How do you find the weakest precondition?

How do you find the 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.

What does the weakest precondition of a program specify?

The weakest precondition of S with respect to R, normally written wp (S,R) is a predicate that characterizes this set of states. Use of the adjective weakest explicitly indicates that the predicate must characterize all states that guarantee termination of S in a state for which R is true.

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.

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 is precondition and postcondition?

A precondition is a predicate that should hold upon entry into a function. It expresses a function’s expectation on its arguments and/or the state of objects that may be used by the function. A postcondition is a predicate that should hold upon exit from a function.

What does partial correctness mean for a loop construct?

What does partial correctness mean for a loop construct? If loop termination can be shown, the axiomatic description. of the loop is called total correctness. If the other conditions can be met but. termination is not guaranteed, it is called partial 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.

Is this Hoare triple True or false?

The Hoare triple This notation is itself a true-false statement with this meaning: If S is executed in a state in which P is true, then S is guaranteed to terminate, and when it does, Q will be true.

What should a good precondition do?

A) A good precondition should do the following (of course, non-exhaustive list): Specify invalid values for input (example: if you divide by something, better put in that it may not be zero). Specify any valid ranges for input (example: if your function will only work as expected for values 0, 1, and 2, specify that).

How do you write preconditions?

// Precondition: letter is an uppercase or // lowercase letter (in the range ‘A’ ‘Z’ or ‘a’ ‘z’) . // Postcondition: The value returned by the // function is true if Letter is a vowel; // otherwise the value returned by the function is // false.

On what branch of mathematics is axiomatic semantics based?

mathematical logic
Unsourced material may be challenged and removed. Axiomatic semantics is an approach based on mathematical logic for proving the correctness of computer programs. It is closely related to Hoare logic.