LQL DAG Calculus: Compositional AI
SmartHaus Research • 2024 • Patent Pending
Abstract
We introduce Lattice Query Language (LQL), a category-theoretic approach to AI composition. LQL enables mathematical guarantees on complex AI workflows through functorial properties and natural transformations, ensuring consistency across all operations.
Core Theorems
L: Cat → Cat, where L(f∘g) = L(f) ⊗ L(g)
Key Contributions
- Functorial composition preserving categorical structure
- Natural transformations for systematic operation morphing
- Monadic error handling with mathematical guarantees
- DAG representation with provable acyclicity
Example
query DataPipeline {
F: Dataset → Filter
G: Filter → Transform
H: Transform → Result
composition: H ∘ G ∘ F
proof: associative(composition)
}