Agda VS fgl

Still, there are many useful tools based on these ideas, used by programmers and mathematicians alike. What you describe sounds rather like Datalog (e.g. Soufflé Datalog), where you supply some rules and an initial fact, and the system repeatedly expands out the set of facts until nothing new can be derived. (This has to be finite, if you want to get anywhere.) In Prolog (e.g. SWI Prolog) you also supply a set of rules and facts, but instead of a fact as your starting point, you give a query containing some unknown variables, and the system tries to find an assignment of the variables that proves the query. And finally there is a rich array of theorem provers and proof assistants such as Agda, Coq, Lean, and Twelf, which can all be used to help check your reasoning or explore new ideas.

Haskell and Agda are probably the most obvious examples. Ocaml too, but it is much older, so its type system is not as categorical. There is also Idris, which is not as well-known but is very cool.

Most of the proof assistants out there: Lean, Coq, Dafny, Isabelle, F*, Idris 2, and Agda. And the main concepts are dependent types, Homotopy Type Theory AKA HoTT, and Category Theory. Warning: HoTT and Category Theory are really dense, you're going to really need to research them.

Does this come with plans to separately unify the body with each of the contexts induced by matching on each of the respective patterns (similar to what’s discussed here), or will it behave like the _ pattern and use only the most general context?

Coq, Agda, Lean, Isabelle, and probably some others which are not coming to my mind at the moment, but those would be considered the major ones.

Funny that you say this, because there are some obvious long standing open feature requests with looking up the type of the term under cursor — № 4295 and № 516. I am not blaming anyone in particular — this is the way it is. I wish I could find time to rewrite the proof search engine (how hard can it be), but I am already buried under a pile of other commitments and a good chunk of overwhelming sadness.

"Haskal is a mess, that's why I use a language that's written with Haskal."

Do it in Agda.

Agda is fun[1]. And there's also Idris[2] - more programming language, less proof assistant.

[1] https://wiki.portal.chalmers.se/agda/pmwiki.php https://github.com/agda/agda

I am about to start a new project in Haskell, model checking with (new) tree-like data structures. I think it is best to start building on a library such that i can already have elegant base functions, yet i am wondering what library is currently the standard? I read about fgl ( https://hackage.haskell.org/package/fgl ), yet it is a very old library.

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.