Questions tagged [hoare-logic]
Questions about Hoare's logical framework for program correctness proofs and variants.
76
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Hoare Triple Derivation Example (Precondition False)
How can i derivate this Hoare Tripel?
(Q; P; R) {false} x := x + 1; {x = 0}
I do not know which rule should i use on this.
I am confused on this wrong precondition.
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1
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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 )
0
votes
1
answer
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Logic foundation for formal verification
What types of logic should one study as foundation before diving into the area of software verification? What I can think of are:
Hoare Logic (for proving correctness of imperative programs)
Linear ...
- 101
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0
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21
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Looking for a reference for "structured programming for data structures"
In a talk by Tony Hoare, he said something interesting and I'm looking for more reading on the topic
minute 57:
"Languages don't recognize the different structuring principles that are being ...
- 276
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vote
1
answer
65
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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, ...
- 11
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31
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Hoare Triple Logic
I'm having trouble understanding the logic behind Hoare Triples. The question asks for the missing value of the precondition {X}
...
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0
answers
33
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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 ...
- 113
1
vote
1
answer
42
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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 ...
- 113
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votes
2
answers
161
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proving program equivalence
I understand that the general problem of program equivalence is undecidable, but I'm wondering what approaches exist to tackle the problem? I am familiar with Hoare-style verification, but are there ...
- 51
1
vote
1
answer
92
views
Hoare Logic for Factorial
I came across this hoare logic for factorials but I don't quite understand it. We multiply F and X but we're not adding up all values of F so how do we get the sum/factorial at the end?
Precondition: ...
- 167
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vote
0
answers
22
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Is true * true = true in Separation Logic?
I am trying to show that the following interference is unsound in terms of Separation Logic:
$$
(p_0 \implies p_1) \implies ((p_0 * q) \implies (p_1 * q))
$$
I came up with the following values for ...
0
votes
1
answer
504
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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
...
- 103
4
votes
2
answers
449
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Why is the assignment rule the way it is in Hoare Logic?
Why is the assignment rule the way it is in Hoare Logic/Axiomatic Semantics?
I can't wrap my head around why the assignment rule is backwards from what I expected.
I understand Hoare logic is use to ...
- 2,920
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1
answer
40
views
I cannot find an invariant for the following program
I have the following:
(|$y=0; x=c$|) while(x > 0){y=y+a; x=x-1;} (|$y= a*c$|)
This seems like a fairly simple program and I can intuitively tell that the post ...
- 153
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0
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107
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How to prove program solves the problem?
I am preparing for the exam on Theory of Programming class. Now I am trying to solve the task from the sample paper:
Task description starts here
Given the following problem:
A problem is given by ...
- 69
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votes
1
answer
137
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Confusion about assignment axiom in Hoare logic
I wanted to know if we are given the f.f.g. Hoare triple:
{x = 43}x := x + 1{x = 44}
How do we show that this is a valid Hoare triple?
My attempt was:
Using the assignment axiom:
{x + 1 = 43} x := ...
- 251
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votes
1
answer
36
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Formal semantics of a mutable/imperative stack
When introducing formal semantics for data structures, immutable stacks are a nice simple example :
$\mathit{is\_empty}(\mathit{create()})=\mathrm{True}$
$\mathit{is\_empty}(\mathit{push}(e, s))=\...
- 233
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votes
1
answer
187
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Hoare triple: Loop invariant and correctness
The following Hoare triple in which variable a is an array of integers, and len, max, i, n, j and m are integer-valued variables. Provide a loop invariant (using predicate logic) suitable for proving ...
- 21
2
votes
0
answers
118
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Hoare triple: Loop invariant and partial correctness
Below there is Hoare triple in which variable $a$ is an array of integers, $len$, $x, i$ are integer-valued variables, and $r$ is a Boolean-valued variable. I have to provide a loop invariant (using ...
- 21
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vote
0
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Can we ignore the postcondition in the Hoare conditional rule when there is a return statement?
I'm proving the correctness of naive string matching using Hoare logic. I have the following pseudocode:
...
- 215
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1
answer
389
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Hoare logic, proving conjunction rule from basic rules, possible or not?
(This is HW.) Suppose I have these following proof rules given.
I am currently considering if I can prove the conjunction rule (given below) from the above given Hoare logic rules.
My answer would ...
- 189
3
votes
1
answer
368
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The Law of Excluded Miracle in the language of guarded commands
The definition of weakest precondition is familiar (let me use Isabelle's syntax here):
definition "wp c Q s ≡ ∃t. (c,s) ⇒ t ∧ Q t"
the weakest precondition ...
- 2,230
2
votes
1
answer
47
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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 ...
- 23
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votes
1
answer
81
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How to solve for the precondition give a postcondtion that must satisfy two conditions
I tried solving past exam question but there is this one that I haven't been able to solve.
The question states that a suitable precondition should be found for the statement.
$$
a= i +2; i++\{(a = ...
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1
vote
2
answers
92
views
How to prove a side effect in a function
I asked a question earlier about Saving to the Database, which was very general and about the requirements for a proof when you go through many layers of non-verified systems such as the network and ...
- 1,911
1
vote
1
answer
150
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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 ...
- 1,911
4
votes
2
answers
161
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The difference between a Hoare Triple/Assertion and a Typed Function
I have been trying to wrap my head around applying Hoare Logic and am running into the question of how Hoare triples are any different from (simply) a typed function.
That is, say you have a typed ...
