What programming language does this skill support?

This skill is specifically designed for Julia environments, utilizing Julia's performance strengths for mathematical and topological computing.

What is the non-backtracking constraint?

It implements Friedman's B operator, which ensures no u→v→u cycles exist in the navigation graph, enabling linear resource-aware evaluation where proofs are consumed exactly once.

Is this skill optimized for large datasets?

Yes, it is designed to handle over 5,000 theorems with O(1) forward and backward lookup performance after the initial index creation.

How does it support Linear Homotopy Type Theory?

By verifying the non-backtracking operator, it ensures the system satisfies the requirements for LHoTT's linear type system and resource tracking.

Bidirectional Proof Navigator

Name: Bidirectional Proof Navigator
Author: plurigrid

byplurigrid

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개발자 도구

Optimizes theorem-proof navigation using Friedman's B operator for resource-aware evaluation in Julia.

The Bidirectional Navigator is a specialized skill for formal methods and mathematical computing that implements a high-performance graph index structure. It enables O(1) lookups between theorems and proofs while strictly enforcing non-backtracking constraints via Friedman's B operator. Designed for Linear Homotopy Type Theory (LHoTT) environments, it ensures that proofs are treated as linear resources—consumed exactly once—making it an essential tool for automated reasoning, proof discovery, and managing massive mathematical catalogs efficiently.

주요 기능

01Friedman's non-backtracking (B) operator enforcement

02Linear Homotopy Type Theory (LHoTT) compatibility

037 GitHub stars

04Bidirectional O(1) theorem-proof mapping and lookups

05Scalable architecture supporting 5,000+ theorem catalogs

06Resource-aware proof consumption tracking

사용 사례

01Resource-aware evaluation in linear type systems

02Large-scale mathematical knowledge management

03Automated proof discovery and theorem indexing

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi bidirectional-navigator

For use in Claude.ai and ChatGPT

Download Skill