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Confluence via strong normalisation in an algebraic lambda-calculus with rewriting

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.
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https://hal.inria.fr/hal-00924938
Contributor : Alejandro Díaz-Caro <>
Submitted on : Tuesday, January 7, 2014 - 12:26:15 PM
Last modification on : Tuesday, November 24, 2020 - 4:06:01 PM

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Pablo Buiras, Alejandro Díaz-Caro, Mauro Jaskelioff. Confluence via strong normalisation in an algebraic lambda-calculus with rewriting. LSFA - 6th Workshop on Logical and Semantic Frameworks with Applications - 2011, Aug 2011, Belo Horizonte, Brazil. pp.16-29, ⟨10.4204/EPTCS.81.2⟩. ⟨hal-00924938⟩

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