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Standardization of a Call-By-Value Lambda-Calculus

Authors Giulio Guerrieri, Luca Paolini, Simona Ronchi Della Rocca

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Giulio Guerrieri
Luca Paolini
Simona Ronchi Della Rocca

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Giulio Guerrieri, Luca Paolini, and Simona Ronchi Della Rocca. Standardization of a Call-By-Value Lambda-Calculus. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 211-225, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.TLCA.2015.211

Abstract

We study an extension of Plotkin's call-by-value lambda-calculus by means of two commutation rules (sigma-reductions). Recently, it has been proved that this extended calculus provides elegant characterizations of many semantic properties, as for example solvability. We prove a standardization theorem for this calculus by generalizing Takahashi's approach of parallel reductions. The standardization property allows us to prove that our calculus is conservative with respect to the Plotkin's one. In particular, we show that the notion of solvability for this calculus coincides with that for Plotkin's call-by-value lambda-calculus.
Keywords
  • standardization,sequentialization,lambda-calculus,sigma-reduction,par- allel reduction
  • call-by-value
  • head reduction
  • internal reduction
  • solvability

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References

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