Finite-Tree Analysis for Constraint Logic-Based Languages: The Complete Unabridged Version

Logic languages based on the theory of rational, possibly infinite, trees have muchappeal in that rational trees allow for faster unification (due to the safe omission ofthe occurs-check) and increased expressivity (cyclic terms can provide very efficientrepresentations of grammars and other useful objects). Unfortunately, the use ofinfinite rational trees has problems. For instance, many of the built-in and librarypredicates are ill-defined for such trees and need to be supplemented by run-timechecks whose cost may be significant. Moreover, some widely-used program analysisand manipulation techniques are correct only for those parts of programs workingover finite trees. It is thus important to obtain, automatically, a knowledge of theprogram variables (the finite variables) that, at the program points of interest, willalways be bound to finite terms. For these reasons, we propose here a new data-flow analysis, based on abstract interpretation, that captures such information. Wepresent a parametric domain where a simple component for recording finite variablesis coupled, in the style of the open product construction of Cortesi et al., with ageneric domain (the parameter of the construction) providing sharing information.The sharing domain is abstractly specified so as to guarantee the correctness ofthe combined domain and the generality of the approach. This finite-tree analysisdomain is further enhanced by coupling it with a domain of Boolean functions, calledfinite-tree dependencies, that precisely captures how the finiteness of some variablesinfluences the finiteness of other variables. We also summarize our experimentalresults showing how finite-tree analysis, enhanced with finite-tree dependencies, isa practical means of obtaining precise finiteness information.