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

9.5 A Computational Interleaving Semantics 281
Axioms (8’) and (9’) concern the initialisation of an instance of a process class respectively
of an instance of a cluster class. The initialisation of process object C p (E1 ¥¡ ¡ ¡ ¥ Er) starts
with the evaluation of data expressions E1 ¡ ¡ Er from left to right, starting from an empty
state ¡ (it has proc as its only domain element), an empty stack ps and an empty type ¡ .
The results of these evaluations are data objects ¤ 1 ¡ ¡ ¤ r , state ¡ r, stack psr and type ¡ r.
Then domain element proc of the resulting state ¡ r is bound to a newly created (instance
variable) environment £ to obtain state ¡ ¡ . In £ each of the instance variables yi is bound
to its corresponding ¤ i. Each instance variable xj that is different from every yi, is bound
to nil. The initialisation of a process object is not observable by the environment. Upon
initialisation, behaviour specification C p (E1 ¥¡ ¡ ¡ ¥ Er) therefore performs a ¡ action. The
statement that remains to be executed by process object Cp ¥¡ ¡ ¡ ¥ (E1 Er) after the ¡ action
is performed is the initial method call statement ¥¡ ¡ ¡ ¥ m(E¡1 E¡q )().
Upon the initialisation of a cluster C c (E1 ¥¡ ¡ ¡ ¥ Er) of some cluster class C c P1 ¥¡ ¡ ¡ ¥ Pr
each expression parameter Pi in BSpec p is syntactically substituted by data expression Ei.
BSpec p is the parameterised behaviour specification of the cluster class. The initialisation
results in § BSpec p § § g C c E1£ ¡ ¡ ¡£ Er¢ indicating that behaviour specification BSpec p § § g remains
to be executed by cluster C c (E1 ¥¡ ¡ ¡ ¥ Er). g is a syntactic substitution function that maps
each Pi onto the corresponding Ei. Cluster initialisation is not externally observable.
Finally we will take a closer look at the rules for parallel composition and for channel
hiding.
(s’) Parallel composition 1
BSpec e 1 ¥ envs1 ¥ Sys p ¥ Sys
e BSpec ¢ 1 BSpece 2 ¥ envs1 ¥ envs2 Sysp Sys
¥
e BSpec ¡ ¢ 1 BSpece 2 ¥ envs¡1 envs2 Sys ¥ p Sys ¥
(t’) Parallel composition 2
BSpec e 2 ¥ envs2 ¥ Sys p ¥ Sys
e BSpec ¢ 1 BSpece 2 ¥ envs1 ¥ envs2 Sysp Sys
¥
e BSpec ¢ 1 BSpece 2 ¡ ¥ envs1 envs¡2 ¥ Sysp Sys ¥
(u’) Parallel composition 3
(v’) Channel hiding
BSpec e 1 ¥ envs1 ¥ Sys p ¥ Sys
BSpec e 2 ¥ envs2 ¥ Sys p ¥ Sys
£
£
£
£
a
a
l
l
BSpec e 1 ¡ ¥ envs¡1 ¥ Sysp ¥ Sys
BSpec e 2 ¡ ¥ envs¡2 ¥ Sysp ¥ Sys
BSpec e 1 ¡ ¥ envs¡1 ¥ Sysp ¥ Sys
BSpec e 2 ¡ ¥ envs¡2 ¥ Sysp ¥ Sys
e BSpec ¢ 1 BSpece 2 ¥ envs1 ¥ envs2 Sysp Sys £
¥
e BSpec ¡ ¢ 1 BSpece 2 ¡ ¥ envs¡1 envs¡2 ¥ Sysp Sys ¥
¥ envs¥ e p
¥ Sys
BSpec Sys
e
BSpec
¡
if a ¡ ¡ or Chan(a) L
L¥ envs¥ Sys p ¥ Sys
£
a
BSpec e ¡ ¥ envs¡ ¥ Sys p ¥ Sys
£
a
BSpec e ¡
£
£
a
a
L¥ envs¡ ¥ Sys p ¥ Sys