Related papers: A Structural and Nominal Syntax for Diagrams
Diagrammatic notation has become a ubiquitous computational tool; early examples include Penrose's graphical notation for tensor calculus, Feynman's diagrams for perturbative quantum field theory, and Cvitanovic's birdtracks for Lie…
These are lectures notes for a mini-course given at the conference Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras, and Categorification in June 2018. The goal is to introduce the reader to string diagram…
A visual programming language uses pictorial tools such as diagrams to represent its structural units and control stream. It is useful for enhancing understanding, maintenance, verification, testing, and parallelism. This paper proposes a…
A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the…
This short paper examines diagrams describing neural network systems in academic conference proceedings. Many aspects of scholarly communication are controlled, particularly with relation to text and formatting, but often diagrams are not…
We introduce here the notion of syntactic lattice algebra which is an analogy of the syntactic monoid and of the syntactic semiring. We present a unified approach to get those three structures.
The book is devoted to two research areas: (1) Designing programming languages along with their denotational models. A denotational model of a language consists of two many-sorted algebras - an algebra of syntax and an algebra of…
We extend the theory of formal languages in monoidal categories to the multi-sorted, symmetric case, and show how this theory permits a graphical treatment of topics in concurrency. In particular, we show that Mazurkiewicz trace languages…
Visual language is a system of communication that conveys information through symbols, shapes, and spatial arrangements. Diagrams are a typical example of a visual language depicting complex concepts and their relationships in the form of…
Topologists are sometimes interested in space-valued diagrams over a given index category, but it is tricky to say what such a diagram even is if we look for a notion that is stable under equivalence. The same happens in (homotopy) type…
Recently, there has been renewed interest in the theory and applications of de Paiva's dialectica categories and their relationship to the category of polynomial functors. Both fall under the theory of generalized polynomial categories,…
In this paper, we use the language of operads to study open dynamical systems. More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones. The syntactic architecture of…
Monoidal computer is a categorical model of intensional computation, where many different programs correspond to the same input-output behavior. The upshot of yet another model of computation is that a categorical formalism should provide a…
Diagrammatically speaking, grammatical calculi such as pregroups provide wires between words in order to elucidate their interactions, and this enables one to verify grammatical correctness of phrases and sentences. In this paper we also…
We present a new model of computation, described in terms of monoidal categories. It conforms the Church-Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most…
Equality saturation, a technique for program optimisation and reasoning, has gained attention due to the resurgence of equality graphs (e-graphs). E-graphs represent equivalence classes of terms under rewrite rules, enabling simultaneous…
Classic grammars and regular expressions can be used for a variety of purposes, including parsing, intent detection, and matching. However, the comparisons are performed at a structural level, with constituent elements (words or characters)…
Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two fields with a fresh look at Prolog encodings for the…
We present a Rocq library for monoidal categories, which includes a decision procedure for proving equality of morphisms as well as notations that make it possible to reason as if they were strict, inferring MacLane isomorphims…
Human syntactic structures are usually represented as graphs. Much research has focused on the mapping between such graphs and linguistic sequences, but less attention has been paid to the shapes of the graphs themselves: their topologies.…