Corollary 3.11 in .NET Use QR-Code in .NET Corollary 3.11

Corollary 3.11 using .net vs 2010 togenerate qrcode in web,windows application Microsoft Office Excel Website If x2 does not occur QR Code 2d barcode for .NET in E1 then x1 := E1 ; x2 := E2 x2 := (E2 )E1 x1 ; x1 := E1 . For example, we may move the rst assignment statement downwards in the program segment, x := x + y; z := x + 1; and write z := x + y + 1; x := x + y; We may not do the same to the following statements, however, x := x + y; y := y + 2; because y, the variable on the left-hand side of the second statement, occurs on the right-hand side of the rst statement.

. Subprogram Simpli cation The purpose of an ass qr barcode for .NET ignment statement is to assign a value to a variable so that it can be used in some statements downstream. Now if the preceding rule is used to move an assignment statement downstream past all statements in which the assigned value is used, the statement becomes redundant and thus can be deleted.

. De nition 3.12 A statement in a prog Denso QR Bar Code for .NET ram is said to be redundant if its sole purpose is to de ne the value of a data structure, and this particular value is not used anywhere in the program. Obviously a redundant statement can be removed without changing the computation performed by the program.

. Corollary 3.13 If x1 := E1 ; x2 := E .net vs 2010 QR Code 2 is a sequence of two assignment statements such that, = by interchanging these two statements, x1 : E1 becomes redundant, then x1 := E1 ; x2 := E2 x2 : (E2 )E1 x1 . = In general, Corollary 3.

13 becomes applicable when x2 : E2 is the last = statement to make use of de nition provided by x1 : E1 . For example, = x := x + y z := x + 1 return z; z := x + y + 1; return z;. Corollaries 3.11 and 3.13 can be used to reduce the number of assignment statements in a program, and thus the number of steps involved in computation.

The end result is often a simpler and more understandable program as demonstrated in Example A.1 in Appendix A. Finally, it should be pointed out that certain sequences of assignment statements can be simpli ed through symbolic execution and heuristics, but not through the use of Corollaries 3.

10, 3.11, and 3.13.

For example, consider the following sequence of assignment statements (where % denotes a modulus operator):. S1 : r : a % b; =. Path-Oriented Program Analysis a b r a b : = : = : = QR Code for .NET : = : = b; r; a % b; b; r;. We cannot simplify th is sequence with the previously mentioned corollaries. Nevertheless, if we perform a symbolic execution of this sequence of statements with the symbolic values: a A, b B, and r R, the net result will be r B%(A%B) a A%B b B%(A%B) Some re ection will show that this result can be produced by using the following sequence of assignment statements:. S2 : a : a % b; = b : QR Code 2d barcode for .NET b % a; = r : b; =. That is to say, the previous S1 can be reduced to S2 . Program Set As mentioned before, by inserting a constraint into a program, we shrink the domain for which it is de ned. To reverse this process, we need to be able to speak of, and make use of, a set of subprograms. To this end, a new programming construct called a program set is now introduced.

The meaning of a program set, or a set of programs, is identical to the conventional notion of a set of other objects. As usual, a set of n programs is denoted by {P1 , P2 , . .

. , Pn }. When used as a programming construct, it describes the computation prescribed by its elements.

Formally, the semantics of such a set is de ned in Axiom 4.1..

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