Questions about Hoare's logical framework for program correctness proofs and variants.
Questions tagged [hoare-logic]
83 questions
7
votes
1 answer
Hoare logic - total correctness of loops
Consider a while loop of the form :
$\texttt{while (C) {S}}$
with $\texttt{C}$ the condition and $\texttt{S}$ the body of the loop.
Let $\texttt{I}$ and $\texttt{V}$ respectively be an invariant and a variant of this loop. The rule for total…
Dory
- 73
- 5
6
votes
3 answers
Intuitive explanation of Hoare assignment axiom
$\small\textit{''The obvious things are the most difficult to understand''}$
May be the question does not make sense, but let me ask it anyway.
The Hoare assignment axiom is
$$
\dfrac{}{\{Q[v \mapsto expr]\} \;\; v:=expr \;\; \{Q\}}
$$
Is there an…
Ayrat
- 1,065
- 1
- 8
- 23
2
votes
1 answer
Bottleneck in Hoare Logic unable to arrive at my {P} from {Q}
{Q} = {n>0}
C1 = i := 1;
C2 = c := 1;
C3 = p := 0;
{P} = {i<=n, p = fib(i-1), c = fib(i)}
My lack of understanding towards the rule of consequence in hoare logic is blocking me from find the solution which i hope someone can shed some light on how…
Jerry Sui
- 23
- 3
2
votes
1 answer
Hoare logic - invariant of loop
I am trying to prove partial corectness of following program:
{s = 0 and j = 0}
while j <= n do begin
{ s + j = (j - 1)j/2 and j <= n + 1}
s := s + j;
{ s = (j-1)j/2 and j <= n + 1}
{ s = j(j+1)/2 and j + 1 <= n + 1}
j := j + 1;
{ s…
user54001
1
vote
1 answer
How to prove $c = a + b$ using Program Verification Techniques
I am trying to prove an elementary thing, but it seems at some point you get down to atoms where you can't prove anything else. This is why I am wondering about proving $c = a + b$, it seems like an atom.
\begin{align}
\{a, b\}\\
c = a + b\\
…
Lance
- 2,213
- 1
- 17
- 31
1
vote
1 answer
Hoare-Logic: Requirements for imperfect data types
Theoretically, Hoare-Logic let's one prove the correctness of an algorithm, given pre- and post-condition.
However, as far as I've seen it so far, one idealizes his data-types to a mathematical set like $\mathbb{N}$ or $\mathbb{R}$.
So, even though…
Sudix
- 709
- 3
- 12
1
vote
1 answer
Hoare's Axiom Scheme Precondition
I have a question about determining preconditions for Hoare's Axiom Scheme. For example, if we have P { x=2 } x==1 and we are trying to determine the precondition, P, could we just set P as false giving us False { x=2 } x==1. I've read some of the…
James Teller
- 11
- 1
1
vote
1 answer
How to determine the pre and post conditions of a program (Hoare-logic)
Problem
Below is a program named X:
y = 1;
while(y < x){
y = 10 * y;
}
What does this program X do? What are appropriate pre and post conditions?
(Assume that x and y are integers).
My solution
Given a whole number x > 1, X should give us a…
August Jelemson
- 113
- 5
0
votes
0 answers
Why is the strongest postcondition for a program that just allocates x "exists x :: P"
I'm working my way through Leino's "Program Proofs" and I was following as far as the semantics of variable assignment, but I'm not quite sure why this is a valid Hoare triple:
{forall x::Q} var x; {exists x :: P}
where P is the weakest precondition…
John Gann
- 101
- 1
0
votes
0 answers
How to prove a segment of a program (Hoare-logic)
Problem:
A segment of a program is shown below:
⋮
_ _ _ _ _ _
z = x - 7;
(|z = 5 ∧ n = 4|)
⋮
What is the dashed line hiding?
My solution:
I think the dashed line is hiding: (|x - 7 = 5|)
However, I am not sure if it is the correct solution, it…
August Jelemson
- 113
- 5
0
votes
1 answer
How to find the loop invariant in hoare triples
Hey I am new to Hoare triples, and I can't understand on finding the loop invariants in hypothesis. For example this while loop
[x>1 & y>1] WHILE x>0 DO x:=x-1; y:=y+2 END [x+y>5].
The invariant is [2x + y > 5] but I don't understand on how to find…
HelloWorld
- 103
- 3
-2
votes
1 answer
Use Hoare axiom for array-componenet assignment to determine the weakest pre-condition
ASSERT( P ) /* determine what is P */
A[i] = A[m];
A[k] = 2;
ASSERT( A[i] == x + 5 )
