wiwinwlh VS Agda

wiwibwlh

In this respect, The Haskell Guide is not a tutorial, project-based guide or textbook, which aims to give a more complete walk through the language, in a linear fashion, but more like a reference guide that is carefully designed to be accessible and clear. In that respect, it's like a beginner level version of What I Wish I Knew When I Learned Haskell, with more cross-referencing. (By the way, I don't think this is a substitute for more in-depth or didactically rich resources at all; it's trying to address a different problem.)

Many libraries try to stick to Haskell 98. Also whenever someone writes a paper about some new techniques, they always seem to take a lot of pleasure in pointing out when their technique works in Haskell 98.

I like that you can mix and match GHC extensions even in the same project. So one library (or even just one module) might use some crazy and messy extensions, but you can still use it from vanilla Haskell.

http://dev.stephendiehl.com/hask/#language-extensions has a list of extensions and some judgement on them.

For example, I really like TupleSections. They are not strictly necessary for anything, they are purely cosmetic / syntactic sugar. But they also don't cause any mess. https://ghc.gitlab.haskell.org/ghc/doc/users_guide/exts/tupl...

Also: TypedHoles are really neat for developing, and will never show up in your final code. https://ghc.gitlab.haskell.org/ghc/doc/users_guide/exts/type...

Maybe try to implement something using Haskell? For example, try to read through: https://en.wikibooks.org/wiki/Write_Yourself_a_Scheme_in_48_Hours to see how the concepts are used in a "real world" setting. Also, https://github.com/sdiehl/wiwinwlh is an underrated resource imo. Anyways, the best way to learn Haskell is to just use it. I'm still learning myself, so I don't have much to say beyond that.

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.