82 lines
2.6 KiB
Markdown
82 lines
2.6 KiB
Markdown
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# Geolog Summary
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*Date: 2026-03-19*
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## What Is Geolog?
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Geolog is a **Geometric Logic REPL** — a reasoning engine written in Rust that implements type theory with semantics in topoi. It was AI-generated by Claude Opus 4.5.
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## Core Concepts
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### Axioms
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An axiom is an "if-then" rule: "If premises are true, then conclusion must be true."
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```
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forall x, y, z. friends(x,y), friends(y,z) |- knows(x,z)
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```
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Similar to Datalog rules, but extended with:
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- Existentials in conclusions (`|- exists x. R(x)`)
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- Disjunctions (`|- A \/ B`)
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- Equality conclusions (`|- x = y`)
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### Chase Algorithm
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Repeatedly applies axioms until no new facts can be derived (fixpoint). Basic blocks:
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1. **Axioms** — the rules to apply
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2. **Structure** — carriers (element sets), functions, relations
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3. **Bindings** — variable-to-element mappings
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4. **Tensor system** — finds violations (premises true, conclusion false)
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5. **Fire conclusion** — adds relations, defines functions, creates elements, adds equations
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6. **Congruence closure** — union-find for tracking element equality
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### Union-Find
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Data structure for tracking equivalence classes. Used for congruence closure when axioms conclude `x = y`. More efficient than naive dictionary + sets approach:
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- Naive: O(n) per union
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- Union-find: O(1) amortized per union
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### Language Syntax
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Geolog's syntax is not based on any single existing language. Influences:
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- **Postfix application** (`x f` not `f(x)`) — category theory
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- **Sequent notation** (`premises |- conclusion`) — proof theory
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- **Path separators** (`/` not `.`) — unique to Geolog
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## Skeptical Assessment of Applications
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### Claimed Use Cases
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- Business process workflow orchestration
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- Formal verification
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- Database query design
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- Petri net reachability
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### Reality
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| Claim | Assessment |
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|-------|------------|
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| Workflow orchestration | No APIs, no integrations, no distributed execution — just a REPL |
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| Formal verification | Lean4 proofs "in progress"; not comparable to Coq/Lean/TLA+ |
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| Database query design | Not a database — no persistence at scale, no SQL, no transactions |
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| Petri net reachability | Toy examples only, not industrial-scale |
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### What It Actually Is
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A **research/educational tool** for:
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- Learning geometric logic and chase algorithms
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- Experimenting with category-theoretic ideas
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- Prototyping constraint systems
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- Academic exploration
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**Not suitable for:** Production systems, real workflow orchestration, industrial formal verification, or database replacement.
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## Project Status
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- Version: 0.1.0
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- 30,000+ lines of Rust
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- 168 tests (all passing)
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- 30 example files
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- Well-documented but unproven in real-world use
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