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Paper detail

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

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.

preprint2012arXivOpen access
Pablo BuirasAlejandro Díaz-CaroMauro Jaskelioff
Logic in Computer Science
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Pablo BuirasAlejandro Díaz-CaroMauro Jaskelioff

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