Experiments with applicative updating: Practical results

Abstract

Large scale computing applications often consist of calculations that are repeated for many sets of input data. If the variance between the data sets is small, there may be portions of the computation which are not affected by the changes in the input values. The effort required for such systems can be reduced with efficient methods of recomputation. This paper presents an approach for efficient recomputation over function graphs. A change to an input value of a previously computed function initiates a process of retraction along the data paths dependent on that input. The retraction process consists of first tracing the paths from the input to the output, noting along the way that a change is impending, then tracing back from the output to the input, removing the previously computed values from the intermediate nodes. The modified input value is then released into the function graph, and the retracted portions of the graph are recomputed. Throughout this process, all nonretracted output values are an accurate reflection of the current input values. A retraction mechanism that allows efficient recomputation increases the usefulness of functional programming systems. We present the results of some experiments showing the time taken by the recomputation for two different types of problems. We propose the characteristics of function graphs for which this technique will be most effective.