Related papers: DisCoPy: Monoidal Categories in Python
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
HolPy is an interactive theorem proving system implemented in Python. It uses higher-order logic as the logical foundation. Its main features include a pervasive use of macros in producing, checking, and storing proofs, a JSON-based format…
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 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,…
In this paper, we present pomdp_py, a general purpose Partially Observable Markov Decision Process (POMDP) library written in Python and Cython. Existing POMDP libraries often hinder accessibility and efficient prototyping due to the…
We introduce the monoidal closed category qCPO of quantum cpos, whose objects are "quantized" analogs of omega-complete partial orders (cpos). The category qCPO is enriched over the category CPO of cpos, and contains both CPO, and the…
FlowPy is a numerical toolbox for the solution of partial differential equations encountered in Functional Renormalization Group equations. This toolbox compiles flow equations to fast machine code and is able to handle coupled systems of…
SpeechPy is an open source Python package that contains speech preprocessing techniques, speech features, and important post-processing operations. It provides most frequent used speech features including MFCCs and filterbank energies…
We introduce string diagrams for graded symmetric monoidal categories. Our approach includes a definition of graded monoidal theory and the corresponding freely generated syntactic category. Also, we show how an axiomatic presentation for…
QuaPy is an open-source framework for performing quantification (a.k.a. supervised prevalence estimation), written in Python. Quantification is the task of training quantifiers via supervised learning, where a quantifier is a predictor that…
This article offers an intuitive introduction to monoidal categories through the lens of painting, presenting abstract mathematical concepts with visual and tactile analogies. Aimed at curious undergraduates and non-specialists, it seeks to…
Machine learning is a general-purpose technology holding promises for many interdisciplinary research problems. However, significant barriers exist in crossing disciplinary boundaries when most machine learning tools are developed in…
PyPOTS is an open-source Python library dedicated to data mining and analysis on multivariate partially-observed time series with missing values. Particularly, it provides easy access to diverse algorithms categorized into five tasks:…
The categorical compositional distributional (DisCoCat) model of meaning rigorously connects distributional semantics and pregroup grammars, and has found a variety of applications in computational linguistics. From a more abstract…
Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive…
We introduce context-free languages of morphisms in monoidal categories, extending recent work on the categorification of context-free languages, and regular languages of string diagrams. Context-free languages of string diagrams include…
This paper introduces the concept of distorted monoidal categories, a generalization of monoidal and braided monoidal categories that supports non-reversible and direction-sensitive tensor structures. Unlike the classical setting, where the…
SciPy is an open source scientific computing library for the Python programming language. SciPy 1.0 was released in late 2017, about 16 years after the original version 0.1 release. SciPy has become a de facto standard for leveraging…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
Premonoidal categories and Freyd categories provide an encompassing framework for the semantics of call-by-value programming languages. Premonoidal categories are a weakening of monoidal categories in which the interchange law for the…