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Program verification in Software Maker Code39 in Software Program verification




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4 Program verification use software barcode 39 printer toadd 3 of 9 in software Recommended GS1 barcodes for mobile apps 3. Another control stru Software barcode 3/9 cture is if B {C1 } else {C2 }. It rst evaluates the boolean expression B in the current state of the store; if that result is true, then C1 is executed; if B evaluated to false, then C2 is executed.

4. The third control construct while B {C} allows us to write statements which are executed repeatedly. Its meaning is that: a the boolean expression B is evaluated in the current state of the store; b if B evaluates to false, then the command terminates, c otherwise, the command C will be executed.

If that execution terminates, then we resume at step (a) with a re-evaluation of B as the updated state of the store may have changed its value. The point of the while-statement is that it repeatedly executes the command C as long as B evaluates to true. If B never becomes false, or if one of the executions of C does not terminate, then the while-statement will not terminate.

While-statements are the only real source of non-termination in our core programming language.. Example 4.2 The factori al n! of a natural number n is de ned inductively by 0! = 1 (n + 1)! = (n + 1) n!. def def def (4.4). For example, unwinding Software Code 39 Extended this de nition for n being 4, we get 4! = 4 3! = = 4 3 2 1 0! = 24. The following program Fac1: y = 1; z = 0; while (z != x) { z = z + 1; y = y * z; } is intended to compute the factorial2 of x and to store the result in y. We will prove that Fac1 really does this later in the chapter.

. 4.2.2 Hoare triples Pro gram fragments generated by (4.

3) commence running in a state of the machine. After doing some computation, they might terminate. If they do, then the result is another, usually di erent, state.

Since our programming. Please note the di eren barcode 39 for None ce between the formula x! = y, saying that the factorial of x is equal to y, and the piece of code x != y which says that x is not equal to y.. 4.2 A framework for software verification language does not have Software Code 39 Extended any procedures or local variables, the state of the machine can be represented simply as a vector of values of all the variables used in the program. What syntax should we use for R , the formal speci cations of requirements for such programs Because we are interested in the output of the program, the language should allow us to talk about the variables in the state after the program has executed, using operators like = to express equality and < for less than. You should be aware of the overloading of =.

In code, it represents an assignment instruction; in logical formulas, it stands for equality, which we write == within program code. For example, if the informal requirement R says that we should. Compute a number y whose square is less than the input x. then an appropriate spe bar code 39 for None ci cation may be y y < x. But what if the input x is 4 There is no number whose square is less than a negative number, so it is not possible to write the program in a way that it will work with all possible inputs. If we go back to the client and say this, he or she is quite likely to respond by saying that the requirement is only that the program work for positive numbers; i.

e., he or she revises the informal requirement so that it now says. If the input x is a positive number, compute a number whose square is less than x. This means we need to b ANSI/AIM Code 39 for None e able to talk not just about the state after the program executes, but also about the state before it executes. The assertions we make will therefore be triples, typically looking like P which (roughly) means:. If the program P is run in a state that satis es , then the state resulting from P s execution will satisfy .. (4.5). The speci cation of the program P , to calculate a number whose square is less than x, now looks like this: x>0 P y y <x . (4.6).

It means that, if we ru barcode 3 of 9 for None n P in a state such that x > 0, then the resulting state will be such that y y < x. It does not tell us what happens if we run P in a state in which x 0, the client required nothing for non-positive values of x. Thus, the programmer is free to do what he or she wants in that case.

A program which produces garbage in the case that x 0 satis es the speci cation, as long as it works correctly for x > 0..
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