Related papers: Rendering string diagrams recursively
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…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
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…
In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…
The correspondence between monoidal categories and graphical languages of diagrams has been studied extensively, leading to applications in quantum computing and communication, systems theory, circuit design and more. From the categorical…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…
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 introduce nominal string diagrams as, string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we…
The algebraic zigzag construction has recently been introduced as a combinatorial foundation for a higher dimensional notion of string diagram. For use in a proof assistant, a layout algorithm is required to determine the optimal rendering…
Neural networks are typically represented as data structures that are traversed either through iteration or by manual chaining of method calls. However, a deeper analysis reveals that structured recursion can be used instead, so that…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
We introduce string diagrams for physical duoidal categories (normal $\otimes$-symmetric duoidal categories): they consist of string diagrams with wires forming a zigzag-free partial order and order-preserving nodes whose inputs and outputs…
Turi and Plotkin's bialgebraic semantics is an abstract approach to specifying the operational semantics of a system, by means of a distributive law between its syntax (encoded as a monad) and its dynamics (an endofunctor). This setup is…
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,…
We discuss the foundations of 2-dimensional graphical languages, with a view towards their computer implementation in a 'compiler' for monoidal categories. In particular, we discuss the close relationship between string diagrams, pasting…
Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…