1. Model-based vs. Functional Program Specification and Correctness
Software Testing and Verification
Bonus Review Material
Prepared by
Stephen M. Thebaut, Ph.D.
University of Florida

2. Model-based vs. Functional Specification
{true}
temp := x
x := y
y := temp
{x=y’ Л y=x’ Л temp=x’}
Comparable specified function (f):
f = (x,y,temp := y,x,x)
Function computed by the program ([S]):
[S] = (x,y,temp := y,x,x)
Is the program “correct”?
{P} S {Q} ?
{P} S {Q} strongly ?
f = [S] ?
f  [S] ?

3. Weakened Post-Condition
{true}
temp := x
x := y
y := temp
{x=y’ Л y=x’}
Comparable specified function (f):
f = (x,y := y,x)
Function computed by the program ([S]):
[S] = (x,y,temp := y,x,x)
Is the program “correct”?
{P} S {Q} ?
{P} S {Q} strongly ?
f = [S] ?
f  [S] ?

4. Strengthened Pre-Condition
{x>0 Л y>0}
temp := x
x := y
y := temp
{x=y’ Л y=x’}
Comparable specified function (f):
(x>0 Л y>0  x,y := y,x)
Function computed by the program ([S]):
[S] = (x,y,temp := y,x,x)
Is the program “correct”?
{P} S {Q} ?
{P} S {Q} strongly ?
f = [S] ?
f  [S] ?

5. A different program… {x>0 Л y>0} if (x>0 & y>0) then
temp := x
x := y
y := temp
end_if
{x=y’ Л y=x’}
Comparable specified function (f):
(x>0 Л y>0  x,y := y,x)
Function computed by the program ([S]):
(x>0 Л y>0  x,y,temp := y,x,x | true  I)
Is the program “correct”?
{P} S {Q} ?
{P} S {Q} strongly ?
f = [S] ?
f  [S] ?

6. A really different program…
{x>0 Л y>0}
if (x>0 & y>0) then
temp := x
x := y
y := temp
else
while (1=1) do
no-op
end_while
end_if_else
{x=y’ Л y=x’}
Comparable specified function (f):
(x>0 Л y>0  x,y := y,x)
Function computed by the program ([S]):
(x>0 Л y>0  x,y,temp := y,x,x)
Is the program “correct”?
{P} S {Q} ?
{P} S {Q} strongly ?
f = [S] ?
f  [S] ?

7. Pre-condition weakened again
{true}
if (x>0 & y>0) then
temp := x
x := y
y := temp
else
while (1=1) do
no-op
end_while
end_if_else
{x=y’ Л y=x’}
Comparable specified function (f):
f = (x,y := y,x)
Function computed by the program ([S]):
(x>0 Л y>0  x,y,temp := y,x,x)
Is the program “correct”?
{P} S {Q} ?
{P} S {Q} strongly ?
f = [S] ?
f  [S] ?

8. Model-based vs. Functional Program Specification and Correctness
Software Testing and Verification
Bonus Review Material
Prepared by
Stephen M. Thebaut, Ph.D.
University of Florida