Pablo Buiras,  Alejandro Díaz-Caro,  Mauro Jaskelioff. 

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.

http://www.lbd.dcc.ufmg.br/colecoes/lsfa/2011/002.pdf

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