Semantics for a Real-Time Object-Oriented Programming Language

Writer def = new Writer :getid(i):id Writer (i):(ClassDec 0 Writer j run:(LocY j (t stat) :idle:Body 0 Writer;i)) n LY Body 0 Writer;i def = calli;start(j):(LocX jwriteX(j):run:reti;start(true): (t stat) :idle: run:(hcallj;put(^ 1):retj;put(x):reply(x):0 ; abort:0i3 j hreply(y):writeY (y): (t stat) :idle: 1 1 1 1 1 1Body 0 Writer;i ; reply(y):0 + abort:0 j write Y (error): (t stat) :idle: 1 1 1 1 1 1 Body 0 Writer;i i 3) n freply;abortg) n L X [ [classReader var Y 1 1 1endc] ] T ClassDec 0 Reader where ClassDec 0 Reader def = newReader:getid(i):idReader(i):(ClassDec 0 Reader j run:(LocY j (t stat) :idle:Body 0 Reader;i)) n LY Body 0 Reader;i def = calli;start(j):(LocX jwriteX(j):run:reti;start(true): (t stat) :idle: run:(hcallj;get(^ 0):retj;get(x):reply(x):0 ; abort:0i3 j hreply(y):writeY (y): (t stat) :idle: 1 1 1 1 1 1Body 0 Reader;i ; reply(y):0 + abort:0 j writeY (error): (t stat) :idle: 1 1 1 1 1 1 Body 0 Reader;i i3) n freply;abortg) n LX 5 run:new Buer :id Buer (i): (t stat) :idle: run:new Writer :id Writer (j): (t stat) :idle: run:new Reader :id Reader (k): (t stat) :idle: A A def = run:(hcallj;start(i):retj;start(x):reply(x):0 ; abort:0i5 j hreply(y): (t stat) :idle:B ; reply(y):0 + abort:0 j (t stat) :idle:Bi5) n freply;abortg B def = run:(hcall k;start (i):ret k;start (x):reply(x):0 ; abort:0i5 j hreply(y): (t stat) :idle:0 ; reply(y):0 + abort:0 j (t stat) :idle:0i5) n freply;abortg The above proposition shows that the timed observation equivalence is preserved by all operators that are used to combine RtCCS expressions translated from R T 's class declarations, statements, and expressions. Therefore, we guarantee that the above simplied expressions are substitutable for their own original expressions. The entire program can be constructed by a parallel composition of the simplied expressions as follow: Prog T Prog 0 where Prog 0 def = (ClassDec 0 Buer jClassDec 0 Writer j ClassDec 0 Reader jObjId 0 j MachineN jInitial 0) By expanding the above simplied expressions 9 , we can analyze both the behavioral properties of the en-9 We omit the expansion and the detail analysis for lack of space. tire program and its temporal properties through the theoretical framework of RtCCS. Particularly, the upper bound of available processors can be specied as N in Machine N and thus we can predict the execution of programs with a given number of processors. From the above expression we know that, for example , let …