Two Approaches to Interprocedural Data Flow Analysis

Cover Two Approaches to Interprocedural Data Flow Analysis
Two Approaches to Interprocedural Data Flow Analysis
Micha Sharir
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n n Proof : (VJhich is quite similar to the proof of an analagous theorem of Kildall for a bounded semilattice [KI]): (a) Let n c N* and p = (r, ,3- / . • - » s, ,n) e path ^(r, n). By (4. 1) we have X* (x* ) ^3 ^^2'^3^ ^2 X* y* for all i > 0, n G N* . N — ■' n — Indeed, let i=0. If np^r, then x*^^' = ^* > y* . On the other hand.
In — ■'n the null execution path p- e path_^ (r, ,r, ), so that y* 0. Then x* ' = x* ' > y*, and for each ^1 ^1 - ^1 n c N* - {r, } we have x n *(i+l) = A f* (x*^^^
...> A f* (V*) by the induction hypothesis. We now need the following Lemma 4.

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