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

PABLO BUIRAS; ALEJANDRO DÍAZ CARO; MAURO JASKELIOFF

Belo Horizonte

Workshop; Workshop on Logical and Semantic Frameworks with Applications; 2011

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.