Can this skill help with CRDT implementation?

Yes, it maps specific lattice operations to CRDT behaviors, such as 'Delete' for forward cleanup and 'Merge' for backward unification, providing a formal structure for distributed state.

What is the difference between covariant and contravariant negation?

In this logic, bivariant types have two introduction rules for negation (NotIntroCov and NotIntroCon) that result in different operational behaviors despite sharing the same type-level signature.

What is bidirectional programming in this context?

It refers to a paradigm where data and control flow can move both forward (covariant) and backward (contravariant) in time, allowing for consistent updates between related data structures like views and models.

How does the GF(3) correspondence work?

It projects the 4-kind lattice onto the integers modulo 3. Covariant types act as +1, contravariant as -1, and bivariant as 0. This allows the logic of tensor products to be calculated using standard GF(3) multiplication.

Bidirectional Lens Logic

Name: Bidirectional Lens Logic
Author: plurigrid

byplurigrid

•

Developer Tools

Implements Hedges' 4-kind lattice and GF(3) correspondence for advanced bidirectional programming and state synchronization.

This skill provides Claude with a rigorous framework for bidirectional programming based on Jules Hedges' foundations of the 4-kind lattice. It allows developers to model complex systems where information flows in multiple temporal directions—forwards (covariant) and backwards (contravariant)—using GF(3) multiplication to govern tensor products. This is especially valuable for building mathematically sound CRDTs, compositional game theory models, and cybernetic systems. By defining specific scoping rules for bivariant and invariant types, the skill ensures that operational semantics for data synchronization and state updates remain consistent and predictable across distributed environments.

Key Features

012 GitHub stars

02Implements Hedges’ 4-kind lattice for temporal scoping (Covariant, Contravariant, Bivariant, Invariant).

03Integrates with Open Games structures to manage play and coplay strategy flows.

04Supports dual introduction rules for negation based on directional semantics.

05Maps type composition to GF(3) multiplication tables for verified tensor products.

06Provides operational semantics for CRDT operations like stop-share, share, and connect.

Use Cases

01Developing distributed state systems using CRDTs with verified bidirectional synchronization.

02Architecting economic or strategic simulations using compositional game theory (Open Games).

03Implementing advanced functional lenses and optics for bidirectional data transformation in Idris or similar languages.

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi bidirectional-lens-logic

For use in Claude.ai and ChatGPT

Download Skill