Is this skill compatible with standard Cubical Agda?

Yes, it provides implementation patterns and best practices for both Rzk and Cubical Agda based on the Riehl-Shulman 2017 paper.

How does this skill assist with chemical computing?

It provides the 'Chemputer Semantics' mapping, where the interval represents reaction progress, endpoints represent reactants/products, and higher simplices model multi-step synthesis.

What are extension types in this skill?

Extension types are a generalization of path types that allow for the definition of functions with prescribed boundaries on directed cubes, essential for synthetic infinity-category theory.

What is a directed interval in this context?

A directed interval (2) is a mathematical primitive representing a unique morphism from 0 to 1, used to model processes that cannot be reversed, such as time or chemical reactions.

Directed Interval (Rzk & Cubical)

Name: Directed Interval (Rzk & Cubical)
Author: plurigrid

byplurigrid

•

開発者ツール

Axiomatizes time-directed homotopy and reaction progress using directed intervals for synthetic infinity-categories.

The Directed Interval skill implements the Riehl-Shulman 2017 framework for directed cubes, enabling Claude to model irreversible processes where 'time flows forward.' It replaces the undirected interval of standard cubical type theory with a directed version (0 → 1), making it indispensable for formalizing chemical reactions, directed homotopy, and synthetic higher category theory. By providing formal definitions for Rzk and Cubical Agda, it allows for the precise modeling of 'walking arrows' and higher simplices in computational chemistry and formal methods.

主な機能

017 GitHub stars

02Provides integration patterns for Rzk, Cubical Agda, and Julia ACSets

03Implements extension types for functions with prescribed boundaries

04Axiomatizes the directed interval (2) as a primitive walking arrow

05Maps chemical reaction progress (Reactants → Products) to directed cubes

06Defines directed cubes, squares, and higher simplices (Δ¹, Δ², Δ³)

ユースケース

01Formalizing multi-step chemical synthesis as directed simplices in a chemputer

02Proving properties in synthetic infinity-categories using Rzk syntax

03Modeling irreversible computational workflows and time-directed state transitions

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi directed-interval

For use in Claude.ai and ChatGPT

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