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.

Self-adjusting computation enables writing programs that can automatically and efficiently respond to changes to their data (e.g., inputs). The idea behind the approach is to store all data that can change over time in modifiable references and to let computations construct traces that can drive change propagation. After changes have occurred, change propagation updates the result of the computation by re-evaluating only those expressions that depend on the changed data. Previous approaches to selfadjusting computation require that modifiable references be written at most once during execution—this makes the model applicable only in a purely functional setting. In this paper, we present techniques for imperative self-adjusting computation where modifiable references can be written multiple times. We define a language SAIL (Self-Adjusting Imperative Language) and prove consistency, i.e., that change propagation and from-scratch execution are observationally equivalent. Since SAIL programs are imperative, they can create cyclic data structures. To prove equivalence in the presence of cycles in the store, we formulate and use an untyped, step-indexed logical relation, where step indices are used to ensure well-foundedness. We show that SAIL accepts an asymptotically efficient implementation by presenting algorithms and data structures for its implementation. When the number of operations (reads and writes) per modifiable is bounded by a constant, we show that change propagation becomes as efficient as in the non-imperative case. The general case incurs a slowdown that is logarithmic in the maximum number of such operations. We describe a prototype implementation of SAIL as a Standard ML library. 1

Abstract. This paper presents a semantics of self-adjusting computation and proves that the semantics is correct and consistent. The semantics integrates change propagation with the classic idea of memoization to enable reuse of computations under mutation to memory. During evaluation, reuse of a computation via memoization triggers a change propagation that adjusts the reused computation to reflect the mutated memory. Since the semantics combines memoization and change-propagation, it involves both non-determinism and mutation. Our consistency theorem states that the non-determinism is not harmful: any two evaluations of the same program starting at the same state yield the same result. Our correctness theorem states that mutation is not harmful: self-adjusting programs are consistent with purely functional programming. We formalized the semantics and its meta-theory in the LF logical framework and machine-checked the proofs in Twelf. 1

We present an overview of our ongoing work on parallelizing self-adjusting-computation techniques. In self-adjusting computation, programs can respond to changes to their data (e.g., inputs, outcomes of comparisons) automatically by running a change-propagation algorithm. This ability is important in applications where inputs change slowly over time. All previously proposed self-adjusting computation techniques assume a sequential execution model. We describe techniques for writing parallel self-adjusting programs and a change propagation algorithm that can update computations in parallel. We describe a prototype implementation and present preliminary experimental results. 1.

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

and by donations from Intel Corporation. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. Keywords: self-adjusting computation, adaptivity, memoization, change-propagation, continuation-passing style, typed compilation, cost semantics, trace distance, traceable Self-adjusting computation is a paradigm for programming incremental computations that efficiently respond to input changes by updating the output in time proportional to the changes in the structure of the computation. This dissertation defends the thesis that high-level programming abstractions improve the experience of reading, writing, and reasoning about and the efficiency of self-adjusting programs. We show that high-level language constructs are suitable for writing readable self-adjusting programs and can be compiled into low-level primitives. In particular, language constructs such as ML-style modifiable references and memoizing functions provide orthogonal mechanisms for identifying stale computation