Straight ROBDDs are not the Best for Pos

The subject of groundness analysis for (constraint) logic programs has been widely studied, and interesting domains have been proposed. Pos has been recognized has the most suitable domain for capturing the kind of dependencies arising in groundness analysis. Its (by now standard) implementation is directly based on reduced ordered binary-decision diagrams (ROBDDs), a well-known symbolic representation for Boolean functions [4]. Even though several authors have reported positive experiences using ROBDDs for groundness analysis, in the literature there is no reference to the problem of the efficient detection of those variable which are deemed to be ground (or true, at the abstract level) in the context of a ROBDD. This is not surprising, since most currently implemented analyzers need to derive this information only at the end of the analysis and only for presentation purposes. Things are much different when this information is required during the analysis. This need arises when dealing with languages which employ some sort of delay mechanism, which are typically based on groundness conditions. In these cases, the näıf approaches are too inefficient, since the abstract interpreter must quickly (and often) decide whether a constraint is delayed or not. Fast access to ground variables is also necessary when aliasing analysis is performed using a domain not keeping track of ground dependencies. We have shown that, by using an hybrid representation instead of the standard (purely ROBDD-based) one, it is possible to have constant-time, fast access to ground variables. Moreover, the new representation improves (not make worse, as it can be expected) the overall efficiency (on both time and space) of groundness analysis. Due to extreme space limitations we just give a rough idea of how the hybrid representation and its operations look like. We also report on the experimental results we obtained with the China analyzer. The interested reader is referred to [3] for a complete account of this work.