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

306 Behaviour-Preserving Transformations
C(E ,...,E )
c h 1
c h 1
c h
c h
k
k
c h c h
2 2
...
...
c h c h
k-1 k-1
So a process object (during execution) is represented by a rounded rectangle 1 . The
name of the rectangle is the class name with the initialisation expressions between
brackets. If the number of initialisation expressions is zero (r 0), then the name
of the class suffices. The solid ellipses denote the channels of the configuration.
Every channel has an inner name and an outer name. The configuration itself knows
its channels by their inner names, whereas the outer world knows these channels
by their outer names. In the case of process objects, the inner names equal the
outer names. However, after channel renaming (see (5)) the names may differ. In
general we name a channel after its outer name, so if we write ’channel ch’, we
mean ’the channel with outer name ch’.
(2) If BSpec e C c (E1 ¥¡ ¡ ¡ ¥ Er) or BSpec e § BSpec e ¡ C c E1£ ¡ ¡ ¡£ Er¢ where C c is the
name of a cluster class defined in Sys p by cluster class C c P1 ¥¡ ¡ ¡ ¥ Pr communication
channels ch1 ¡ ¡ chk ¡ ¡ behaviour specification BSpec p , then first
ISD(BSpec p § § E1© P1 ¥¡ ¡ ¡ ¥ Er© Pr ¥ Sys p ) respectively ISD(BSpec e ¡ ¥ Sys p ) is drawn. If the
edge of the drawing is a single unnamed rounded rectangle, then this rectangle
is named C c (E1 ¥¡ ¡ ¡ ¥ Er) (or C c if r 0). Otherwise the drawing is surrounded
by a rounded rectangle named C c (E1 ¥¡ ¡ ¡ ¥ Er) (or C c if r 0) with k channels
ch1 ¥¡ ¡ ¡ ¥ chk (the inner names equal the outer ones). Each channel chi is internally
connected by a single arc to all observable channels, with outer name chi, of
ISD(BSpec p § § E1© P1 ¥¡ ¡ ¡ ¥ Er© Pr ¥ Sys p ) respectively of ISD(BSpec e ¡ ¥ Sys p ). An observable
channel is a channel that lies at some edge of a Instance Structure Diagram and is
not surrounded by a rounded rectangle.
For example, assume that r 2 and suppose that ISD(BSpec p § § E1© P1 ¥ E2© P2 ¥ Sys p ) is
shown at the left-hand side of the following figure. Then both ISD(C c (E1 ¥ E2)¥ Sys p )
and ISD(§ BSpec e ¡ C c E1£ E2¢ ¥ Sys p £ are represented by the right-hand side.
1 Sometimes we use hexagons in stead of rectangles. These hexagons represent the terminators of a
system.