Agda
distributive
Agda  distributive  

27  6  
2,417  41  
1.0%    
9.8  2.7  
7 days ago  about 1 year ago  
Haskell  Haskell  
MIT License  BSD 3clause "New" or "Revised" License 
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Agda

Types versus sets (and what about categories?)
This was recently deemed inappropriate:
"Bye bye Set"
"Set and Prop are removed as keywords"
https://github.com/agda/agda/pull/4629

If given a list of properties/definitions and relationship between them, could a machine come up with (mostly senseless, but) true implications?
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.

What can Category Theory do?
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 wellknown but is very cool.

What are the current hot topics in type theory and static analysis?
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.

Amendmend proposal: Changed syntax for Or patterns
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?

Functional Programming and Maths <> How can a code monkey learn Agda?
That's absolutely untrue. From the horse's mouth:
 Doom emacs and agdamode

FP language idea  would this is possible to infer and type check?
Agda has the socalled 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/mixfixoperators.html  https://github.com/agda/agda/blob/master/examples/Introduction/Operators.agda  https://github.com/agda/agdastdlib/blob/master/src/Data/Product/Base.agda

Best Programming Language for Computational Proof
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.

Do you use Idris or Coq, and why?
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.
distributive
 stack

Is there an idiomatic way to have a record but with enum values as keys?
Moving discussion to a github issue.

Issue 302 :: Haskell Weekly newsletter
In main branch of distributive, Distributive is gone. There is only Representable. See current state https://github.com/ekmett/distributive/blob/117377d7ba38efc5b115169b565dfb80de8ad407/src/Data/Rep/Internal.hs

Monthly Hask Anything (November 2021)
Seems like a neat signature. Is it an instance of some deeper concept or property? Is there a general typeclass for it? It looks a little bit like distribute from distributive.

Chris Penner  Intro to Higher Kinded Data Types
The upcoming version of distributive includes a lot of hkd toys. It might be up your alley.
What are some alternatives?
lean  Lean Theorem Prover
miso  :ramen: A tasty Haskell frontend framework
coq  Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semiinteractive development of machinechecked proofs.
parameterizedutils  A set of utilities for using indexed types including containers, equality, and comparison.
opentyperep  Open type representations and dynamic types
fgl  A Functional Graph Library for Haskell
HoleyMonoid  Automatically exported from code.google.com/p/monoidcont
typelevelsets  Typelevel sets for Haskell (with valuelevel counterparts and various operations)
lean4  Lean 4 programming language and theorem prover
containers  Assorted concrete container types
agdavim  Agda interaction in vim
igraph  Incomplete Haskell bindings to the igraph library (which is written in C)