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The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits

Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad $\mcT$, capturing this self-similarity. We discuss the algebra $\Rel$ of mathematical relations on $\mcT$, and in so doing use wiring diagrams as a graphical language with which to structure queries on relational databases. We give the example of circuit diagrams as a special case. We move on to show how plug-and-play devices and also recursion can be formulated in the operadic framework as well. Throughout we include many examples and figures.

Introduction - redo: a recursive build system

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Generic deriving of generic traversals | Proceedings of the ACM on Programming Languages

Functional programmers have an established tradition of using traversals as a design pattern to work with recursive data structures. The technique is so prolific that a whole host of libraries have been designed to help in the task of automatically ...

The Rust Programming Language - The Rust Programming Language

by Steve Klabnik, Carol Nichols, and Chris Krycho, with contributions from the Rust Community

Categorical Data Structures for Technical Computing

Many mathematical objects can be represented as functors from finitely-presented categories $\mathsf{C}$ to $\mathsf{Set}$. For instance, graphs are functors to $\mathsf{Set}$ from the category with two parallel arrows. Such functors are known informally as $\mathsf{C}$-sets. In this paper, we describe and implement an extension of $\mathsf{C}$-sets having data attributes with fixed types, such as graphs with labeled vertices or real-valued edge weights. We call such structures "acsets," short for "attributed $\mathsf{C}$-sets." Derived from previous work on algebraic databases, acsets are a joint generalization of graphs and data frames. They also encompass more elaborate graph-like objects such as wiring diagrams and Petri nets with rate constants. We develop the mathematical theory of acsets and then describe a generic implementation in the Julia programming language, which uses advanced language features to achieve performance comparable with specialized data structures.

Alpaca – Algorithmic Pattern Catalogue

The Alpaca 2025 festival and conference on algorithmic patterns in the creative arts is happening this September 2025. Please see…

Logic for Programmers

Practical math for the working programmer.

A theory of type polymorphism in programming

The aim of this work is largely a practical one. A widely employed style of programming, particularly in structure-processing languages which impose n…

Embracing AI and formalization: Experimenting with tomorrow’s mathematical tools

Embracing AI and formalization: Experimenting with tomorrow’s mathematical tools. By Jarod Alper

Crafting Interpreters

Ever wanted to make your own programming language or wondered how they are designed and built?

Axioms for Organizers by Fred Ross, Sr. | Fred Ross, Sr.

Structured planning and debugging | Proceedings of the 5th international joint conference on Artificial intelligence - Volume 2

We introduce a new approach to planning in STRIPS-like domains based on constructing and analyzing a compact structure we call a Planning Graph. We describe a new planner, Graphplan, that uses this paradigm. Graphplan always returns a shortest-possible ...