# Datalog Fixpoint

> Datalog bottom-up fixpoint iteration for recursive queries

- Skill: `majiayu000/datalog-fixpoint` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds add majiayu000/datalog-fixpoint`
- Raw SKILL.md: https://api.skillmd.com/api/skills/majiayu000/datalog-fixpoint/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: majiayu000 (https://skillmd.com/u/majiayu000)
- Updated: 2026-09-09
- Page: https://skillmd.com/skills/majiayu000/datalog-fixpoint

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# Datalog Fixpoint Skill

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

## Core Concept

Datalog computes fixpoints via iterative saturation:
```
T^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:

```
Trit: 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