How does this skill apply to chemical computing?

It maps chemical reactions to directed edges where the start of the interval represents reactants and the end represents products, ensuring simulations respect thermodynamic irreversibility.

What are extension types?

Extension types are functions with prescribed boundaries that generalize path types, allowing for the definition of functions that must match specific values at the interval's endpoints.

What is a directed interval in this context?

A directed interval, or 'walking arrow,' is a mathematical structure modeling a one-way path from state 0 to state 1, preventing the 'reversibility' found in standard cubical type theory.

Which programming languages does this skill support?

The skill provides implementation patterns for Rzk (formal proofs), Julia (via Catlab/ACSets for categorical structures), and Ruby (for epoch-based time modeling).

Directed Interval Logic

Name: Directed Interval Logic
Author: plurigrid

byplurigrid

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Data Science & ML

Axiomatizes the directed interval 0 → 1 to model irreversible processes and time-directed homotopy in synthetic infinity-categories.

The Directed Interval skill provides a specialized framework for modeling time-irreversible processes using directed cubical type theory. By replacing the traditional undirected interval with a directed 'walking arrow,' this skill allows Claude to reason about causal dependencies, chemical reaction pathways, and state transitions where transport only flows forward. It is designed for researchers and developers working in topological chemputing, formal verification of stateful systems, and synthetic category theory, providing the mathematical primitives needed to ensure compositional coherence in directed workflows.

Key Features

01Maps chemical reaction semantics (reactants to products) to directed homotopy types

022 GitHub stars

03Axiomatizes the directed interval [0 → 1] for modeling time-irreversible processes

04Implements Rzk-based definitions for directed cubes and higher simplices

05Integrates with Julia ACSets for representing categorical data structures and synthesis pathways

06Supports extension types for prescribing partial elements and boundary conditions

Use Cases

01Modeling causal order and time-sensitive state transitions in distributed computing

02Developing synthetic infinity-category proofs for directed graphs and simplices

03Formalizing multi-step chemical synthesis pathways where reactions cannot be reversed

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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