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Abstracting definitional interpreters (functional pearl)

Authors:

David Darais,

Nicholas Labich,

Phúc C. Nguyen,

David Van HornAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 1, Issue ICFP

Article No.: 12, Pages 1 - 25

https://doi.org/10.1145/3110256

Published: 29 August 2017 Publication History

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Abstract

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 meta-language and requires no further technical mechanism to achieve.

Supplementary Material

Auxiliary Archive (icfp17-main114-s.zip)

This reusable artifact is an open-format virtual machine containing the Abstracting Definitional Interpreters framework, implementations, tests, and paper. See the included README for full instructions. To build the library, run the unit tests, and compile/execute the paper as a literate racket program, just boot the virtual machine and run the following commands: $ cd ~/monadic-eval $ make $ make test $ make pdf

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References

[1]

Mads S. Ager, Olivier Danvy, and Jan Midtgaard. A functional correspondence between monadic evaluators and abstract machines for languages with computational effects. Theoretical Computer Science, 2005.

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