[1102.0749v3] Confluence via strong normalisation in an algebraic λ-calculus with rewriting
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arXiv:1102.0749v3 (cs)
[Submitted on 3 Feb 2011 (v1), last revised 28 Mar 2012 (this version, v3)]

Title:Confluence via strong normalisation in an algebraic λ-calculus with rewriting

Authors:Pablo Buiras, Alejandro Díaz-Caro, Mauro Jaskelioff
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Abstract:The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while the latter uses equalities. When given by rewrites, algebraic lambda-calculi are not confluent unless further restrictions are added. We provide a type system for the linear-algebraic lambda-calculus enforcing strong normalisation, which gives back confluence. The type system allows an abstract interpretation in System F.
Comments: In Proceedings LSFA 2011, arXiv:1203.5423
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:1102.0749 [cs.LO]
  (or arXiv:1102.0749v3 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.1102.0749
Journal reference: EPTCS 81, 2012, pp. 16-29
Related DOI: https://doi.org/10.4204/EPTCS.81.2

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Thu, 3 Feb 2011 18:54:30 UTC (53 KB)
[v2] Tue, 27 Mar 2012 08:35:20 UTC (1 KB) (withdrawn)
[v3] Wed, 28 Mar 2012 05:06:08 UTC (33 KB)
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