| A. Mycroft, Completeness and predicate-based abstract interpretation, Proc. ACM Symp. on Partial Evaluation and Semantics-Based Program Manipulation (PEPM93), Copenhagen, Denmark, June 1993. |
....of the program, viz. ae(lfp(T ) and, in general, lfp(aeffiT ) 6= ae(lfp(T ) However, it is known (see e.g. 9] that for any monotonic operator T , ae(lfp(T ) lfp(aeffiT ) holds. Completeness of the abstraction is a well known sufficient condition assuring that the equality holds (see [9, 21]) The abstraction ae 2 uco(D) is complete if aeffiT = aeffiT ffiae; analogously, the abstraction given by the Galois insertion (D ; ff; A; fl) is complete if ffffiT = ffffiT ffifl ffiff. Thus, we will say that an abstract least fixpoint semantics [ Delta] ae or [ Delta] ff is complete if the ....
A. Mycroft. Completeness and predicate-based abstract interpretation. In Proc. ACM PEPM '93 , 1993.
....B F complete for a semantic function as follows. De nition 2. Let C be a complete lattice and 2 uco(C) be an abstract domain. is B(F) complete for f if f = f (f = f ) While B completeness is well known in abstract interpretation and it corresponds to the standard notion of completeness [18, 14], the notion of forward completeness is less known. B completeness means that the domain is expressive enough such that no loss of precision is accumulated by abstracting in the arguments of a function f . Conversely, F completeness means that no loss of precision is accumulated by ....
A. Mycroft. Completeness and predicate-based abstract interpretation. In Proc. of the ACM Symp. on Partial Evaluation and Program Manipulation (PEPM '93 ), pages 179-185. ACM Press, New York, 1993.
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A. Mycroft, Completeness and predicate-based abstract interpretation, Proc. ACM Symp. on Partial Evaluation and Semantics-Based Program Manipulation (PEPM93), Copenhagen, Denmark, June 1993.
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