What is the 'Pattern runs on matter' concept in this skill?

It refers to the mathematical module action where a free monad (representing decision trees or scripts) is executed over a cofree comonad (representing behavior trees or the environment), allowing for structured interaction modeling.

What are 'Open Games' in the context of this skill?

Open Games are a framework for compositional game theory using lenses. This skill uses them to model bidirectional transformations where information flows forward and utility or constraints flow backward.

How does this skill support dynamical systems?

It provides implementation patterns for discrete and continuous dynamical systems, including update functions, readout maps, and compositional wiring diagrams for connecting multiple systems.

Which programming languages does this skill utilize?

The skill includes implementations and examples across a diverse range of languages including Python, Ruby, Clojure, Hy, and Lisp, reflecting its multi-platform category-theoretic roots.

Polynomial Operads & Compositional AI

Name: Polynomial Operads & Compositional AI
Author: plurigrid

byplurigrid

•

Ciencia de Datos y ML

Integrates polynomial functors and category-theoretic operads to model complex interaction patterns and dynamical systems within AI workflows.

The ASI Polynomial Operads skill provides a robust framework for implementing advanced category theory concepts like polynomial functors, free monads, and cofree comonads. Based on the work of Spivak, Libkind, and Bumpus, it enables Claude to reason about 'Pattern running on Matter'—the interaction between decision logic and behavioral environments. This skill is essential for developers building complex concurrent systems, open games, or compositional AI architectures that require rigorous mathematical foundations for interaction, state management, and causal reasoning.

Características Principales

01Polynomial functor modeling for structured interaction sets

02Bidirectional transformation support via open games and lenses

03Free monad and cofree comonad pairing for pattern/matter execution

042 GitHub stars

05Compositional algorithm decomposition using spined categories

06Dynamical systems integration with wiring diagrams and ODEs

Casos de Uso

01Implementing compositional AI reasoning frameworks using category theory

02Modeling and verifying concurrent state machines and dynamical systems

03Designing complex multi-agent game mechanics and equilibrium logic

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi asi-polynomial-operads

For use in Claude.ai and ChatGPT

Download Skill