Related papers: Fast Automated Reasoning over String Diagrams usin…
This article presents a novel algorithmic methodology for performing automated diagrammatic deductions over combinatorial structures, using a combination of modified equational theorem-proving techniques and the extended Wolfram model…
Categorical quantum mechanics and the Wolfram model offer distinct but complementary approaches to studying the relationship between diagrammatic rewriting systems over combinatorial structures and the foundations of physics; the objective…
In this paper we adapt previous work on rewriting string diagrams using hypergraphs to the case where the underlying category has a traced comonoid structure, in which wires can be forked and the outputs of a morphism can be connected to…
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…
We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on context-free families of string diagrams which we represent using…
String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories. In the last few years, they have found application in the modelling of various computational structures, in fields as…
Term graph rewriting is important as "conceptual implementation" of the execution of functional programs, and of data-flow optimisations in compilers. One way to define term graph transformation rule application is via the well-established…
String diagrams are pictorial representations for morphisms of symmetric monoidal categories. They constitute an intuitive and expressive graphical syntax, which has found application in a very diverse range of fields including concurrency…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or discarded at will. In SMTs, traditional tree-like terms are…
In this paper, we first study hypergraph rewriting in categorical terms in an attempt to define the notion of events and develop foundations of causality in graph rewriting. We introduce novel concepts within the framework of double-pushout…
String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, rewriting string diagrams results in shorter equational proofs,…
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout…
We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along an overlap that is associative in a natural sense. Notably,…
This work is about diagrammatic languages, how they can be represented, and what they in turn can be used to represent. More specifically, it focuses on representations and applications of string diagrams. String diagrams are used to…
Critical pair analysis provides a convenient and computable criterion of confluence, which is a fundamental property in rewriting theory, for a wide variety of rewriting systems. Bonchi et al. showed validity of critical pair analysis for…
Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra, programming language semantics, representation theory,…
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
In this paper we address the problem of proving confluence for string diagram rewriting, which was previously shown to be characterised combinatorically as double-pushout rewriting with interfaces (DPOI) on (labelled) hypergraphs. For…
We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm…