The Zoo of Lambda-Calculus Reduction Strategies, And Coq

Authors Małgorzata Biernacka , Witold Charatonik , Tomasz Drab

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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


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.

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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)


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
  • Lambda calculus
  • Reduction strategies
  • Coq


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