We prove a linearity theorem for an extension of linear logic with addition and multiplication by a scalar: the proofs of some propositions in this logic are linear in the algebraic sense. This work is part of a wider research program that aims at defining a logic whose proof language is a quantum programming language.

翻译：我们证明了线性逻辑延伸的线性理论的线性理论,用一个标度来增加和乘以线性逻辑:这一逻辑中某些论点的证据在代数意义上是线性的。 这项工作是一个更广泛的研究方案的一部分,其目的是界定一种逻辑,其证明语言是一种量子编程语言。