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

9.6 Example: A Simple Handshake Protocol 289
conf p
conf p
start) Receiver)
£
¥ )¥ y¦ ¥ ¥ Sys
x¥ ) p envS( envR( Sys
14 (
start) ¢ (§ § ) start = (y?ack; Sender start £
start)
)¥ ¥ ¥ ) Sys
(y!ack; Receiver)
p envS( envR( Sys
y¦ x¥ ¥
(start) ¢ § (§ 15( ) start = Sender start (start) £
¥ )¥ ¥ Sys )
Receiver)
p envS( envR( Sys
conf p
16( ) =
conf p
x¥ y¦ ¥
§ start start) ¢
§
(in?receive(dS); x!transfer(dS); y?ack; Sender start (start) Receiver)
£
¥ envS(nil)¥ Sys ) ¥
p envR( Sys
y¦ x¥ ¥
17 (
(start) ¢ (§ § ) start = Sender start (x?transfer(dR); out!deliver(dR); y!ack;
£
)¥ envR(nil) ¥ envS( Sysp Sys ¥
conf p
18( S ¥ R) =
start) Receiver)
x¥ y¦ ¥
§ start (x!transfer(dS); start) y?ack; ¢ § Sender start Receiver)
£
(start)
¥ x¥ S)¥ R) y¦ ¥ envS( envR( Sysp ¥ Sys
Here, envS and envS( ) denote environments of the Sender process. In envS no local
variables are allocated on the stack (the stack is empty), whereas in envS( ) variable dS
is allocated and bound to primitive object . Environments envR and envR( ) have a
similar meaning for the Receiver process. The environments are defined as
£
¦ ¥ ¥ ¤
envS £
proc £ ¤
¦ ¥ ¥ ¤
envR
proc £
£ £ ¤
¤ ¦ ¥ proc¥
envS( £ ¦ ¥ ¤
)
proc £
dS £
£
¤ ¦ ¥ proc¥
envR( £ ¦ ¥ ¤
) proc dR £
We mentioned that the protocol externally behaves as a 1-place buffer (see Figure 9.3).
We will show this by giving an explicit specification of such a buffer and by proving that
in Buffer
out
Figure 9.3: A 1-place Buffer
this specification is transformation equivalent to the protocol.
The 1-place buffer is specified as
Buffer¥
where Sys =
¥ Sys p ¡ ¥ Sys
and where Sys p ¡
process class Buffer
instance variables
communication channels in out
message interface in?receive(dB) out!deliver(dB)