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The Zoo of Lambda-Calculus Reduction Strategies, And Coq

Authors Małgorzata Biernacka , Witold Charatonik , Tomasz Drab

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Author Details

Małgorzata Biernacka
  • University of Wrocław, Faculty of Mathematics and Computer Science, Poland
Witold Charatonik
  • University of Wrocław, Faculty of Mathematics and Computer Science, Poland
Tomasz Drab
  • University of Wrocław, Faculty of Mathematics and Computer Science, Poland

Funding

This research is supported by the National Science Centre of Poland, under grant number 2019/33/B/ST6/00289.

Acknowledgements

We thank the anonymous reviewers for their comments and references to the literature. The last author thanks his wife, Monika, for taking care of everything around during proof completion.

Cite AsGet BibTex

Małgorzata Biernacka, Witold Charatonik, and Tomasz Drab. The Zoo of Lambda-Calculus Reduction Strategies, And Coq. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ITP.2022.7

Abstract

We present a generic framework for the specification and reasoning about reduction strategies in the lambda calculus, representable as sets of term decompositions. It is provided as a Coq formalization that features a novel format of phased strategies. It facilitates concise description and algebraic reasoning about properties of reduction strategies. The formalization accommodates many well-known strategies, both weak and strong, such as call by name, call by value, head reduction, normal order, full β-reduction, etc. We illustrate the use of the framework as a tool to inspect and categorize the "zoo" of existing strategies, as well as to discover and study new ones with particular properties.

Subject Classification

ACM Subject Classification
  • Theory of computation → Lambda calculus
  • Theory of computation → Operational semantics
  • Theory of computation → Automated reasoning
Keywords
  • Lambda calculus
  • Reduction strategies
  • Coq

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