Incremental computing with abstract data structures

Abstract

Incremental computing is a method of keeping consistency between an input and an output. If only a small portion of the input is modified, it is natural to expect that the corresponding output can be obtained more efficiently than full re-computation. However, for abstract data structures such as self-balancing binary search trees, even the most primitive modifications may lead to drastic change of the underlying structure. In this paper, we develop an incremental computing method, which can deal with complex modifications and therefore is suitable for abstract data structures. The key idea is to use shortcut fusion in order to decompose a complex modification to a series of simple ones. Based on this idea, we extend Jeuring’s incremental computing method, which can deal with algebraic data structures, so as to deal with abstract data structures. Our method is purely functional and does not rely on any run-time support. Its correctness is straightforward from parametricity. Moreover, its cost is often proportional to that of the corresponding modification.