In this functional pearl, we examine the use of definitional interpreters as a basis for abstract interpretation of higher-order programming languages. As it turns out, definitional interpreters, especially those written in monadic style, can provide a nice basis for a wide variety of collecting semantics, abstract interpretations, symbolic executions, and their intermixings.But the real insight of this story is a replaying of an insight from Reynold's landmark paper, Definitional Interpreters for Higher-Order Programming Languages, in which he observes definitional interpreters enable the defined-language to inherit properties of the defining-language. We show the same holds true for definitional abstract interpreters. Remarkably, we observe that abstract definitional interpreters can inherit the so-called "pushdown control flow" property, wherein function calls and returns are precisely matched in the abstract semantics, simply by virtue of the function call mechanism of the defining-language.The first approaches to achieve this property for higher-order languages appeared within the last ten years, and have since been the subject of many papers. These approaches start from a state-machine semantics and uniformly involve significant technical engineering to recover the precision of pushdown control flow. In contrast, starting from a definitional interpreter, the pushdown control flow property is inherent in the metalanguage and requires no further technical mechanism to achieve.

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 NOMI-NAL 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 unfoldsand 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.

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 NOMI-NAL 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 unfoldsand 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.

The technique of abstracting abstract machines (AAM) provides a systematic approach for deriving computable approximations of evaluators that are easily proved sound. This article contributes a complementary step-by-step process for subsequently going from a naive analyzer derived under the AAM approach, to an efficient and correct implementation. The end result of the process is a two to three order-of-magnitude improvement over the systematically derived analyzer, making it competitive with hand-optimized implementations that compute fundamentally less precise results.

Abstracting abstract machines has been proposed as a lightweight approach to designing sound and computable program analyses. The approach derives abstract interpreters from existing machine semantics and has been applied to a variety of languages with features widely considered difficult to analyze. Although sound analyzers are straightforward to build under this approach, they are also prohibitively inefficient.This article contributes a step-by-step process for going from a naive analyzer derived under the abstracting abstract machine approach to an efficient program analyzer. The end result of the process is a two to three order-of-magnitude improvement over the systematically derived analyzer, making it competitive with hand-optimized implementations that compute fundamentally less precise results.