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

Author José Espírito Santo

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Author Details

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

Funding

The author was supported by Fundação para a Ciência e a Tecnologia (FCT) through project UID/MAT/00013/2013.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.CSL.2020.35

Abstract

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
Keywords
  • Generalized applications
  • Natural deduction
  • Strong normalization
  • Standardization
  • Call-by-name
  • Call-by-value
  • Protecting-by-a-lambda

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References

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