We revisit the Vectorial Lambda Calculus, a typed version of Lineal. Vectorial (as well as Lineal) has been originally designed for quantum computing, as an extension to System F where linear combinations of lambda terms are also terms and linear combinations of types are also types. In its first presentation, Vectorial only provides a weakened version of the Subject Reduction property. We prove that our revised Vectorial Lambda Calculus supports the standard version of said property, answering a long standing issue. In addition we also introduce the concept of weight of types and terms, and prove a relation between the weight of terms and of its types.

翻译：我们重新审视了Vecumental Lambda Calculus(以及线性),这是线性计算的一种打印版本。脉性(以及线性)最初是为量性计算设计的,作为F系统的一个扩展,其中羊羔术语的线性组合也是术语,而种类的线性组合也是类型。在第一次介绍中,镇性只提供了“减少主题”属性的弱化版本。我们证明,我们经过修订的“边性兰巴达计算”支持上述属性的标准版本,回答了一个长期存在的问题。此外,我们还引入了类型和条件权重的概念,并证明了条款权重与类型权重之间的关系。