- 1,911
1
vote
1
answer
236
views
How to use Hoare Logic to Prove this Assertion
Given this assertion in Hoare Logic:
\begin{align}
&\mathbf{\{p >= 0\}}\\
&s = 0 ; n = 1 ;\\
&\mathtt{while}\ (n <= p)\ \{\\
&\quad s = s + n ;\\
&\quad n = n + 1\\
&\}\\...
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2
votes
1
answer
255
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Understanding Hoare Logic Axioms
Given these 5 axioms of Hoare Logic:
\begin{array}{cl}
\frac{}{\{\phi([x \leftarrow E])\}\ x := E\ \{\phi(x)\}} & \mathtt{Assignment}\\\\
\frac{\{\phi\}\ P_1\ \{\eta\} \quad \{\eta\}\ P_2\ \{\psi\...
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vote
0
answers
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How to apply Hoare Logic to this function
I would like to apply Hoare Logic to realistic, complex imperative programs that use while loops, if statements, functions, modules, etc. and have side effects (e.g. access the network). In order to ...
- 1,911
1
vote
1
answer
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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 ...
- 659
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1
answer
187
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Loop termination - Loop invariant
(x >= 0 && y >= 0)
q = 0;
r = x;
while ( r >=y ) {
r = r - y;
q = q + 1;
}
(x = q*y +r) && (r >= 0) && (r < y)
For ...
user87320
2
votes
1
answer
289
views
Find the loop invariant of the given while loop
I don't know how to find a loop invariant. I'm not sure where to start. Can anyone find the loop invariant of the given program and explain your method please.
...
- 123
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1
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Inference rules for deriving invariants in Hoare logic
The following algorithm is supposed to compare two strings $S_1$ and $S_2$ ("/\" for empty string):
...
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4
votes
1
answer
111
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Developing invariants for comparing two strings
The following algorithm is supposed to compare two strings $S_1$ and $S_2$ ("/\" for empty string):
...
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1
vote
1
answer
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what is the 'x :=' part mean in a hoare triple?
In Hoare logic, there's a thing called a Hoare triple, e.g.$$
\begin{array}{ccccc}
\{x = 2\} & & x := x+1 & & \{x = 3\}
\end{array}.
$$
What does '$x :=$' mean?
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2
answers
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how to solve Hoare logic problems
I'm having trouble proving Hoare logic questions as I'm not sure of the process that is taken to prove them. I understand that they're rules such as assignment axiom, pre-condition strengthening, post-...
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answers
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Counting the number of occurences - loop invariant
I'm trying to come up with loop invariant for the following program.
k = a[0]
m = 1
p = 1
while p < n:
if a[p] == k:
m += 1
p += 1
return m
I ...
- 9
1
vote
1
answer
290
views
True Postcondition, with true Precondition
In my exam preparation I stumbled across the follwoing exercise regarding pre and postconditions:
As far as I understood the question, we need to express some condition for p, such that if that ...
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votes
1
answer
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views
Finding weakest precondition
I have the following program
x := y + 1;
if (y > 0) then
x := x + y
else x := y + 100;
x := x + y;
I want to compute the weakest precondition for getting <...
- 101
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1
answer
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How to get Loop invariants to prove program is correct in Hoare logic
start off stating the definition of a loop invariant. It is a condition that must be true at the start of the loop and must be true after each iteration of the loop. I understand what it is but i have ...
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votes
1
answer
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Continuation-passing style: what is meant by "CPS'ing"?
I'm reading Dijkstra Monads for Free for a presentation I'll be doing and it's pretty meaty. One of the things that I keep running into is the term "CPS'ing". I've read a little bit on ...
- 337
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votes
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answers
634
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Expression of the weakest precondition of a while loop
I am interested in computing weakest preconditions (WP) of loops.
If I refer to Wikipedia "Predicate Transformer semantics", the WP for e.g. total correction of a loop annotated with an invariant I ...
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0
answers
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Hoare correctness proof for a recursive definition of multiplication
Given the program:
{y=y0 ^ y>=0}
z=0;
while (y>0){
z=z+x; (1)
y=y-1;
}
{z=x*y0}
I am having trouble finding the ...
0
votes
2
answers
173
views
Using the Consequence Rule
I have the following example that I have to prove
{a>7 ^ b>=0} n:=a-b {n<a ^ a+b>=0}
Using the Consequence Rule I assumed that the P is true
...
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vote
1
answer
208
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How to prove the equivalence between Hoare and Floyd assignment axioms?
How to show that these two axioms are equivalent:
1: $\{G[v/e]\} v:=e \{G\}$
2: $\{F\} v:=e \{\exists v' (F[v/v'] \land v=e[v/v'])\}$
I've tried with $G = \exists v' (F[v/v'] \land v=e[v/v']) $and ...
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votes
1
answer
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Relation between Hoare Type Theory and pointers
My understanding is that in Hoare Type Theory every imperative statement has a type of the form {Pre}res:T{Post} where T is the ...
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1
answer
143
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Why does (y < 10) imply everywhere (x > 0 ^ y < 10)?
My lecturer recently released solutions to an assignment. One of the questions was to determine the weakest precondition of:
...
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votes
1
answer
342
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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 ...
- 73
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votes
1
answer
271
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What was the major breakthrough between Hoare-Floyd logic and Scott–Strachey semantics?
I'm reading through a commentary on Milner's "The use of machines to assist in rigorous proof" by Mike Gordon. In this paper, he explains how LCF was born from the ideas of denotational semantics by ...
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