Incremental Computation with Names

TL;DR

This paper introduces NOMINAL ADAPTON, a language with first-class names that enhances incremental computation efficiency, enabling reuse across program runs, formal verification, and significant speedups over previous systems.

Contribution

It presents NOMINAL ADAPTON, a novel language design incorporating first-class names for improved incremental computation and formalizes its correctness.

Findings

Efficient incrementalization of standard patterns like maps, folds, unfolds

Construction of incremental probabilistic trees and tries

Large speedups over from-scratch and previous systems

Abstract

Over the past thirty years, there has been significant progress in developing general-purpose, language-based approaches to incremental computation, which aims to efficiently update the result of a computation when an input is changed. A key design challenge in such approaches is how to provide efficient incremental support for a broad range of programs. In this paper, we argue that first-class names are a critical linguistic feature for efficient incremental computation. Names identify computations to be reused across differing runs of a program, and making them first class gives programmers a high level of control over reuse. We demonstrate the benefits of names by presenting NOMINAL ADAPTON, an ML-like language for incremental computation with names. We describe how to use NOMINAL ADAPTON to efficiently incrementalize several standard programming patterns -- including maps, folds, and unfolds -- and show how to build efficient, incremental probabilistic trees and tries. Since NOMINAL ADAPTON's implementation is subtle, we formalize it as a core calculus and prove it is from-scratch consistent, meaning it always produces the same answer as simply re-running the computation. Finally, we demonstrate that NOMINAL ADAPTON can provide large speedups over both from-scratch computation and ADAPTON, a previous state-of-the-art incremental computation system.