Can this skill be used for formal mathematical modeling?

Yes, it includes specific support for Julia and Catlab, enabling the creation of schemas for graded endofunctors, monoidal units, and multiplication indexed by grade pairs.

What is a graded monad in programming?

A graded monad, also known as an indexed or parametrized monad, is a monad where operations carry an index from a monoidal category. This allows developers to track specific computational effects, like resource consumption or permissions, directly within the type system.

What is the significance of the GF(3) mapping?

The GF(3) mapping allows the skill to coordinate between different computational roles (Validator, Coordinator, Generator) by treating the GF(3) field as an index category, ensuring 'trit balance' and conservation across complex operations.

How does this skill assist with Haskell development?

It provides standardized patterns and best practices for implementing GradedMonad type classes, defining Unit and Mult types, and managing 'gbind' operations for effect-aware codebases.

Graded Monad Specialist

Name: Graded Monad Specialist
Author: plurigrid

byplurigrid

•

開発者ツール

Implements and manages graded monads for tracked computational effects and 2-categorical structures in advanced functional programming.

The Graded Monad skill empowers Claude to architect complex effect systems and indexed monoidal structures by applying formal 2-categorical principles. Drawing on Fujii’s research, it unifies the programming concept of graded effects with categorical 2-monads, facilitating the precise tracking of permissions, resource usage, and session types. This skill is essential for developers working on advanced functional architectures, formal verification, and domain-specific language (DSL) design where effect transparency and trit-based conservation are required.

主な機能

01Provides implementation patterns for effect systems in Haskell and Eff

02Integrates with Julia/Catlab for categorical algebra and schema modeling

03Tracks computational resource usage and permissions via index categories

048 GitHub stars

05Formalizes graded monads as lax 2-functors from monoidal categories to Cat

06Verifies GF(3) grade conservation for balanced tripartite architectures

ユースケース

01Designing type-safe effect systems that track permissions like Read, Write, and ReadWrite

02Developing resource-aware computations with step-counting or latency-bound constraints

03Modeling session types and distributed protocol steps as graded monoidal transformations

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi graded-monad

For use in Claude.ai and ChatGPT

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