论文标题
重新审视矢量lambda演算
The Vectorial Lambda Calculus Revisited
论文作者
论文摘要
我们重新审视矢量lambda cyculus，这是字头线的打字版本。矢量（以及线性）最初是为量子计算而设计的，作为对系统F的扩展，其中lambda项的线性组合也是术语，类型的线性组合也是类型。在第一个演示文稿中，矢量仅提供了削弱的主题还原性能。我们证明，经过修订的矢量lambda演算支持该财产的标准版本，回答了一个长期存在的问题。此外，我们还介绍了类型和术语的重量概念，并证明了术语的重量及其类型之间的关系。
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.
