On the equational consistency of order-theoretic models of the lambda-calculus

Carraro, Alberto; Salibra, Antonino

doi:10.4230/LIPIcs.CSL.2012.152

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On the equational consistency of order-theoretic models of the lambda-calculus

Authors Alberto Carraro, Antonino Salibra

Part of: Volume: Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (CSL 2012)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Computer Science Logic (CSL)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2012-09-03

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Document Identifiers

DOI: 10.4230/LIPIcs.CSL.2012.152
URN: urn:nbn:de:0030-drops-36703

Subject Classification

Keywords

Lambda calculus
order-incompleteness
partially ordered models

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Abstract

Answering a question by Honsell and Plotkin, we show that there are two equations between lambda terms, the so-called  subtractive equations, consistent with lambda calculus but not satisfied in any partially ordered model with bottom element. We also relate the subtractive equations to the open problem of the order-incompleteness of lambda calculus.

Cite As Get BibTex

Alberto Carraro and Antonino Salibra. On the equational consistency of order-theoretic models of the lambda-calculus. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 152-166, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012) https://doi.org/10.4230/LIPIcs.CSL.2012.152

Author Details

Alberto Carraro

Antonino Salibra

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