miso VS Agda

Patching jsaddle by applying this commit made JSaddle usable in Firefox for me, but it has the downside that preventDefault/stopPropagation no longer work (see this issue for more info).

Miso does support jsaddle, docs mention this under the "Live reload with jsaddle" section, although it could be more prominent.

For those interested in DOM-related benchmarks using GHCJS. Miso has some benchmarks here: https://krausest.github.io/js-framework-benchmark/current.html (Ctrl+F `miso`)

ghcjs is the way to go for you, and soon it might be asterius. i do not know how hard it is to set ghcjs up without a framework. but frameworks like obelisk (based on reflex-dom), shpadoinkle, and miso automate that for. i personally like obelisk for its functional reactive programming but it can get awkward and get in your way. so if gui programming is just a means to the end of this one small application and you are not really interested in it nor functional reactive programming, shpadoinkle or miso might suit you better. miso implements the elm architecture (also "TEA", "functional model view controller") and shpadoinkle implements something directly equivalent to the elm architecture. but shpadoinkle achieves more composable widgets by minimalizing the elm architecture. so i recommend shpadoinkle for its better concept although miso is more mature.

This was recently deemed inappropriate:

"Bye bye Set"

"Set and Prop are removed as keywords"

https://github.com/agda/agda/pull/4629

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?

That's absolutely untrue. From the horse's mouth:

Agda has the so-called mixfix operators (which are powerful enough to cover pre/in/postfix cases with an arbitrary number of arguments), check that out: - https://agda.readthedocs.io/en/v2.6.1/language/mixfix-operators.html - https://github.com/agda/agda/blob/master/examples/Introduction/Operators.agda - https://github.com/agda/agda-stdlib/blob/master/src/Data/Product/Base.agda

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.