An adaptive computation maintains the relationship between its input and output as the input changes. Although various techniques for adaptive computing have been proposed, they remain limited in their scope of applicability. We propose a general mechanism for adaptive computing that enables one to make any purely-functional program adaptive. We show

Self-adjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a reasonably broad range of applications. In this article, we describe algorithms and implementation techniques to realize self-adjusting computation and present an experimental evaluation of the proposed approach on a variety of applications, ranging from simple list primitives to more sophisticated computational geometry algorithms. The results of the experiments show that the approach is effective in practice, often offering orders of magnitude speedup from recomputing the output from scratch. We believe this is the first experimental evidence that incremental computation of any type is effective in practice for a reasonably broad set of applications.

Origin Tracking is a technique which, in the framework of first-order term rewriting systems, establishes relations between each subterm t of a normal form and a set of subterms, the origins of t, in the initial term. Origin tracking is based on the notion of residuals. It has been used successfully for the generation of error handlers and debuggers from algebraic specifications of programming languages. Recent experiments with the use of higher-order algebraic specifications for the definition of programming languages revealed a need to extend origin tracking for higher-order term rewriting systems. In this paper, we discuss how origin information can be maintained for fij reductions and expansions, during higher-order rewriting. We give a definition of higher-order origin tracking. The suitability of this definition is illustrated with a small, existing specification. AMS Subject Classification (1991): 68N20, 68Q55, 68Q65. CR Subject Classification (1991): D.2.5, D.2.6, D.3.4, F.3...

Abstract. In self-adjusting computation, programs respond automatically and efficiently to modifications to their data by tracking the dynamic data dependences of the computation and incrementally updating the output as needed. In this tutorial, we describe the self-adjustingcomputation model and present the language ∆ML (Delta ML) for writing self-adjusting programs. 1