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By Howard Barringer
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COMP S :: do beGSn rd11(S) := t r u e end; ~or J := I un~S& N-S ~o___beaSn uS#h M(S), M(S+I) u h e n ~ r d y ( S ) A(S+I) ^ rd~(S+1) := m S n ( A ( ~ ) , B s ) ; ss = = m a z ( a ( S ) , s S ) ; rdy(S) := srue; r~l;(~+1) : = fa~es en~ en___dd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Partial Correctness qf BL S O R T We require as precondition and postcondition:pre-BL_SORT e ~en(&n) = ~en(A) = Den(S) = N ^N~O ^ NP0 = 0 ^ Yl, ~ I .
An Exercise in Proving Parallel Programs Correct Co~. 2 ACM, Vol. 20, No. 12, December 1977, pp. 921-930. OVERVIEW Susan Owicki's work on the correctness of seminal basis sequential programs The first primitive deductive system construct "structured" contained in statements, for proving GPL, contains a cobea~n ... partial formed correctness form of the of resources and their . when .. Initially, the and a the u~uS~ statement, The second language, RPL, contains a parallelism statement; shared read/write variables are the ~$~h sequential process; a statement cQend for synchronisation and mutual exclusion, access is controlled through critical section statement.
5 states the condition for the conservation of elements. 2 Conditional Termination of BL~ORT Now pose -SEND e NP 0 = N pOs¢-COMP N e NP N = i Therefore pose-SEND ^ pos#-COMP N ^ I(M) ~ pos#-BL_SORT It must therefore be shown that SEND and C O M P N b o t h each case the stronger assertion w i l l b e and all terminate. 3 both proved: both SEND and all the COMP~ begin, That they all begin is shown b y t h e COMPs+ I to begin execution. all begin and 7) since the they contain no while loops. cobea~n statement in By the SL_SORTtherefore and so therefore does the program itself.
A Survey of Verification Techniques for Parallel Programs by Howard Barringer