22C:185 — Fall 2004
Homework XI
1. [15 points]
Prove the Hoare while normal form theorem (i.e., provide a construction to replace
if–then– with sequential execution and while–do–), and justify its correctness.
2 (repeated from Homework X). [25 points]
Provide an axiomatic proof of partial correctness for the Wren program fragment using
integer variables:
{true}
if A=B or A=-B
then if A>B then C:= A else C:= B-A+1 end if
else if A*B>0 then C:= A*B else C:= 1-A*B end if
end if
{C>0)
3. [25 points]
Provide an axiomatic proof of partial correctness for the Wren program fragment with
pre/post-conditions below (computing the “square root”), using integer variables:
{N≥1}
R:= 0;
while R*R < N do R:= R+1 end while
{(R-1)2 < N ≤ R2)
4. [25 points]
Provide an axiomatic proof of partial correctness for the Wren program fragment with
pre/post-conditions below (computing the “binary logarithm”), using integer variables:
{N>0}
P:= 0; M:= 1;
while M < N do P:= P+1; M:= 2*M end while
{2P-1< N Ÿ 2P≥N}
