ezno VS egg

> I'm curious if there are any practical reasons we don't see them implemented in more languages.

I believe it's because they're not exactly easy to implement and the resulting extensive type checking might also affect compiler performance.

By the way, another great example of refinement types (in JavaScript) is this one: https://kaleidawave.github.io/posts/introducing-ezno/

Maybe program optimization?

https://egraphs-good.github.io/

For semantic analyzers, check out egg and egglog. They're custom data structures for representing compiler rewrite rules in a non-destructive way.

E-graphs are pretty awesome, and worth keeping in your back pocket. They're like union-find structures, except they also maintain congruence relations (i.e. if `x` and `y` are in the same set, then `f(x)` and `f(y)` must likewise be in the same set).

https://egraphs-good.github.io/

(Incidentally, union-find structures are also great to know about. But they're not exactly "new".)

I would add that Equality saturation/E-graphs has become quite a hot topic recently, since their POPL21 paper, with workshops dedicated to applications of e-graphs. They have even recently been added to Cranelift as an IR for optimizations.

Egraphs solve the rewrite ordering problem quite nicely. https://egraphs-good.github.io/

Note that one solution to this problem is to use equality saturation (which, coincidentally, has a great implementation in rust!).

Have you thought about trying to parallelize e-graphs? This way you can do a bunch of rewrite rules in parallel and then extract your desired graph at the end instead of having conflicts.

I think the equality saturation papers are a good start. A good start is egg. They have a presentation, a research paper and code you can play with. I think ultimately you want to translate arithmetic operations into logical operation that can be understood by the fpga. So I think it would be good to research how adders and multipliers are implemented in logic and ultimately include equalities between adders/multipliers with their logical counterpart. Note the this translation also depends on the representations of your numbers and their bit width.

For rewriting, you may also find interesing equality saturation: https://egraphs-good.github.io/