Questions tagged [hoare-logic]

Questions about Hoare's logical framework for program correctness proofs and variants.

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1answer
1k views

How to find loop invariant from weakest precondition?

Consider this code: Precondition: Postcondition: rv == i <==> ∃i, 0 ≤ i ≤ a.length-1, a[i] == key ...
2
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0answers
204 views

How to show equivalence of the Hoare assignment axiom vs Floyd assignment axiom?

I know from several sources that they are equivalent, but couldn't find a reasonable explanation. My first approach was to show their equivalence by using the logical consequence rule and both axioms, ...
6
votes
1answer
860 views

Question about the formal proof of the inorder traversing

In Don Knuth's famous series of books, The Art of Computer Programming, section 2.3.1, he describes an algorithm to traverse binary tree in inorder, making use of an auxiliary stack: T1 [Initialize.] ...
4
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1answer
105 views

Developing invariants for comparing two strings

The following algorithm is supposed to compare two strings $S_1$ and $S_2$ ("/\" for empty string): ...
2
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1answer
230 views

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\...
5
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3answers
1k views

Hoare triple for assignment P{x/E} x:=E {P}

I am trying to understand Hoare logic presented at Wikipedia, Hoare logic at Wikipedia Apparently, if I understand correctly, a Hoare triple $$\{P\}~ C ~\{Q\}$$ means if P just before C, then Q ...
4
votes
2answers
154 views

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
vote
2answers
77 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
vote
1answer
134 views

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
vote
1answer
225 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\\ &\}\\...
1
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0answers
126 views

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 ...