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

We present a framework for applying memoization selectively. The framework provides programmer control over equality, space usage, and identification of precise dependences so that memoization can be applied according to the needs of an application. Two key properties of the framework are that it is efficient and yields programs whose performance can be analyzed using standard techniques. We describe the framework in the context of a functional language and an implementation as an SML library. The language is based on a modal type system and allows the programmer to express programs that reveal their true data dependences when executed. The SML implementation cannot support this modal type system statically, but instead employs run-time checks to ensure correct usage of primitives.

This paper describes a general approach for automatic and accurate time-bound analysis. The approach consists of transformations for building time-bound functions in the presence of partially known input structures, symbolic evaluation of the time-bound function based on input parameters, optimizations to make the overall analysis efficient as well as accurate, and measurements of primitive parameters, all at the source-language level. We have implemented this approach and performed a number of experiments for analyzing Scheme programs. The measured worst-case times are closely bounded by the calculated bounds. 1 Introduction Analysis of program running time is important for real-time systems, interactive environments, compiler optimizations, performance evaluation, and many other computer applications. It has been extensively studied in many fields of computer science: algorithms [20, 12, 13, 41], programming languages [38, 21, 30, 33], and systems [35, 28, 32, 31]. It is particularl...

Dynamic programming is an important algorithm design technique. It is used for solving problems whose solutions involve recursively solving subproblems that share subsubproblems. While a straightforward recursive program solves common subsubproblems repeatedly and often takes exponential time, a dynamic programming algorithm solves every subsubproblem just once, saves the result, reuses it when the subsubproblem is encountered again, and takes polynomial time. This paper describes a systematic method for transforming programs written as straightforward recursions into programs that use dynamic programming. The method extends the original program to cache all possibly computed values, incrementalizes the extended program with respect to an input increment to use and maintain all cached results, prunes out cached results that are not used in the incremental computation, and uses the resulting incremental program to form an optimized new program. Incrementalization statically exploits semantics of both control structures and data structures and maintains as invariants equalities characterizing cached results. The principle underlying incrementalization is general for achieving drastic program speedups. Compared with previous methods that perform memoization or tabulation, the method based on incrementalization is more powerful and systematic. It has been implemented and applied to numerous problems and succeeded on all of them. 1

This paper describes a method for transforming any given set of Datalog rules into an efficient specialized implementation with guaranteed worst-case time and space complexities, and for computing the complexities from the rules. The running time is optimal in the sense that only useful combinations of facts that lead to all hypotheses of a rule being simultaneously true are considered, and each such combination is considered exactly once. The associated space usage is optimal in that it is the minimum space needed for such consideration modulo scheduling optimizations that may eliminate some summands in the space usage formula. The transformation is based on a general method for algorithm design that exploits fixed-point computation, incremental maintenance of invariants, and combinations of indexed and linked data structures. We apply the method to a number of analysis problems, some with improved algorithm complexities and all with greatly improved algorithm understanding and greatly simplified complexity analysis.

Analysis of program running time is important for reactive systems, interactive environments, compiler optimizations, performance evaluation, and many other computer applications. It has been extensively studied in many elds of computer science: algorithms [21, 12, 13,40], programming languages [38, 22,31, 35, 34], and systems [36, 29,33,32]. Being able to predict accurate time bounds automatically and e ciently

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.

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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

An aggregate array computation is a loop that computes accumulated quantities over array elements. Such computations are common in programs that use arrays, and the array elements involved in such computations often overlap, especially across iterations of loops, resulting in signi cant redundancy in the overall computation. This paper presents a method and algorithms that eliminate such overlapping aggregate array redundancies and shows both analytical and experimental performance improvements. The method is based on incrementalization, i.e., updating the values of aggregate array computations from iteration to iteration rather than computing them from scratch in each iteration. This involves maintaining additional information not maintained in the original program. We reduce various analysis problems to solving inequality constraints on loop variables and array subscripts, and we apply results from work on array data dependence analysis. Incrementalizing aggregate array computations produces drastic program speedup compared to previous optimizations. Previous methods for loop optimizations of arrays do not perform incrementalization, and previous techniques for loop incrementalization do not handle arrays.