论文标题
拓扑声音较高的图表重写的数据结构
Data Structures for Topologically Sound Higher-Dimensional Diagram Rewriting
论文作者
论文摘要
我们提出了示意图集的计算实现，这是一个重写“拓扑声音”的高维图的模型：图表将功能解释允许在细胞络合物中作为同质性。这在高级代数和类别理论的形式上以及计算代数拓扑中都具有潜在的应用。我们描述了任意维度图的形状良好形状的数据结构，并为时间O（n^3 log n）提供了解决其同构问题的解决方案。最重要的是，我们定义了一种在图表集中重写的类型理论，并提供了其句法类别的语义表征。所有数据结构和算法均在Python库Rewalt中实现，该库还支持图表的各种可视化。
We present a computational implementation of diagrammatic sets, a model of higher-dimensional diagram rewriting that is "topologically sound": diagrams admit a functorial interpretation as homotopies in cell complexes. This has potential applications both in the formalisation of higher algebra and category theory and in computational algebraic topology. We describe data structures for well-formed shapes of diagrams of arbitrary dimensions and provide a solution to their isomorphism problem in time O(n^3 log n). On top of this, we define a type theory for rewriting in diagrammatic sets and provide a semantic characterisation of its syntactic category. All data structures and algorithms are implemented in the Python library rewalt, which also supports various visualisations of diagrams.
