Universit a Di Pisa Functional Compositions of Abstract Interpretations Functional Compositions of Abstract Interpretations
نویسندگان
چکیده
In the context of standard abstract interpretation theory, we deene and study a systematic operator of reduced relative power for composing functionally abstract domains. The reduced relative power of two abstract domains D1 (the exponent) and D2 (the base) consists in a suitably deened lattice of monotone functions from D1 to D2, called dependencies, and it is a generalization of the Cousot and Cousot operator of reduced (cardinal) power. The relationship between the reduced relative power and Nielson's tensor product is also investigated. The case of autodependencies (when base and exponent are the same domain) turns out to be particularly interesting: Under certain hypotheses, the domain of autodependencies corresponds to a suitable powerset-like completion of the base abstract domain, providing a compact lattice-theoretic representation for autodependencies. The usefulness of the reduced relative power is shown by a number of applications to abstract domains used both for program analysis and for semantics design. Notably, we prove that the domain Def for logic program ground-dependency analysis can be characterized as autodependencies of a standard more abstract domain representing plain groundness only, and we show how to exploit reduced relative power to systematically derive compositional logic program semantics.
منابع مشابه
Universit a Di Pisa Making Abstract Interpretations Complete Making Abstract Interpretations Complete
Completeness in abstract interpretation is an ideal situation where the abstract semantics is able to take full advantage of the power of representation of the underlying abstract domain. Thus, complete abstract interpretations can be rightfully considered as optimal. In this article , we develop a general theory of completeness in abstract interpretation, also dealing with the most frequent ca...
متن کاملUniversit a Di Pisa Using Mpi for P3l Implementation Universit a Degli Studi Di Pisa Dipartimento Di Informatica Using Mpi for P3l Implementation
This document concerns with the implementation of the P3L parallel programming language on the MPI abstract Machine. First we focus our attention on the characteristics of the MPI Abstract Machine, then we present a preliminary implementaton for each P3L construct based on that architecture.
متن کاملUniversit a Di Pisa Logical Formalizations of Syntactical Properties (extended Abstract) Logical Formalizations of Syntactical Properties (extended Abstract)
متن کامل
Abstract state machines and high-level system design and analysis
State Machines and High-Level System Design and Analysis A special issue of the TCS Journal, edited 2004 by Egon Borger, aDipartimento di Informatica, Universit a di Pisa, Via F. Buonarroti 2, I-56127 Pisa, Italy
متن کاملUniversit a Di Pisa Programming by Combining General Logic Programs Programming by Combining General Logic Programs
The program composition approach can be fruitfully applied to combine general logic programs, i.e. logic programs possibly containing negative premises. We show how the introduction of a basic set of (meta-level) composition operations over general programs increases the knowledge representation capabilities of logic programming for non-monotonic reasoning. Examples of modular programming, hier...
متن کامل