hegg VS asami

Equality graphs (e-graphs) for theorem proving and equality saturation and other equality-related things.

They're awesome data structures that efficiently maintain a congruence relation over many expressions

> At a high level, e-graphs extend union-find to compactly represent equivalence classes of expressions while maintaining a key invariant: the equivalence relation is closed under congruence.

e.g. If I were to represent "f(x)" and "f(y)" in the e-graph, and then said "x == y" (merged "x" and "y" in the e-graph), then the e-graph, by congruence, would be able to tell me that "f(x) == f(y)"

e.g. If I were to represent "a(2/2)", in the e-graph, then say "2/2 == 1", and "x1 == x", by congruence the e-graph would know "a*(2/2) == a" !

The most recent description of e-graphs with an added insight on implementation is https://arxiv.org/pdf/2004.03082.pdf to the best of my knowledge.

P.S: I'm currently implementing them in Haskell https://github.com/alt-romes/hegg

Unlike some other commenters, I agree that graph models are usually a better fit for most data than relational models. There's been some interesting work in recent years developing this idea: in the Clojure world there's Datomic, XTDB, and a host of competitors, all of which build on work from Semantic Web/SPARQL/triplestores and logic programming. Some are even intended to be used as primary datastores: they support some amount of schema and constraints, have well-defined consistency and ACID guarantees, etc. This makes them unlike graph databases like Neo4J and others, which fill an architectural role more like Elasticsearch as a read-optimization tool. Here's an interesting talk making a case for triple-based databases.

Despite the documentation that exists, I've heard many people who have been confused about how to query Datomic, Datascript, Asami, or other graph databases. So I've made an attempt at explaining it https://github.com/threatgrid/asami/wiki/Introduction

The first Graph implementation for Asami was a simple in-memory data structure, described in my ClojureD talk. The code for this appears in asami.index. This file started much smaller (as referenced above), but has since expanded with the needs extended functionality, such as transactions, and transitive closure operations.