Related papers: DisCoPy: the Hierarchy of Graphical Languages in P…
We introduce DisCoPy, an open source toolbox for computing with monoidal categories. The library provides an intuitive syntax for defining string diagrams and monoidal functors. Its modularity allows the efficient implementation of…
DisCoPy (Distributional Compositional Python) is an open source toolbox for computing with string diagrams and functors. In particular, the diagram data structure allows to encode various kinds of quantum processes, with functors for…
We introduce functorial language models: a principled way to compute probability distributions over word sequences given a monoidal functor from grammar to meaning. This yields a method for training categorical compositional distributional…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been…
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
We propose a new definition of higher-order DisCoCat (categorical compositional distributional) models where the meaning of a word is not a diagram, but a diagram-valued higher-order function. Our models can be seen as a variant of Montague…
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…
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…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…
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…
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…
String diagrams are a graphical language used to represent processes that can be composed sequentially or in parallel, which correspond graphically to horizontal or vertical juxtaposition. In this paper we demonstrate how to compute the…
PaPy, which stands for parallel pipelines in Python, is a highly flexible framework that enables the construction of robust, scalable workflows for either generating or processing voluminous datasets. A workflow is created from user-written…
Visualization of multidimensional, categorical data is a common challenge across scientific areas and, in particular, the life sciences. The goal is to create a comprehensive overview of the underlying data which allows to assess multiple…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
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…
Misconceptions about program execution hinder many novice programmers. We introduce SimpliPy, a notional machine designed around a carefully chosen Python subset to clarify core control flow and scoping concepts. Its foundation is a precise…
Premonoidal categories are monoidal categories without the interchange law while effectful categories are premonoidal categories with a chosen monoidal subcategory of interchanging morphisms. In the same sense that string diagrams,…