Confluence via strong normalisation in an algebraic \lambda-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. 
Pablo Buiras, Alejandro D\'iaz-Caro, Mauro Jaskelioff
cs.LO