Steffen, B. 1989. Optimal data flow analysis via observational equivalence. In Proc. of the 14th Internat.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....condition. The classical naive 1 There is not presently an agreement on a name for what we call completeness and full completeness. For instance: Cousot [1997b, Section 12] Cousot [1997a, Section 12] and Clarke et al. 1994, Section 4. 3] call exactness our notion of (nonfull) completeness; Steffen [1989, Section 3.1] uses instead the term full abstraction; Comini and Levi [1994] use the term precision; while Dams et al. 1997, Section 4] use the term optimality for the same notion. We follow Cousot and Cousot [1994] Mycroft [1993] Reddy and Kamin [1992] and Sekar et al. 1997] by using the ....

....a denotational like environment. They obtained two completeness results, respectively, for first order and typed higher order functional languages, that in a certain precise sense subsume the completeness result of Sekar et al. Thus, also their approach substantially differs from our perspective. Steffen [1989] is one of the first authors isolating completeness as a key property for analysis. He introduces a concept of observation equivalence for abstract interpretations, which is similar to our notion of completeness. However, these approaches have a quite different viewpoint. Steffen s approach is ....

Steffen, B. 1989. Optimal data flow analysis via observational equivalence. In Proc. of the 14th Internat.

....ffffi ff is a collecting semantics. is therefore a pre order on 0 and naturally defines an observational equivalence on collecting semantics: S X iff S X and X S. Note that if hC ; T i hC 0 ; T 0 i then C = C 0 . Moreover, let hC ; T i be a collecting semantics, we follow [22] 1 by defining an observation as an element in O(S) fX j X 2 0 X Sg. It is immediate to prove that S X iff O(S) O(X ) Equivalent collecting semantics allow the same set of possible observations. In the following we abuse by denoting 0 the set 0= Moreover we assume S 6 X while S ....

....hC ; T i is model complete then fp(T ) fM j M is a collecting model of Pg. Thus, the fixpoints of the operator T provide only a partial characterization of the class of collecting models for a program. An interpretation M such that T (M ) vC M will be called a reachable collecting model . 1 [22] defines an observation for a semantics hC ; T i as a complete lattice isomorphic to an upper closure of C . In our case, this naturally induces a (more abstract) semantics, i.e. an object in O(hC ; T i) 3.3 Herbrand s, Clark s, Heyting s and s collecting semantics In this section we consider ....

B. Steffen. Optimal data flow analysis via observational equivalence. In Proc. MFCS'89 , LNCS 379, pp. 492-502, 1989.

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