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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数据科学与机器学习

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

关于

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.

主要功能

Maps chemical reaction semantics (reactants to products) to directed homotopy types
2 GitHub stars
Axiomatizes the directed interval [0 → 1] for modeling time-irreversible processes
Implements Rzk-based definitions for directed cubes and higher simplices
Integrates with Julia ACSets for representing categorical data structures and synthesis pathways
Supports extension types for prescribing partial elements and boundary conditions

使用场景

Modeling causal order and time-sensitive state transitions in distributed computing
Developing synthetic infinity-category proofs for directed graphs and simplices
Formalizing multi-step chemical synthesis pathways where reactions cannot be reversed

关于

主要功能

Maps chemical reaction semantics (reactants to products) to directed homotopy types
2 GitHub stars
Axiomatizes the directed interval [0 → 1] for modeling time-irreversible processes
Implements Rzk-based definitions for directed cubes and higher simplices
Integrates with Julia ACSets for representing categorical data structures and synthesis pathways
Supports extension types for prescribing partial elements and boundary conditions

使用场景

Modeling causal order and time-sensitive state transitions in distributed computing
Developing synthetic infinity-category proofs for directed graphs and simplices
Formalizing multi-step chemical synthesis pathways where reactions cannot be reversed