Abstract machine for $\mathcal{L}\mathcal{D}\mathcal{L}$

Abstract

We propose an abstract machine for $\mathcal{L}\mathcal{D}\mathcal{L}$ that maintains a high-level view of an $\mathcal{L}\mathcal{D}\mathcal{L}$ program while incorporating aspects of its execution that make a performance difference. A canonical AND/OR graph corresponding to the $\mathcal{L}\mathcal{D}\mathcal{L}$ program provides the skeleton of its execution. The nodes in the AND/OR graph are annotated to specify relevant details of the execution, such as access methods, join methods, execution strategies, intelligent backtracking etc. We formalize four execution methods (top-down, bottom-up as well as two hybrid methods that incorporate memoing) and two recursive computations (fixpoint and stack-based). The two computations and four execution methods are combined to cater to a rich variety of recursive techniques. This annotated AND/OR graph represents a declarative program for the abstract machine. The set of all possible annotated AND/OR graphs constitutes the execution space that defines the abstract machine.

To prove the feasibility of this declarative abstract machine, we demonstrate an actual realization by presenting a code generation algorithm that proceeds by translating each node in the annotated AND/OR graph into a sequence of imperative statements that include calls to a tuple-level interface of an underlying DBMS. The $\mathcal{L}\mathcal{D}\mathcal{L}$ compiler — which supports Datalog, sets, updates, negation, non-deterministic choice and other advanced features — has been implemented using this approach.