Agda VS css-turing-machine

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.

> Technically html + css + user interaction can be turing complete: https://github.com/brandondong/css-turing-machine

Turing completeness is about what computations can be expressed, not what user interactions can be performed. The lambda calculus is Turing complete, but, if I whip up a lambda calculus interpreter and don't give it a print statement, then you'll never know anything about the computations it's performing.

Allow css in there and you get this

Seems like regex is not turing complete, bit its not a programming langauge ether. I thought i remembered that it was, i listed as one of the joke langauges as i know someome showed that PowerPoint is turing complete, but i think i mixed up regex and CSS here(that again is not a programming langauge but is in fact turing complete: https://github.com/brandondong/css-turing-machine)

It is definetly a borderline case (because of the need for clicking) , but html + css combined can be used to simulate the rule 110 automaton. Therefore it is possible to simulate a turing machine which means that it is in fact turing complete.

I understand CSS and I've done a fair bit of webdesign myself. CSS has evolved to the point where it can be used abusively. Hell some consider it turing complete (https://github.com/brandondong/css-turing-machine). From ads, to fingerprinting, to exploits there are valid reasons for wanting a little less functionality while still allowing for some basic styling. I mean, it's cool that there are computer games written in pure CSS and other neat tricks, but sometimes you just want a browser to behave itself even in hostile spaces. If that makes my locked down browser a "horse drawn cart" I'm happy to trot forward.

Yeah, someone even made a basic Turing machine to demonstrate it. As u/sext-scientist said, you have to click a button to perform each operation, but technically this means that you could write any program using HTML+CSS. Though the user might need an autoclicker to run even a "Hello World" program.