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Additional info for Reasoning about program transformations: imperative programming and flow of data
Sample text
The lack of precise knowledge on execution paths has an impact on all the analyses and optimizations a compiler may want to apply to a program. In other words, a compiler has to approximate some information, to remember that some information may or may not hold—and to live with it, that is, to keep optimizing the program as much as possible while preserving correctness. One perspective is to say that 0 is a possible or “maybe” value of x. Another way to consider things is to say that the most precise information we can deliver is the union of all possible values.
This simplification can be treacherous because different program executions having the same execution trace can have very different properties. 2. 1. 1 2 read i; a[i] := 0 . . . . . . . . . 1. The importance of memory states. . . . . . . . . Statement 1 reads the value of i from the keyboard. At compile time we have no idea what this value will be. We know, however, that only one execution trace is possible (1 then 2, assuming no exception occurred in 1). Still, the set of memory locations potentially modified by this program is as large as array a.
10. 1. . Of course, one necessary condition for the transformed program to be correct is that each computation described in the original program be performed once and only once after transformation. 10 satisfy this condition? 11. p 4 3 2 1 t 2 3 4 5 6 7 8 . . . . . . . . 11. 10. . . . . . . . 11.