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首页> 外文会议>Annual ACM/IEEE Symposium on Logic in Computer Science >Rewriting modulo symmetric monoidal structure
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Rewriting modulo symmetric monoidal structure

机译：重写模数对称的单侧结构

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String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory. An important role in many such approaches is played by equational theories of diagrams, typically oriented and applied as rewrite rules. This paper lays a comprehensive foundation for this form of rewriting. We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure. We illustrate our approach with a proof of termination for the theory of non-commutative bimonoids.
机译：字符串图是一个强大而直观的图形语法，用于对称尾样类（SMC）。他们在计算机科学中发现了许多应用，并且在物理和控制理论之类的其他领域变得越来越相关。在许多此类方法中的重要作用是通过图的实际理论来扮演的，通常是面向的，并应用为重写规则。本文为这种重写形式奠定了全面的基础。我们将图中的图解为键入的超图，并在重写模拟中建立了一方面的SMC规律的精确对应关系，并且在另一方面，超微的推出（DPO）重写的重写（DPO）重写，受到称为凸性的声音条件。这结果依赖于更常见的特征定理，我们展示了用所选的特殊Frobenius结构图案重写模拟SMC定律的类型的超图DPO重写金额。我们说明了我们对非换向辅音理论的终止证明的方法。

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