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Program verification in Software Deploy ANSI/AIM Code 39 in Software Program verification

4 Program verification using barcode integration for software control to generate, create code39 image in software applications. Beaware of Malicious QR Codes This requi Software Code-39 res 177 iterations of the while-statement to reach a terminating state. Although it is re-assuring that some program runs terminate, the irregular pattern of + and above make it seem very hard, if not impossible, to come up with a variant that proves the termination of Collatz on all executions in which the initial value of x is positive. Finally, let s consider a really big integer: 32498723462509735034567279652376420563047563456356347563\\ 96598734085384756074086560785607840745067340563457640875\\ 62984573756306537856405634056245634578692825623542135761\\ 9519765129854122965424895465956457 where \\ denotes concatenation of digits.

Although this is a very large number indeed, our program Collatz requires only 4940 iterations to terminate. Unfortunately, nobody knows a suitable variant for this program that could . Observe how the use of as prove the validity of tot 0 < x Collatz a postcondition emphasizes that this Hoare triple is merely concerned about program termination as such.

Ironically, there is also no known initial value of x greater than 0 for which Collatz doesn t terminate. In fact, things are even subtler than they may appear: if we replace 3*c + 1 in Collatz with a di erent such linear expression in c, the program may not terminate despite meeting the precondition 0 < x; see exercise 6 on page 303..

4.5 Programming by contract For a vali Software 39 barcode d sequent tot P , the triple P may be seen as a contract between a supplier and a consumer of a program P . The supplier insists that consumers run P only on initial state satis es . In that case, the supplier promises the consumer that the nal state of that run satis es .

For a valid par P , the latter guarantee applies only when a run terminates. For imperative programming, the validation of Hoare triples can be interpreted as the validation of contracts for method or procedure calls. For example, our program fragment Fac1 may be the .

.. in the method body int factorial (x: int) { .

.. return y; } The code for this method can be annotated with its contractual assumptions and guarantees.

These annotations can be checked o -line by humans, during compile-time or even at run-time in languages such as Ei el. A possible format for such contracts for the method factorial is given in Figure 4.4.

. 4.5 Progra mming by contract method name: input: assumes: guarantees: output: modifies only: factorial x ofType int 0 <= x y = x! ofType int y. Figure 4.4. A contract for the method factorial. The keywor d assumes states all preconditions, the keyword guarantees lists all postconditions. The keyword modifies only speci es which program variables may change their value during an execution of this method. Let us see why such contracts are useful.

Suppose that your boss tells you to write a method that computes n read n choose k a notion of k combinatorics where 1/ 49 is your change of getting all six lottery numbers 6 right out of 49 numbers total. Your boss also tells you that n k = n! k! (n k)! (4.16).

holds. The Code 39 for None method factorial and its contract (Figure 4.4) is at your disposal.

Using (4.16) you can quickly compute some values, such as 5 = 2 5!/(2! 3!) = 10, 10 = 1, and 49 = 13983816. You then write a method 0 6 choose that makes calls to the method factorial, e.

g. you may write int choose(n : int, k : int) { return factorial(n) / (factorial(k) * factorial (n - k)); } This method body consists of a return-statement only which makes three calls to method factorial and then computes the result according to (4.16).

So far so good. But programming by contract is not just about writing programs, it is also about writing the contracts for such programs! The static information about choose e.g.

its name are quickly lled into that contract. But what about the preconditions (assumes) and postconditions (guarantees) At the very least, you must state preconditions that ensure that all method calls within this method s body satisfy their preconditions. In this case, we only call factorial whose precondition is that its input value be non-negative.

Therefore, we require that n, k, and n k be non-negative. The latter says that n is not smaller than k. What about the postconditions of choose Since the method body declared no local variables, we use result to denote the return value of this.

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