An External Module for Implementing Linear Tabling in Prolog

In previous work [1], we have presented a proposal to combine the power of tabling with the Extended Andorra Model (EAM) in order to produce an execution model with advanced control strategies that guarantees termination, avoids looping, reduces the search space, and is less sensitive to goal ordering. To address the integration between tabling and the EAM, through the BEAM system [2], we have identified several tasks [1]. In particular, to study how tabling interacts with the BEAM, we proposed the ability to use an external module for implementing tabling primitives that provide direct control over the search strategy. This approach may compromise efficiency, if compared to systems that implement tabling support at the low-level engine, but allows tabling to be easily incorporated into any Prolog system. For our work, it will serve as the basis to study and detect in advance the potential integration problems before extending the BEAM system to support tabling running within the EAM environment. In the past years several alternative mechanisms for tabling have been proposed and implemented in systems like XSB, Yap, B-Prolog, ALS-Prolog and Mercury. In these implementations, we can distinguish two main categories of tabling mechanisms: delaying-based tabling mechanisms in the sense that the computation state of suspended tabled subgoal calls has to be preserved, either by freezing the whole stacks or by copying the execution stacks to separate storage; and linear tabling mechanisms where a new call always extends the latest one, therefore maintaining only a single SLD tree in the execution stacks. Delaying-based mechanisms can be considered more complicated to implement but obtain better results. The weakness of the linear mechanisms is the necessity of re-computation for computing fix-points. Implementing tabling through an external module restrict us to linear tabling mechanisms, because external modules cannot directly interact with the execution stacks. Therefore, we have decided to design a module that implements the two available mechanisms that, to the best of our knowledge, implement linear tabling: the SLDT strategy of Zhou et al. [3]; and the DRA technique of Guo and Gupta [4]. The key idea of the SLDT strategy is to let a tabled subgoal call