Agda
Agda is a dependently typed programming language / interactive theorem prover. (by agda)
open-typerep
Open type representations and dynamic types (by emilaxelsson)
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| Agda | open-typerep | |
|---|---|---|
| 27 | 1 | |
| 2,368 | 4 | |
| 1.4% | - | |
| 9.8 | 0.0 | |
| 2 days ago | almost 8 years ago | |
| Haskell | Haskell | |
| MIT License | BSD 3-clause "New" or "Revised" License |
The number of mentions indicates the total number of mentions that we've tracked plus the number of user suggested alternatives.
Stars - the number of stars that a project has on GitHub. Growth - month over month growth in stars.
Activity is a relative number indicating how actively a project is being developed. Recent commits have higher weight than older ones.
For example, an activity of 9.0 indicates that a project is amongst the top 10% of the most actively developed projects that we are tracking.
Stars - the number of stars that a project has on GitHub. Growth - month over month growth in stars.
Activity is a relative number indicating how actively a project is being developed. Recent commits have higher weight than older ones.
For example, an activity of 9.0 indicates that a project is amongst the top 10% of the most actively developed projects that we are tracking.
Agda
Posts with mentions or reviews of Agda.
We have used some of these posts to build our list of alternatives
and similar projects. The last one was on 2023-07-11.
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Types versus sets (and what about categories?)
This was recently deemed inappropriate:
"Bye bye Set"
"Set and Prop are removed as keywords"
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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.
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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 well-known but is very cool.
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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.
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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?
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Functional Programming and Maths <|> How can a code monkey learn Agda?
That's absolutely untrue. From the horse's mouth:
- Doom emacs and agda-mode
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FP language idea - would this is possible to infer and type check?
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
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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.
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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.
open-typerep
Posts with mentions or reviews of open-typerep.
We have used some of these posts to build our list of alternatives
and similar projects. The last one was on 2022-12-28.
What are some alternatives?
When comparing Agda and open-typerep you can also consider the following projects:
lean - Lean Theorem Prover
helf - Haskell implementation of the Edinburgh Logical 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 semi-interactive development of machine-checked proofs.
cubical - Implementation of Univalence in Cubical Sets
HoleyMonoid - Automatically exported from code.google.com/p/monoid-cont
eliminators - Dependently typed elimination functions using singletons
distributive - Dual Traversable
agda-snippets - Library and tool to render the snippets in literate Agda files to hyperlinked HTML, leaving the rest of the text untouched.
agda-vim - Agda interaction in vim
singletons - Fake dependent types in Haskell using singletons
zig - General-purpose programming language and toolchain for maintaining robust, optimal, and reusable software.
hoq - A language based on homotopy type theory with an interval