Efficient Computation via Incremental Computation

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 \Phi, the approach yields an incremental program that computes f(x \Phi y) efficiently by using the result of f(x), the intermediate results of f(x), and auxiliary information about 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 in general, by computing each iteration incrementally using an appropriate incremental program. This method has been applied to problems in interactive systems, optimizing compilers, transformational programming, etc. The design and implementation of a prototype system, CACHET, for deriving incremental programs is also described. Ke..