Categorical Meta-Prompting Framework
Category theory-based prompt engineering with mathematical rigor and practical power
A production-ready Claude Code plugin implementing categorical structures (functors, monads, comonads, natural transformations) for rigorous, composable prompt engineering with quality visualization and error handling.
Features
✨ 6 Categorical Structures
- F (Functor): Task → Prompt transformation
- M (Monad): Iterative refinement with quality convergence
- W (Comonad): Context extraction and meta-observation
- α (Natural Transformation): Strategy switching between functors
- E (Exception Monad): Error handling with monad semantics
- [0,1]-Enriched: Quality tracking and visualization
✨ 4 Composition Operators
→ Sequential (Kleisli composition)|| Parallel (concurrent execution)⊗ Tensor (quality-degrading combination)>=> Kleisli refinement (monadic with quality gates)
✨ Advanced Features
- Quality flow visualization (Phase 5)
- Error handling and recovery (Phase 3)
- Multi-dimensional quality assessment
- Categorical law verification
- Progressive disclosure (Layer 1-3)
Quick Start
Installation
git clone https://github.com/categorical-meta-prompting/plugin.git
cd plugin
./INSTALL.sh
Restart Claude Code to activate the plugin.
First Command
# Simple meta-prompting
/meta "implement rate limiter"
# Quality-gated iteration
/rmp @quality:0.85 "optimize algorithm"
# Command composition
/chain [/meta→/review] "build feature"
Categorical Coverage
| Structure | Symbol | Command | Description |
|---|
| Functor | F | /meta | Task → Prompt (structure-preserving) |
| Monad | M | /rmp | Prompt →^n Prompt (iterative refinement) |
| Comonad | W | /context | History → Context (extraction) |
| Nat. Trans. | α | /transform | F ⇒ G (strategy switching) |
| Exception | E | @catch:, @fallback: | Error handling |
| Enriched | [0,1] | @quality:, @quality:visualize | Quality tracking |
Contents
Skills (1 total)
- meta-self: Master reference for unified categorical syntax. Contains all modifiers, operators, composition patterns, and execution protocols.
Commands (5 total)
| Command | Description | Key Syntax |
|---|
/meta | Categorical meta-prompting | @mode:, @tier:, @template: |
/rmp | Recursive meta-prompting loop | @quality:, @max_iterations: |
/chain | Command composition | [/cmd1→/cmd2→/cmd3] |
/context | Comonad operations | @mode:, @focus:, @depth: |
/transform | Natural transformations | @from:, @to:, @verify: |
Core Concepts
1. Functor F: Task → Prompt
Transform tasks to prompts while preserving structure.
/meta "implement authentication"
# With explicit tier
/meta @tier:L5 "design microservices architecture"
# With template components
/meta @template:{context:expert}+{mode:cot}+{format:code} "build API"
Categorical Laws:
F(id) = id (Identity)F(g ∘ f) = F(g) ∘ F(f) (Composition)
2. Monad M: Iterative Refinement
Refine prompts until quality threshold met.
/rmp @quality:0.85 "optimize database query"
# With iteration limit
/rmp @quality:0.9 @max_iterations:3 "build robust system"
Categorical Laws:
return >=> f = f (Left Identity)f >=> return = f (Right Identity)(f >=> g) >=> h = f >=> (g >=> h) (Associativity)
3. Comonad W: Context Extraction
Extract context from execution history.
# Extract recent context
/context @mode:extract @focus:recent @depth:5 "summarize progress"
# Create meta-observation
/context @mode:duplicate "why did this approach fail?"
# Context-aware transformation
/context @mode:extend @transform:summarize "create summary"
Categorical Laws:
extract ∘ duplicate = id (Left Identity)duplicate ∘ duplicate = fmap duplicate ∘ duplicate (Associativity)
4. Natural Transformation α: Strategy Switching
Switch between prompting strategies.
# Transform to chain-of-thought
/transform @from:zero-shot @to:chain-of-thought "explain algorithm"
# Compare strategies
/transform @mode:compare @from:few-shot @to:chain-of-thought "task"
# Analyze optimal strategy
/transform @mode:analyze "complex reasoning problem"
Categorical Law:
α_B ∘ F(f) = G(f) ∘ α_A (Naturality condition)
5. Exception Monad E: Error Handling
Handle errors with monad semantics.
# Retry on failure
/chain @catch:retry:3 [/api-call→/process] "fetch data"
