ix-category

Verify monad laws and Free-Forgetful adjunction for Option and Result in Rust.

Updated Mar 12, 2026

Search Tags:#functional programming #Rust #category theory #monad #Free-Forgetful adjunction

Ready to run

npx skills add https://github.com/GuitarAlchemist/ix --skill ix-category

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: ix-category
Source: https://github.com/GuitarAlchemist/ix/tree/main/.claude/skills/ix-category
Command: npx skills add https://github.com/GuitarAlchemist/ix --skill ix-category

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

This Skill simplifies the understanding and verification of category theory principles, allowing users to explore complex concepts with practical implementations.

Core Features & Use Cases

Monad Laws Verification: Check the left unit, right unit, and associativity for Option and Result monads.
Free-Forgetful Adjunction: Investigate the relationship between the Free and Forgetful functors, which are key components in category theory.
Round-trip Verification: Validate that applying the Forgetful functor to a value created by the Free functor results in the original value.
Use Case: When working with functional programming in Rust, this Skill aids in the correct implementation of monads, ensuring code consistency and adherence to category theory principles.

Quick Start

Verify monad laws for Option using the monad_laws operation provided by the ix_category tool.

Frequently Asked Questions about ix-category

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I verify monad laws for Option and Result in Rust?▼

You can verify monad laws in Rust by using the `monad_laws` operation to check left unit, right unit, and associativity for Option and Result monads. This ensures your code adheres to category theory principles within your functional programming environment.

What is the Free-Forgetful adjunction in functional programming?▼

The Free-Forgetful adjunction in functional programming describes the relationship between the Free and Forgetful functors. You can use this Skill to investigate these key category theory components and perform round-trip verification on values created by the Free functor.

How do I check if my Rust monad implementation satisfies associativity?▼

To check if your Rust monad implementation satisfies associativity, use the `monad_laws` operation. It validates left unit, right unit, and associativity specifically for Option and Result monads to confirm correct functional programming implementations.

Can I validate round-trip verification between Free and Forgetful functors in Rust?▼

Yes, you can validate round-trip verification in Rust. This Skill examines the Free ⊣ Forgetful adjunction to confirm that applying the Forgetful functor to a value created by the Free functor successfully results in the original value.

Do I need prior category theory knowledge to verify Rust monad implementations?▼

You do not need extensive category theory knowledge to verify Rust monad implementations. This Skill simplifies understanding by validating monad laws and examining the Free-Forgetful adjunction for Option and Result through concrete, practical examples.