swipl-devel
Agda
swipl-devel | Agda | |
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19 | 27 | |
902 | 2,378 | |
1.4% | 0.6% | |
9.9 | 9.8 | |
2 days ago | 5 days ago | |
C | Haskell | |
GNU General Public License v3.0 or later | MIT License |
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swipl-devel
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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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Scryer Prolog
SWIProlog[1] has so far been my go to due to the extensive support system it has. However, I've been meaning to explore higher order logic a bit and Ciao[2] caught my attention there, with sugar for function-like notation and higher order programming including "lambda" style predicate expressions .... and it compiles down to executable. The function notation in this context is along the same lines as Mozart/Oz and can be convenient. Not explore the higher order aspects much though.
[1]: https://www.swi-prolog.org/
[2]: https://en.wikipedia.org/wiki/Ciao_(programming_language)
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Not all possible results of a simple predicate given by backtracking.
?- version(). Welcome to SWI-Prolog (threaded, 64 bits, version 9.0.0)SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software. Please run ?- license. for legal details.For online help and background, visit https://www.swi-prolog.org For built-in help, use ?- help(Topic). or ?- apropos(Word). true. ?- del(a, L, [1,2,3]). L = [a, 1, 2, 3] ; L = [1, a, 2, 3] ; L = [1, 2, a, 3] ; L = [1, 2, 3, a] ; false.
- Looking for suggestions of interesting language to learn
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Could this code calculating primes be much more optimized?
$ swipl Welcome to SWI-Prolog (threaded, 64 bits, version 8.5.10) SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software. Please run ?- license. for legal details. For online help and background, visit https://www.swi-prolog.org For built-in help, use ?- help(Topic). or ?- apropos(Word). ?- [fm2gp_primes]. true. ?- time( setup_call_cleanup(open('prolog-primes.txt', write, Out), with_output_to(Out, primes(500_000)), close(Out)) ). % 8,766,852 inferences, 1.055 CPU in 1.198 seconds (88% CPU, 8311018 Lips) Out = (0x600000648100).
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Anyone got lots of trivial DCG examples?
The utilities in dgc/bacics.pl that you linked yourself are not too advanced, too quickly. Understanding those is exactly what you need in order to be able to write useful grammars for two reasons. They show how to approach many common issues with DCGs; and you know what building blocks you have at your disposal. I feel you discarded those too fast and strongly suggest you try to revisit them.
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Is Datalog a good language for authorization?
- And last but not least... the ability to convert authorization logic into SQL [4]. Which is done by having the language return constraints over any unbound (free) variables.
To me this is what makes logic programming exciting for authorization. It gives you this small kernel of declarative programming, and gives you a ton of freedom to build on top.
[1] https://www.swi-prolog.org/
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What is your favorite programming language that isn't Haskell?
(Btw. I'm using SWI Prolog.)
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What happened to clumped/2 in SWI-Prolog?
Welcome to SWI-Prolog (threaded, 64 bits, version 8.0.2) SWI-Prolog comes with ABSOLUTELY NO WARRANTY. This is free software. Please run ?- license. for legal details. For online help and background, visit http://www.swi-prolog.org For built-in help, use ?- help(Topic). or ?- apropos(Word). ?- use_module(library(lists)). true. ?- clumped([a,a,a,b,b,c], Rs). ERROR: Undefined procedure: clumped/2 (DWIM could not correct goal) ?-
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Choicepoints and empty lists
Many library predicates do the argument reordering to take advantage of this special case argument indexing as explained in the answer by u/mycl. For example library(apply) in SWI-Prolog. is full of those.
Agda
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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"
https://github.com/agda/agda/pull/4629
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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.
What are some alternatives?
scryer-prolog - A modern Prolog implementation written mostly in Rust.
lean - Lean Theorem Prover
tau-prolog - An open source Prolog interpreter in JavaScript
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.
the-power-of-prolog - Introduction to modern Prolog
open-typerep - Open type representations and dynamic types
Vim - The official Vim repository
HoleyMonoid - Automatically exported from code.google.com/p/monoid-cont
biscuit-rust - Rust implementation of the Biscuit authorization token
distributive - Dual Traversable
MongoDB - The MongoDB Database
lean4 - Lean 4 programming language and theorem prover