Expression Decomposition in a Rely/Guarantee Context

Deriving Laws for Developing Concurrent Programs in a Rely-Guarantee Style

“…Stability of a property p over the execution of a command is an important property and, in the context of concurrency, stability of a property over interference from the environment is especially important [Col08,WDP10a]. This section examines stability properties that are useful for later laws.…”

“…Related work. Coleman [Col08] and Wickerson et al [WDP10b] use a stronger property that requires that no variables used within e are modified; none of the examples above are handled under their definition unless x and y are assumed to be unmodified. The source of the additional generality of our definition is that it is defined in terms of the semantics of expressions rather than being based on their syntactic form.…”

“…Related work. Coleman [Col08] and Wickerson et al [WDP10b] use a stronger single unstable variable property that requires at most one variable, x , within e is modified by the interference and x is only referenced once in e. For example, abs(x ) + y does not satisfy their single unstable variable property under interference that negates x . Overall this gives us more general laws about single-reference expressions, which are used to handle expression evaluation within assignments (Sect.…”

Explicit Stabilisation for Modular Rely-Guarantee Reasoning

“…Coleman [5] proposes the following rule for reasoning about one-armed conditional statements whose test conditions are evaluated non-atomically in the presence of interference.…”

“…Retrieved from the Unix Heritage Society. 5 #define WORD sizeof(st) #define BLOCK 1024 #define testbusy(p) ((int)(p)&1) #define setbusy(p) (st *)((int)(p)|1) #define clearbusy(p) (st *)((int)(p)&~1) struct store { struct store *ptr; }; typedef struct store st; static st s [2]; /*initial arena*/ // static struct store *allocp; (bug removed) static st *t; /*arena top*/ char* sbrk(); char* malloc(unsigned nbytes) { register st *p, *q; register nw; static temp; // omitted: initialisation code nw = (nbytes+WORD+WORD-1)/WORD; for(p=s; ; ) { for(temp=0; ; ) { if(!testbusy(p->ptr)) { while(!testbusy((q=p->ptr)->ptr)) p->ptr = q->ptr; if(q>=p+nw && p+nw>=p) goto found; } q = p; p = clearbusy(p->ptr); if(p>q) ; else if(q!=t || p!=s) return 0; else if(++temp>1) break; } temp = ((nw+BLOCK/WORD) /(BLOCK/WORD))*(BLOCK/WORD); q = (st *)sbrk(0); if(q+temp < q) return 0; q = (st *)sbrk(temp*WORD); if((int)q == -1) return 0; t->ptr = q; if(q!=t+1) t->ptr = setbusy(t->ptr); t = q->ptr = q+temp-1; t->ptr = setbusy(s); } found: if(q>p+nw) ((st *)(p+nw))->ptr = p->ptr; p->ptr = setbusy(p+nw); return((char *)(p+1)); } free(register char *ap) { register st *p = ((st *)ap)-1; p->ptr = clearbusy(p->ptr); }…”