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

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数据科学与机器学习

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

关于

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.

主要功能

Polynomial functor modeling for structured interaction sets
Bidirectional transformation support via open games and lenses
Free monad and cofree comonad pairing for pattern/matter execution
2 GitHub stars
Compositional algorithm decomposition using spined categories
Dynamical systems integration with wiring diagrams and ODEs

使用场景

Implementing compositional AI reasoning frameworks using category theory
Modeling and verifying concurrent state machines and dynamical systems
Designing complex multi-agent game mechanics and equilibrium logic

关于

主要功能

Polynomial functor modeling for structured interaction sets
Bidirectional transformation support via open games and lenses
Free monad and cofree comonad pairing for pattern/matter execution
2 GitHub stars
Compositional algorithm decomposition using spined categories
Dynamical systems integration with wiring diagrams and ODEs

使用场景

Implementing compositional AI reasoning frameworks using category theory
Modeling and verifying concurrent state machines and dynamical systems
Designing complex multi-agent game mechanics and equilibrium logic