Boolean Functions for Finite-Tree Dependencies

Several logi -based languages, su h as Prolog II and its su essors, SICStus Prolog and Oz, o er a omputation domain in luding rational trees. In nite rational trees allow for inreased expressivity ( y li terms an provide eÆ ient representations of grammars and other useful obje ts) and for faster uni ation (due to the safe omission of the o urshe k). Unfortunately, the use of in nite rational trees has problems. For instan e, many of the built-in and library predi ates are ill-de ned for su h trees and need to be supplemented by run-time he ks whose ost may be signi ant. In a ompanion paper [3℄ we have proposed a dataow analysis aimed at the knowledge of those program variables (the nite variables) that will always be bound to nite terms. The analysis domain introdu ed in [3℄ orre tly aptures the reation and propagation of y li terms, but is not apable of propagating the guarantees of niteness that ome from built-in predi ates and program annotations. Here we present a domain of Boolean fun tions that pre isely aptures how the niteness of some variables inuen es the niteness of other variables. This domain of nite-tree dependen ies provides relational information that is important for the pre ision of the overall niteness analysis. It also ombines obvious similarities, interesting di eren es and somewhat unexpe ted onne tions with lassi al domains for groundness dependen ies.