egglog

When symbolic approaches to Decapodes were last demonstrated, they were accomplished by defining rules that inter-operate by building off of Symbolics.jl/ Metatheory.jl and similar libraries.

However, in the interim, the egglog project which combines the e-graph data structure with datalog-style declarative programming has advanced sufficiently to where you may be able to "one-shot" support for equations written in the (discrete) exterior calculus. This has been roughly demonstrated in a similar context for certain models by the CatCoLab project.

So, we should look at what an egglog backend for equations in the DEC can look like. This is a standalone project that doesn't need to integrate with DiagrammaticEquations.jl, but it would be neat to see integration in some format.