The Call-By-Value Lambda-Calculus with Generalized Applications

Author José Espírito Santo

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José Espírito Santo
  • Centre of Mathematics, University of Minho, Portugal

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José Espírito Santo. The Call-By-Value Lambda-Calculus with Generalized Applications. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 35:1-35:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


The lambda-calculus with generalized applications is the Curry-Howard counterpart to the system of natural deduction with generalized elimination rules for intuitionistic implicational logic. In this paper we identify a call-by-value variant of the system and prove confluence, strong normalization, and standardization. In the end, we show that the cbn and cbv variants of the system simulate each other via mappings based on extensions of the "protecting-by-a-lambda" compilation technique.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof theory
  • Theory of computation → Lambda calculus
  • Generalized applications
  • Natural deduction
  • Strong normalization
  • Standardization
  • Call-by-name
  • Call-by-value
  • Protecting-by-a-lambda


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