On Quantitative Algebraic Higher-Order Theories
On Quantitative Algebraic Higher-Order Theories
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论定量代数高阶理论
DOI：
10.48550/arxiv.2204.13654
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Paolo Pistone
中科院分区：
文献类型：
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作者：
Ugo Dal Lago;F. Honsell;Marina Lenisa;Paolo Pistone
我们探索了将Mardare等代数扩展到自然而然的结构，这些结构首先是从组合性逻辑和λ级别出现的，我们证明了一些负面的结果，这些结果清楚地描述了我们通过给出几个非平凡的高阶定量代数的示例来列出的。
We explore the possibility of extending Mardare et al quantitative algebras to the structures which naturally emerge from Combinatory Logic and the λ -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.