A correct, precise and efficient integration of set-sharing, freeness and linearity for the analysis of finite and rational tree languages

It is well known that freeness and linearity information positively interact with aliasing information, allowing both the precision and the efficiency of the sharing analysis of logic programs to be improved. In this paper, we present a novel combination of set-sharing with freeness and linearity information, which is characterized by an improved abstract unification operator. We provide a new abstraction function and prove the correctness of the analysis for both the finite tree and the rational tree cases. Moreover, we show that the same notion of redundant information as identified in Bagnara et al. (2000) and Zaffanella et al. (2002) also applies to this abstract domain combination: this allows for the implementation of an abstract unification operator running in polynomial time and achieving the same precision on all the considered observable properties

A Backward Analysis for Constraint Logic Programs

One recurring problem in program development is that of understanding how to re-use code developed by a third party. In the context of (constraint) logic programming, part of this problem reduces to figuring out how to query a program. If the logic program does not come with any documentation, then the programmer is forced to either experiment with queries in an ad hoc fashion or trace the control-flow of the program (backward) to infer the modes in which a predicate must be called so as to avoid an instantiation error. This paper presents an abstract interpretation scheme that automates the latter technique. The analysis presented in this paper can infer moding properties which if satisfied by the initial query, come with the guarantee that the program and query can never generate any moding or instantiation errors. Other applications of the analysis are discussed. The paper explains how abstract domains with certain computational properties (they condense) can be used to trace control-flow backward (right-to-left) to infer useful properties of initial queries. A correctness argument is presented and an implementation is reported.Comment: 32 page

Design of abstract domains using first-order logic

In this paper we propose a simple framework based on first-order logic, for the design and decomposition of abstract domains for static analysis. An assertion language is chosen that specifies the properties of interest, and abstract domains are defined to be suitably chosen sets of assertions. Composition and decomposition of abstract domains is facilitated by their logical specification in first-order logic. In particular, the operations of reduced product and disjunctive completion are formalized in this framework. Moreover, the notion of (conjunctive) factorization of sets of assertions is introduced, that allows one to decompose domains in `disjoint' parts. We illustrate the use of this framework by studying typical abstract domains for ground-dependency and aliasing analysis in logic programming

Non-Strict Independence-Based Program Parallelization Using Sharing and Freeness Information.

The current ubiquity of multi-core processors has brought renewed interest in program parallelization. Logic programs allow studying the parallelization of programs with complex, dynamic data structures with (declarative) pointers in a comparatively simple semantic setting. In this context, automatic parallelizers which exploit and-parallelism rely on notions of independence in order to ensure certain efficiency properties. “Non-strict” independence is a more relaxed notion than the traditional notion of “strict” independence which still ensures the relevant efficiency properties and can allow considerable more parallelism. Non-strict independence cannot be determined solely at run-time (“a priori”) and thus global analysis is a requirement. However, extracting non-strict independence information from available analyses and domains is non-trivial. This paper provides on one hand an extended presentation of our classic techniques for compile-time detection of non-strict independence based on extracting information from (abstract interpretation-based) analyses using the now well understood and popular Sharing + Freeness domain. This includes algorithms for combined compile-time/run-time detection which involve special run-time checks for this type of parallelism. In addition, we propose herein novel annotation (parallelization) algorithms, URLP and CRLP, which are specially suited to non-strict independence. We also propose new ways of using the Sharing + Freeness information to optimize how the run-time environments of goals are kept apart during parallel execution. Finally, we also describe the implementation of these techniques in our parallelizing compiler and recall some early performance results. We provide as well an extended description of our pictorial representation of sharing and freeness information

Information Flow is Linear Refinement of Constancy

Detecting information flows inside a program is useful to check non-interference of program variables, an important aspect of software security. Information flows have been computed in the past by using abstract interpretation over an abstract domain IF which expresses sets of flows. In this paper we reconstruct IF as the linear refinement C->C of a basic domain C expressing constancy of program variables. This is important since we also show that C->C, and hence IF, is closed wrt linear refinement, and is hence optimal and condensing. Then a compositional, input-independent static analysis over IF has the same precision of a non-compositional, input-driven analysis. Moreover, we show that C->C has a natural representation in terms of Boolean formulas, efficiently implementable through binary decision diagrams

Quadtrees as an Abstract Domain

Quadtrees have proved popular in computer graphics and spatial databases as a way of representing regions in two dimensional space. This hierarchical data-structure is flexible enough to support non-convex and even disconnected regions, therefore it is natural to ask whether this datastructure can form the basis of an abstract domain. This paper explores this question and suggests that quadtrees offer a new approach to weakly relational domains whilst their hierarchical structure naturally lends itself to representation with boolean functions