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.

We describe a machine model for automatically dynamizing static algorithms and apply it to historyindependent data structures. Static programs expressed in this model are dynamized automatically by keeping track of dependences between code and data in the form of a dynamic dependence graph. To study the performance of such automatically dynamized algorithms we present an analysis technique based on trace stability. As an example of the use of the model, we dynamize the Parallel Tree Contraction Algorithm of Miller and Reif to obtain a history-independent data structure for the dynamic trees problem of Sleator and Tarjan. 1

Abstract. This paper describes FrTime, an extension of Scheme designed for writing interactive applications. Inspired by functional reactive programming, the language embeds dynamic dataflow within a call-by-value functional language. The essence of the embedding is to make program expressions evaluate to nodes in a dataflow graph. This strategy eases importation of legacy code and permits incremental program construction. We have integrated FrTime with the DrScheme programming environment and have used it to develop several novel applications. We describe FrTime’s design and implementation in detail and present a formal semantics of its evaluation model. 1

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

Change propagation is a technique for automatically adjusting the output of an algorithm to changes in the input. The idea behind change propagation is to track the dependences between data and function calls, so that, when the input changes, functions affected by that change can be re-executed to update the computation and the output. Change propagation makes it possible for a compiler to dynamize static algorithms. The practical effectiveness of change propagation, however, is not known. In particular, the cost of dependence tracking and change propagation may seem significant. The contributions of the paper are twofold. First, we present some experimental evidence that change propagation performs well when compared to direct implementations of dynamic algorithms. We implement change propagation on tree-contraction as a solution to the dynamic trees problem and present an experimental evaluation of the approach. As a second contribution, we present a library for dynamic-trees that support a general interface and present an experimental evaluation by considering a broad set of applications. The dynamic-trees library relies on change propagation to handle edge insertions/deletions. The applications that we consider include path queries, subtree queries, leastcommon-ancestor queries, maintenance of centers and medians of trees, nearest-marked-vertex queries, semidynamic minimum spanning trees, and the max-flow algorithm of Sleator and Tarjan.

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Self-adjusting programs respond automatically and efficiently to input changes by tracking the dynamic data dependences of the computation and incrementally updating the output as needed. In order to identify data dependences, previously proposed approaches require the user to make use of a set of monadic primitives. Rewriting an ordinary program into a self-adjusting program with these primitives, however, can be difficult and error-prone due to various monadic and proper-usage restrictions, some of which cannot be enforced statically. Previous work therefore suggests that self-adjusting computation would benefit from direct language and compiler support. In this paper, we propose a language-based technique for writing and compiling self-adjusting programs from ordinary programs. To compile self-adjusting programs, we use a continuationpassing

Abstract. Define a static algorithm as an algorithm that computes some combinatorial property of its input consisting of static, i.e., non-moving, objects. In this paper, we describe a technique for syntactically transforming static algorithms into kinetic algorithms, which compute properties of moving objects. The technique o«ers capabilities for composing kinetic algorithms, for integrating dynamic and kinetic changes, and for ensuring robustness even with fixed-precision floating-point arithmetic. To evaluate the e«ectiveness of the approach, we implement a library for performing the transformation, transform a number of algorithms, and give an experimental evaluation. The results show that the technique performs well in practice. 1

We present DITTO, an automatic incrementalizer for dynamic, sideeffect-free data structure invariant checks. Incrementalization speeds up the execution of a check by reusing its previous executions, checking the invariant anew only on the changed parts of the data structure. DITTO exploits properties specific to the domain of invariant checks to automate and simplify the process without restricting what mutations the program can perform. Our incrementalizer works for modern imperative languages such as Java and C#. It can incrementalize, for example, verification of red-black tree properties and the consistency of the hash code in a hash table bucket. Our source-tosource implementation for Java is automatic, portable, and efficient. DITTO provides speedups on data structures with as few as 100 elements; on larger data structures, its speedups are characteristic of non-automatic incrementalizers: roughly 5-fold at 5,000 elements, and growing linearly with data structure size.