Geolog Summary

Date: 2026-03-19

What Is Geolog?

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.

Core Concepts

Axioms

An axiom is an "if-then" rule: "If premises are true, then conclusion must be true."

forall x, y, z. friends(x,y), friends(y,z) |- knows(x,z)

Similar to Datalog rules, but extended with:

Existentials in conclusions (|- exists x. R(x))
Disjunctions (|- A \/ B)
Equality conclusions (|- x = y)

Chase Algorithm

Repeatedly applies axioms until no new facts can be derived (fixpoint). Basic blocks:

Axioms — the rules to apply
Structure — carriers (element sets), functions, relations
Bindings — variable-to-element mappings
Tensor system — finds violations (premises true, conclusion false)
Fire conclusion — adds relations, defines functions, creates elements, adds equations
Congruence closure — union-find for tracking element equality

Union-Find

Data structure for tracking equivalence classes. Used for congruence closure when axioms conclude x = y. More efficient than naive dictionary + sets approach:

Naive: O(n) per union
Union-find: O(1) amortized per union

Language Syntax

Geolog's syntax is not based on any single existing language. Influences:

Postfix application (x f not f(x)) — category theory
Sequent notation (premises |- conclusion) — proof theory
Path separators (/ not .) — unique to Geolog

Skeptical Assessment of Applications

Claimed Use Cases

Business process workflow orchestration
Formal verification
Database query design
Petri net reachability

Reality

Claim	Assessment
Workflow orchestration	No APIs, no integrations, no distributed execution — just a REPL
Formal verification	Lean4 proofs "in progress"; not comparable to Coq/Lean/TLA+
Database query design	Not a database — no persistence at scale, no SQL, no transactions
Petri net reachability	Toy examples only, not industrial-scale

What It Actually Is

A research/educational tool for:

Learning geometric logic and chase algorithms
Experimenting with category-theoretic ideas
Prototyping constraint systems
Academic exploration

Not suitable for: Production systems, real workflow orchestration, industrial formal verification, or database replacement.

Project Status

Version: 0.1.0
30,000+ lines of Rust
168 tests (all passing)
30 example files
Well-documented but unproven in real-world use

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