STOP statement

The program contains a do loop that iterates the statements within the loop until the condition (A — 1)<0 is true. Try moving the do statement around in the program to see what changes in the output. Explain. If you encounter an infinite loop, True BASIC has a STOP statement to get you out. 

Thus assignment statements can have any number of entries but only one exit, test statements can have any number of entries but two exits, START statements have no entries and one exit and STOP statements have any number of entries but no exits. 

P contains well-formed assignment and test statements, exactly one START statement and at least one STOP statement. 

We can write out explicitly the computation states for computation (P,I,(2,3)) where the initial value of is 2 and of x2 is 3. We have attached letters to the right of the statement boxes except for the unique STMT and STOP statements for convenience in naming the statements executed at each step. 

Notice that T(P) is a proper tree. An execution sequence s of length n 2 2 is consistent with exactly one execution sequence s of length n-1 namely, if s consists of statements (k, k2,...,kn), then s is %, k2,...jk. The tree T(P) is finite branching for if s is an execution sequence of length n and s = (k. .., k ) we need only consider the possibilities far statement k. If it is a STOP statement, s is a complete execution sequence and has no consistent extensions so it labels a node with no sons. If kR is an assignment statement, or a farced transfer, there is exactly one statement kn+1 such that (kpk2,..., k, kn+ ) is consistent, namely the unique statement following. If is a conditional transfer (test) then, since our tests are binary,... 

The scheme above is not free. If we remove the requirement that a scheme contain at least one STOP statement, there are free always looping schemes such as ... 

LEMMA. 4.13 Let P be a flow diagram whose graph S is a line-like single entry single exit graph with entry node e and exit node d, such that either d is labeled with a STOP statement or d has exactly one arc leading out of G. Then P is a well-structured graph. 

Any START statement any STOP statement any assignment statement u t where u is a variable and t is an extended functional term. 

DEFINITION A finite sequence of acceptable constructions starting with START and ending with STOP and containing no other START or STOP statements is a WHILE scheme. If P is a WHILE scheme and I an interpretation of P, then (P,I) is a WHILE program or structured program or GOTO-less - PROGRAM. 

If S is a set of induction points, there is a finite set n(S) of all path segments which start with a member of S, end with a member of S and otherwise do not pass through any point of S. Every path from START to STOP can be divided into path segments from IKS). Sets with these properties do exist for example, the set of all addresses in P is certainly a candidate for S. For a WHILE scheme, It suffices to include in S the initial statement, all STOP statements, and the start of each WHILE statement. 

We wish to see that for any choice of X = a and Y = b each path verification condition in W(P,A,B,I) holds. That is, we must examine each V(P,a,At r,I)(a,b) where o is a consistent path from tagged point t to tagged point r not passing through any other tagged point en route from t to r. If the hypothesis of the conditional expression V(P,a,A, A r,I)(a,b) is false, then the verification condition is vacuously true. If it is true, then A (a,b) is true and by definition of Aj, A(a) is true and computation (P,I,a) at some point enters tagged point t with Y = b. Further a is the continuation of this computation and reaches r with Y = b. So there is certainly a time when computation (P,I,a) reaches r with this specification of Y. Now if r is not a STOP statement, inductive assertion was assigned by our definition and thus Ar(a,b ) holds by definition. 

First suppose that we are dealing with input criterion A and program (P,I). If t is not a STOP statement, let inductive assertion A (a,b) hold if and only A(a) holds and computation (P,I,a) ever enters tagged point t with Y = b. ... 

Call a node in a free scheme "live" if there is a path from it to a STOP statement since the scheme is free this path is an execution sequence. Call a node "dead" if it is not live - if there is no path from it to STOP. We have mentioned previously that it is decidable whether there is a path between two nodes in a finite state graph (although it is rot decidable whether there is an execution sequence between two nodes in a scheme that is not free). Hence it is decidable... 

Insert a Stop statement in the VBA code. See Appendix D for details. 

To remove a breakpoint, click on the breakpoint indicator, or place the cursor on the highlighted line and press the Toggle Breakpoint button, or delete a Stop statement. 

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