Finite-Tree Analysis for Constraint Logic-Based Languages

Abstract

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can provide very efficient representations of grammars and other useful objects). Unfortunately, the use of infinite rational trees has problems. For instance, many of the built-in and library predicates are ill-defined for such trees and need to be supplemented by run-time checks whose cost may be significant. Moreover, some widely-used program analysis and manipulation techniques are correct only for those parts of programs working over finite trees. It is thus important to obtain, automatically, a knowledge of the program variables (the finite variables) that, at the program points of interest, will always be bound to finite terms. For these reasons, we propose here a new dataflow analysis, based on abstract interpretation, that captures such information. We present a parametric domain where a simple component for recording finite variables is coupled, in the style of the open product construction of Cortesi et al., with a generic domain (the parameter of the construction) providing sharing information. The sharing domain is abstractly specified so as to guarantee the correctness of the combined domain and the generality of the approach. This finite-tree analysis domain is further enhanced by coupling it with a domain of Boolean functions, called finite-tree dependencies, that precisely captures how the finiteness of some variables influences the finiteness of other variables. We also summarize our experimental results showing how finite-tree analysis, enhanced with finite-tree dependencies, is a practical means of obtaining precise finiteness information.

Tabling, Rational Terms, and Coinduction Finally Together!

“…This has resulted in generating cyclic terms known as rational terms or rational trees in Prolog. While the introduction of cyclic terms in Prolog was unintentional, soon after applications for cyclic terms emerged in fields such as definite clause grammars (Colmerauer 1982;Giannesini and Cohen 1984), constraint programming (Meister and Frühwirth 2006;Bagnara et al 2001) and coinduction ). But support for rational terms across Prolog systems varies and often fails to provide the functionality required by most applications.…”

cTI: a constraint-based termination inference tool for ISO-Prolog

“…We point out that simple, sufficient syntactic methods for ensuring occurs-check freedom are presented in Apt and Pellegrini (1994), while Søndergaard (1986) and Crnogorac et al (1996) describe abstract-interpretation based solutions. Recently, finite-tree analysis (Bagnara et al 2001a;Bagnara et al 2001b) has been proposed to confine infinite rational terms in programs that are not occurs-check free. Both the approach described in Mesnard and Ruggieri (2003), and the cTI system can be extended, with the help of finite-tree analysis, to deal also with such programs.…”

System-Level State Equality Detection for the Formal Dynamic Verification of Legacy Distributed Applications

“…Many tools exploit dynamic analysis either for the verification of C programs [15,4,16] with abstract interpretation in some cases and focused on memory-related errors [17,18] or in particular for the termination analysis [19,20]. This approach is also commonly used for Java [12] or object-based program analysis, with a garbage collection mechanism [21].…”