Incrementalization: From Clarity to Efficiency

Incrementalization is at the core of a systematic program design method, especially for the design of algorithms and data structures. It takes a function and an input change operation and yields an incremental function that computes each new output by using the old output and additional values. It is the analogue of differentiation in continuous domains. This article gives an overview of a systematic program design method centered on incrementalization. The method starts with a clear specification of a computation and derives an efficient implementation by semantics-preserving program transformations. The method applies to problems specified in imperative, database, functional, logic, and objectoriented programming languages with different data, control, and module abstractions. We illustrate the method through examples from optimizing compilers, graph algorithms, string processing, and program components. The last section discusses directions for future studies.