Datalog Fixpoint

Datalog bottom-up fixpoint iteration for recursive queries

plurigrid 3922d43 3 files · 1.0 MB Updated

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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.

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

plurigrid/asi/tree/main/skills/datalog-fixpoint commit 3922d43f21

Frequently asked questions

npx skillmds@latest add plurigrid/datalog-fixpoint