Garbage-free Abstract Interpretation through Abstract Reference Counting

Abstract garbage collection is the application of garbage collection to an abstract interpreter. Existing work has shown that abstract garbage collection can improve both the interpreter’s precision and performance. Current approaches rely on heuristics to decide when to apply abstract garbage collection. Garbage will build up and impact precision and performance when the collection is applied infrequently, while too frequent applications will bring about their own performance overhead. A balance between these tradeoffs is often difficult to strike.
We propose a new approach to cope with the buildup of garbage in the results of an abstract interpreter. Our approach is able to eliminate all garbage, therefore obtaining the maximum precision and performance benefits of abstract garbage collection. At the same time, our approach does not require frequent heap traversals, and therefore adds little to the interpreters’s running time. The core of our approach uses reference counting to detect and eliminate garbage as soon as it arises. However, reference counting cannot deal with cycles, and we show that cycles are much more common in an abstract interpreter than in its concrete counterpart. To alleviate this problem, our approach detects cycles and employs reference counting at the level of strongly connected components. While this technique in general works for any system that uses reference counting, we argue that it works particularly well for an abstract interpreter. In fact, we show formally that for the continuation store, where most of the cycles occur, the cycle detection technique only requires O(1) amortized operations per continuation push.
We present our approach formally, and provide a proof-of-concept implementation in the Scala-AM framework. We empirically show our approach achieves both the optimal precision and significantly better performance compared to existing approaches to abstract garbage collection.