# Rule Engines and Fixpoint Evaluation

A reference for query engines whose core work is inference, recursion, or repeated rule application.

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## Short answer

Not all query engines are centered on SQL-style scans, joins, and aggregates.

Some are organized around:

- facts
- rules
- recursion
- derivation until no new information appears

That is the world of rule engines, Datalog engines, and chase-style systems.

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## The core idea

Instead of asking only for direct data retrieval, a rule engine often asks:

- what facts follow from these rules?
- what closure or least fixpoint do these inputs imply?
- what new values must exist to satisfy constraints?

This makes the engine iterative in a deeper way than many classical relational plans.

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## Fixpoint evaluation

Fixpoint evaluation means:

1. start with known facts
2. apply rules
3. add newly derived facts
4. repeat until nothing new is produced

That final stable state is the fixpoint.

This is central to:

- recursive Datalog
- transitive closure
- many inference systems

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## How this differs from standard relational execution

Relational engines often execute one finite plan over a fixed input.

Rule engines often need:

- iterative scheduling
- duplicate elimination
- dependency tracking
- recursion support
- possibly witness generation or equality merging

So the runtime model is often different even when some individual operators overlap.

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## Why this matters

Rule/fixpoint execution is especially relevant when the system needs:

- recursive reasoning
- closure computation
- derivation of implicit facts
- chase-like enforcement of dependencies

This makes it a natural topic whenever query engines overlap with logic or theorem-like data processing.

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## Practical mental model

Standard query engines answer:

- what result follows from this query over this data?

Rule engines also ask:

- what additional facts become true once the rules have run to completion?

That is the essential distinction.

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## Changelog

* **April 1, 2026** -- First version created.