论文标题
关于定量代数高阶理论
On Quantitative Algebraic Higher-Order Theories
论文作者
论文摘要
我们探讨了扩展Mardare等人的可能性。定量代数到自然来自组合逻辑和lambda-calculus的结构。首先，我们表明该框架确实适用于这些结构，并给出健全和完整性的结果。然后，我们证明了一些负面的结果，这些结果清楚地描绘了指标空间的类别可以是这种理论的模型。最后，我们给出了几个非平凡的高阶定量代数的例子。
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those structures, and give soundness and completeness results. Then, we prove some negative results which clearly delineate to which extent categories of metric spaces can be models of such theories. We conclude by giving several examples of non-trivial higher-order quantitative algebras.
