Er¢ ¥ ¡ ¡
¥ ps¥ ¥ Sys E1£ ¡ ¡ p Conf ¥ Sys ¡ p
if Cp ¡ ¥ yr y1 is a process class in Sys ¥¡ ¡ p , if no Ei contains variables or self , and if
AASort(Sp£ e p
¥
p ) AASort(C ¥ Sys )
(4)
The first part of the condition is derived from context condition (15’). The second
part requires that S p£ e does not contain any send or receive statements, that do not
conform to the message interface of the process object. Function AASort, defined
later in this subsection, calculates the set of all associated abstract communication
actions.
BSpec e ¥ envs¥ Sys p ¥ Sys ¡ Conf p
BSpec § e C c ¡ ¡ ¡£ Er¢ ¥ envs¥ Sys E1£ p Sys ¡ Conf ¥ p
if Cc ¥¡ ¡ ¡ ¥ Pr P1 is a cluster class in Sysp with behaviour specification BSpecp , if no
Ei contains variables or self , and if Reset(BSpec e ) BSpec p § § E1© P1 ¥¡ ¡ ¡ ¥ Er© Pr
Again, the first part of the condition is derived from context condition (15’). The