How do you find the strongest postcondition?
The strongest postcondition possible is x = 10; this is the most useful postcondition. Formally, if {P} S {Q} and for all Q such that {P} S {Q}, Q ⇒ Q, then Q is the strongest postcondition of S with respect to P.
How do you find your weakest precondition?
The weakest precondition P is simply Q with all free occurrences of x replaced by e. For example, to find wp(x=y+1, x > 0) we replace x with y+1 in the postcondition x > 0, obtaining the weakest precondition y+1 > 0.
Is Hoare triple valid?
If there is a complete proof system for proving assertions in the underlying logic, then all valid Hoare triples have a proof.
What is the meaning of weakest precondition?
For a statement S and a postcondition R, a weakest precondition is a predicate Q such that for any precondition , if and only if . In other words, it is the “loosest” or least restrictive requirement needed to guarantee that R holds after S.
What is WP’s true for any statement s?
in the simple language. The verification condition for a given program S —which, recall, is a formula that is valid if and only if S is free of errors—is therefore the formula wp(S, true) .
What is meant by loop invariant?
In computer science, a loop invariant is a property of a program loop that is true before (and after) each iteration. It is a logical assertion, sometimes checked within the code by an assertion call. Knowing its invariant(s) is essential in understanding the effect of a loop.
What does Hoare mean?
Hoare is an English surname derived from Middle English hor(e) meaning grey- or white-haired. Notable people with the surname include: Albert Alfred Hoare, known as Bert Hoare (1874–1962), South Australian politician. Des Hoare (born 1934), Australian cricketer.
What are components of Hoare notation?
Rules
- Empty statement axiom schema.
- Assignment axiom schema.
- Rule of composition.
- Conditional rule.
- Consequence rule.
- While rule.
- While rule for total correctness.
What does it mean for a predicate transformer function f to be monotonic?
F(P) is monotonic if every occurrence of P in its definition is at a “positive” location. A location is positive if we pass down through an even number of negations to get to it. If P occurs in both positive and negative locations, then it occurrences are said to be mixed.
Why is invariants so important?
An invariant is a property of your data that you expect to always hold. Invariants are important because they allow you to separate business logic from validation—your functions can safely assume that they’re not receiving invalid data.
What makes a good loop invariant?
Loop invariants capture key facts that explain why code works. A good loop invariant should satisfy three properties: Initialization: The loop invariant must be true before the first execution of the loop. Maintenance: If the invariant is true before an iteration of the loop, it should be true also after the iteration.
