fgl VS Agda

Using fgl but only as a data structure this time, with edge labels denoting whether the target is a big room. Not using any of its algorithms as it doesn't have anything built-in for "traversal with re-visiting".

For part 2, instead of trying to union-merge from the lowest points, I simply found all connected regions of <9. I say "simply" because I just threw things at fgl, but setting the graph up first took a bit of work. buildGr is fast but picky about the exact order things come in with.

Learn how to use a formal proof assistant. Coq and Agda are the most popular. Both allow you to write a proof as a program instead of as a paper, and provide various tools for formally checking your proof.

Some programming languages are, https://github.com/agda/agda

If you're looking for stuff pushing the boundaries of PL research, Agda (especially Cubical Agda) might be cool to look at. It's got lots of cutting edge stuff in it, pushing the boundaries of what is currently possible with dependent type theory. It's not the only language out there with cubical features (see also: cooltt), but it's probably one of the more fleshed-out implementations in terms of being practically useful. The 1Lab makes heavy use of it. There's also Introduction to Univalent Foundations of Mathematics with Agda that might be interesting to look at too!

My best guess is that it has not really been maintained lately, there were only 12 commits in the last 7 years, some of which are just global modifications, which include this file as well: https://github.com/agda/agda/commits/136f85386ec43245745b76f03505bda4f5d1ed3f/src/full/Agda/Interaction/Highlighting/Vim.hs

Also I would suggest is that you import a paradox (e.g., https://github.com/agda/agda/blob/master/test/Succeed/Hurkens.agda) and see what it actually does when you construct values with it that you evaluate or proofs that you use.

Andrea had some code relaxing these restrictions at the last AIM (cf. "trying to make termination checker accept more definitions --without-K, fixing #4527" in the wrap-up section) but I don't know if it has been merged into master yet.

Significant nit: this isn't true. The whole domain of "high-assurance software" is about this, with examples such as CompCert and seL4. There are tools like Frama-C that support you in proving things about your C; [proof assistants]() that let you extract Haskell, OCaml, or Scheme from proofs so the code is correct by construction; and languages like CakeML, F*, Agda, Idris, ATS... that are both programming languages and proof assistants.