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.
Is Hoare triple valid?
∀ m, {{X = m}} X := X + 1 {{X = m + 1}}, is a proposition stating that the Hoare triple {{X = m}} X := X + m {{X = m × 2}}) is valid for any choice of m.
What is formal Hoare logic method?
Hoare Logic is a formalism for reasoning about the behaviour of programs by relating their initial and terminal state. It uses an assertion logic based on first-order logic to reason about program states and extends this with Hoare triples to reason about the programs.
What is the formula and semantic of Hoare logic?
Hoare logic can be viewed as the structured essence of such operational proofs. The formulas of Hoare logic are the Hoare triples {P} c {Q}, where P is called the precondition and Q the postcondition.
What is Hoare?
Hoare is an English surname derived from Middle English hor(e) meaning grey- or white-haired.
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. The loop invariants will be true on entry into a loop and following each iteration, so that on exit from the loop both the loop invariants and the loop termination condition can be guaranteed.
What is the central feature of Hoare logic?
Hoare logic provides axioms and inference rules for all the constructs of a simple imperative programming language. In addition to the rules for the simple language in Hoare’s original paper, rules for other language constructs have been developed since then by Hoare and many other researchers.
What is loop invariant computation?
How is loop invariant algorithm used?
Therefore, the loop invariant condition is that at the end of i iteration right most i elements are sorted and in place. for (i = 0 to n-1) for (j = 0 to j arr[j+1]) swap(&arr[j], &arr[j+1]);…The loop invariant must be true:
- before the loop starts.
- before each iteration of the loop.
- after the loop terminates.
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.
What should your loop invariant be?
A loop invariant is a condition [among program variables] that is necessarily true immediately before and immediately after each iteration of a loop….The loop invariant must be true:
- before the loop starts.
- before each iteration of the loop.
- after the loop terminates.