UML is an interesting case; I think that UML Structure diagrams can be compiled, but not the others. This is because UML describes both buildtime and runtime connections between entities, and specifying runtime entities with UML runs into declarative existential claims which are not obviously compilable into static code.

In any case, I'm only thinking about the build step. I think modern applications should be chimeric; they should be built from many modules written in many languages. For example, many compilers and interpreters include at least one page of Zephyr ASDL, which is excellent for the singular task of describing ASTs and ADTs but not anything else.

I'm talking specifically about Mermaid. Something like DOT is slightly better. The ultimate goal is to extract the formal structure. For Mermaid or DOT, this extraction requires a text parser and a walk over an AST; it's about half of a compiler!

This might not sound like a problem compared to something like PBs or JSON, which also require something that looks like a parser and a tree-walker. The difference is in the tooling; the DOT tools can't directly yank a DAG from a file or iterate over its edges, but jq can do that for DAGs encoded in JSON.

For a complete worked example, consider this tool which combines JSON and DOT. It produces diagrams that look like this image by building a DAG, packing the DAG into JSON, compiling the DAG to DOT, compiling the DOT into a PNG, and finally packing the JSON into a custom PNG chunk. This workflow itself is a DAG! The JSON is in the PNG:

$ nix build
$ result/bin/zaha json complexity/decision/hierarchy/polynomial.png 
{"labels": ["P", "coNP", "NP", "\u0394\u2082P", "\u03a3\u2082P", "\u03a0\u2082P", "\u0394\u2083P", "\u03a0\u2083P", "\u03a3\u2083P", "PH"], "structure": 28074104194051, "title": "Polynomial Hierarchy"}

And then I can use this tool to help write a book. In these build instructions, I call zaha several times to prepare some JSON, then use jq and Python to build some tables and emit some Markdown.