Efficiency by incrementalization: an introduction

Incremental computation takes advantage of repeated computations on inputs that differ slightly from one another, computing each output efficiently by exploiting the previous output. This paper gives an overview of a general and systematic approach to incrementalization: given a program f and an operation ⊕, the approach yields an incremental program that computes f(x ⊕ y) efficiently by using the result of f(x), the intermediate results of f(x), and auxiliary information of f(x) that can be inexpensively maintained. Since every non-trivial computation proceeds by iteration or recursion, the approach can be used for achieving efficient computation by computing each iteration incrementally using an appropriate incremental program. This approach has applications in interactive systems, optimizing compilers, transformational programming, and many other areas, where problems were previously solved in less general and systematic ways. This paper also describes the design and implementation of CACHET, a prototype system for incrementalization.