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Extracting Environments from Function Closures

Published: 06 June 2022 Publication History

Abstract

In this paper, we study the mechanism for extracting the environment from a function closure in the framework of the lambda calculus. We propose the lambda calculus with environment extraction, which extends environment calculus. We define the untyped calculus: the syntax and the operational semantics. We show that the operational semantics are consistent using translation of the lambda calculus with environment extraction into the lambda calculus with records and pairs. Next, we give a simple type theory to the lambda calculus with environment extraction and prove that the type system holds the subject reduction theorem.

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Yuta Aoyagi and Shin-ya Nishizaki. 2018. Untyped Call-by-Value Calculus with First-Class Continuations and Environments. In Theory and Practice of Computation. World Scientific, 101–117.
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Oliver Laumann. 1995. Elk – The Extension Language Kit Scheme Reference.
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Shin-ya Nishizaki. 1995. Simply Typed Lambda Calculus with First-class Environments. Publications of Research Institute for Mathematical Sciences Kyoto University 30, 6 (1995), 1055–1121.
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Shin-ya Nishizaki. 2000. A Polymorphic Environment Calculus and its Type Inference Algorithm. Higher-Order and Symbolic Computation 13 (2000), 239–278.
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Shin-ya Nishizaki. 2013. Evaluation Strategy and Translation of Environment Calculus. In Information Computing and Applications. Springer Berlin Heidelberg, 232–242.
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Shin-ya Nishizaki. 2019. Simple type system for call-by-value calculus with first-class continuations and ennvironments. In Theory and Practice of Computation. CRC Press, 119–130.
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Shin-ya Nishizaki and Mizuki Fujii. 2012. Strong reduction for typed lambda calculus with first-class environments. In Lecture Notes in Computer Science, Vol. 7473. Springer-Verlag Berlin Heidelberg, 632–639.
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ICSCA '22: Proceedings of the 2022 11th International Conference on Software and Computer Applications
February 2022
224 pages
ISBN:9781450385770
DOI:10.1145/3524304
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Association for Computing Machinery

New York, NY, United States

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Published: 06 June 2022

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Author Tags

  1. environment
  2. function closure
  3. functional programming language
  4. lambda calculus

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