categorical-meta-prompting

Composable atomic blocks for categorical meta-prompting. Defines 16 reusable blocks across 4 layers (Assessment, Transformation, Refinement, Composition) that can be composed to build custom workflows. Enables progressive disclosure: simple commands work unchanged, power users can override individual blocks or compose freely.

Master reference for categorical meta-prompting unified syntax. Contains all modifiers, operators, composition patterns, and execution protocols. Use this skill for self-reference when executing any prompt workflow, ensuring consistent syntax across all commands and skills.

Dynamic prompt registry with unified categorical syntax. Supports @skills:discover(), @skills:compose(A⊗B), Reader monad for runtime lookup, and quality-tracked prompt libraries. Use for meta-prompts referencing sub-prompts, building prompt libraries, implementing deferred resolution, or composing templates dynamically.

Universal template for implementing categorical structures in meta-prompting frameworks. Applies to functors, monads, comonads, natural transformations, adjunctions, hom-equivalences, limits, colimits, and enriched categories. Use when extending frameworks with new categorical constructs.

Recursive Meta-Prompting (RMP) implementation with unified categorical syntax. Supports @mode:iterative, @quality: thresholds, >=> Kleisli composition, and comonadic context extraction. Use when implementing iterative prompt improvement, quality-gated generation loops, or applying categorical fixed-point semantics with convergence guarantees.

Full categorical framework for meta-prompting with verified laws. Use when implementing functor-based task routing, monadic iterative refinement, comonadic context extraction, or quality-tracked composition. Integrates F (Functor), M (Monad), W (Comonad), and [0,1]-enriched quality categories.

Systematic analysis patterns for categorical AI papers (Gavranović, de Wynter, Bradley, Zhang). Use when analyzing academic papers on categorical deep learning, extracting categorical structures from AI research, mapping meta-prompting concepts to category theory, or building comprehensive literature reviews on categorical approaches to AI.

Property-based testing for functor laws, monad laws, and naturality conditions using fp-ts and fast-check. Use when validating categorical implementations in TypeScript, testing algebraic laws in functional code, verifying functor/monad/applicative instances, or building test suites for categorical abstractions.

CC2.0 seven-function research workflow (observe, reason, create, orchestrate, learn, verify, deploy) for categorical AI research. Use when conducting systematic research on categorical AI topics, coordinating multi-stream research workflows, applying categorical foundations to research methodology, or implementing the L5 meta-prompting research framework.

DisCoPy categorical quantum NLP for string diagrams, monoidal categories, and compositional semantics in Python. Use when implementing compositional distributional semantics, building string diagram computations, working with monoidal category theory in code, creating quantum-inspired NLP models, or applying categorical semantics to natural language processing.

DSPy compositional prompt optimization with categorical signatures, module chaining, and automated prompt tuning. Use when building declarative LLM programs with typed signatures, composing multi-step reasoning modules (ChainOfThought, ReAct, ProgramOfThought), optimizing prompts with MIPROv2/BootstrapFewShot, or creating modular AI pipelines that separate program logic from prompt engineering.

@effect/ai integration patterns for categorical AI composition, typed error handling, and production prompt pipelines. Use when building AI applications with Effect-TS, composing LLM calls with typed errors, creating tool-augmented AI systems, implementing structured output generation, or integrating multiple AI providers (OpenAI, Anthropic) with categorical composition patterns.

Guidance library grammar-constrained generation with categorical structure. Use when implementing structured LLM outputs with grammar constraints, building template-based generation with guaranteed formats, creating type-safe prompt templates with interleaved computation, or applying categorical grammar theory to constrained generation.

Hasktorch type-safe tensor operations with categorical structure preservation. Use when implementing type-safe deep learning in Haskell, leveraging dependent types for tensor shape verification, applying categorical abstractions to neural network design, or building formally verified ML pipelines with strong type guarantees.

LangGraph stateful multi-agent graphs with categorical coordination patterns and cyclic workflows. Use when building stateful AI agent systems, implementing multi-agent orchestration with conditional routing, creating cyclic workflows with persistence, or designing graph-based AI pipelines with checkpointing and human-in-the-loop patterns.

LLM4S Scala functional LLM interfaces with Effect system integration. Use when building LLM applications in Scala with ZIO or Cats Effect, implementing type-safe AI pipelines with functional error handling, creating composable prompt systems in Scala, or leveraging Scala's type system for robust AI applications.

LMQL constraint-guided generation DSL for type-safe prompting with grammar constraints and logical conditions. Use when building structured LLM outputs with guaranteed format compliance, implementing constrained decoding with logical operators, creating type-safe prompt templates, or combining neural generation with symbolic constraints for reliable AI outputs.

MCP (Model Context Protocol) server patterns with categorical tool composition and typed context protocols. Use when building MCP servers with categorical composition patterns, designing tool interfaces using functors and natural transformations, implementing typed context management, or creating composable AI tool ecosystems with categorical guarantees.

Spivak-Niu polynomial functor implementations for learner composition and dynamical systems. Use when modeling learning systems as categorical structures, composing machine learning components with polynomial functors, implementing the categorical framework from Polynomial Functors - A Mathematical Theory of Interaction, or building compositional dynamical systems with lenses and charts.

Systematic prompt evaluation framework with MATH, GSM8K, and Game of 24 benchmarks. Use when evaluating prompt effectiveness on standard benchmarks, comparing meta-prompting strategies quantitatively, measuring prompt quality improvements, or validating categorical prompt optimizations against ground truth datasets.

Domain-specific language for categorical prompt composition with functor combinators and natural transformation operators. Use when building composable prompt templates, implementing typed prompt algebras, creating reusable prompt patterns with categorical structure, or designing prompt DSLs that preserve composition properties.

[0,1]-enriched category implementation for gradient-based prompt quality optimization. Use when implementing quality-aware prompt systems, building enriched categorical structures for prompt evaluation, creating continuous optimization over prompt spaces, or applying Bradley's enriched category theory to language model quality scoring.

VoltAgent multi-agent system design with natural transformation coordination between agents. Use when building TypeScript multi-agent AI systems, implementing agent coordination with categorical patterns, designing supervisor-worker agent hierarchies, or creating composable agent architectures with typed message passing.