I believe there is a family of programming languages named OBJ that are known as "term re-writing" languages that operate at this symbolic/syntatic level.
Are you familiar with them? How does Symbolica compare/contrast with them?
Not the author of Symbolica but I will take a stab at responding. Symbolica is fundamentally a CAS (computer algebra system) so it should be compared with other CAS. And compared with other CAS, Symbolica aims to provide much better performance. In addition it is much more hackable, being written from scratch in Rust.
I used mermaid, which gets live-compiled on the website, that is built using quarto. Here is an example:
```{mermaid}
flowchart LR
A -- 1 --- B
B -- 2 --- C
B -- 8 --- E
C -- 3 --- D
C -- 9 --- F
D -- 10 --- E
D -- 4 --- G
G -- 5 --- H
G -- 6 --- F
E -- 9 --- F
```
Are you familiar with them? How does Symbolica compare/contrast with them?
https://en.m.wikipedia.org/wiki/OBJ_(programming_language)
(While OBJ is old, there are some newer /recent decendents from its family)