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name: datalog-fixpoint description: Datalog bottom-up fixpoint iteration for recursive queries version: 1.0.0

Datalog Fixpoint Skill

Bottom-up fixpoint iteration for recursive Datalog queries without explicit recursion.

Core Concept

Datalog computes fixpoints via iterative saturation:

CopyT^0(∅) → T^1 → T^2 → ... → T^ω (fixpoint)

Where T is the immediate consequence operator.

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Dataframes

• polars [○] via bicomodule
  • High-performance dataframes

Bibliography References

• algorithms: 19 citations in bib.duckdb

Cat# Integration

Fixpoint computation maps to Cat# via coalgebraic semantics:

CopyTrit: 0 (ERGODIC - iterative bridge)
Home: Prof (profunctors/bimodules)
Poly Op: ⊗ (parallel saturation)
Kan Role: Adj (Kleisli adjunction)

GF(3) Naturality

Datalog fixpoint iteration is inherently ERGODIC:

• Each iteration step is a natural transformation
• Convergence = reaching the terminal coalgebra
• The fixpoint IS the bicomodule equilibrium