effekt VS Agda

I like it. Modern languages that distinguish between pure and impure programs like Flix, Koka, and Effekt do so on the type level instead of syntactically. This has three advantages:

The problem with checked exceptions been identified and solved. The same problem and solution applies to effect handlers. Effekt is a language with lexical effect handlers which doesn't have this problem. Consider the following program in Effekt:

Yes, for you this is the right decision. But for us going to CPS makes everything significantly easier and in cases where you do use control effects significantly faster. For our language Effekt we are exploring different tradeoffs in different backends.

This pattern they observe is nicely captured by effect handlers. These examples are written in Effekt.

This is beyond my level of expertise. But effect tracking? There are some cool languages out there that do that consistently! Search for "algebraic effects". My favorite is Koka. Effekt also seems to be a popular choice.

https://effekt-lang.org/ A research language with effect handlers and lightweight effect polymorphism

Examples are languages like Koka, Effekt, Links, or Unison. These languages come with a type-and-effect system: a function's type not only tell you which values the function accepts and which values it returns, but also which effects it has. This is relevant to your question, because throwing an exception is one such effect.

It seems that with Effekt we are pursuing the same goal, but coming from the opposite direction, perhaps one day we will meet in the middle :). We start from a purely functional language and carefully add effects like mutation.

- https://effekt-lang.org/

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.