elaboration-zoo
milewski-ctfp-pdf
elaboration-zoo | milewski-ctfp-pdf | |
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23 | 75 | |
562 | 10,751 | |
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5.3 | 5.3 | |
4 months ago | 9 days ago | |
Haskell | TeX | |
BSD 3-clause "New" or "Revised" License | GNU General Public License v3.0 or later |
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elaboration-zoo
- Dependent types do’s and don’ts
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How to implement dependent type theory I (2012)
I've noticed amongst many peers that when going down the type theory/pl theory journey there is a ton of hidden knowledge and context we all find ourselves collecting.
All of this knowledge and context spread amongst a common set of books, papers, blog posts, and git repos floating around the internet.
At the risk of creating yet another partial silo, I decided earlier this year to create a project similar to the [Elaboration Zoo](https://github.com/AndrasKovacs/elaboration-zoo) but focused on a blessed path to MLTT with a number of the desirable language features via bidirectional typechecking.
https://github.com/solomon-b/lambda-calculus-hs
The project is incomplete and my end goal is a website like the [1 Lab](https://1lab.dev) but focused on Type Theory and PL Theory, but I ran low on steam and could use some collaborators.
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How to implement dependent types in 80 lines of code
Thanks, yeah, I haven't benchmarked the implementation yet, and I see the repeated substitution happening. Would the NbE approach where we have indices for terms and levels for values fix the issue (I believe you wrote the implementation here)?
I find the NbE approach that combines both indices and levels quite appealing. You remain first-order (easier for debugging and etc.), but no need to define substitution now.
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Online courses that use, but don't teach, Haskell?
If you're interested in dependent types, you might like András Kovács' elaboration zoo, which uses Haskell as the implementation language.
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A personal list of Rust grievances
I think it's more a reflection of how Rust evolved, and the techniques and approaches known and understood at the time and the strangeness budget they were (understandably) willing to take on at the time as opposed to something inherent. And also sometimes having separate, complicated features for similar things (as opposed to simple features that compose powerfully) can be useful pedagogically as well.
At any rate, this is something I'm interested in, and so that's why it appears so high up on my list. Often you really do want sub-languages for different purposes, but managing how they interact and work together, what is the same and what is different, and how that impacts usability is interesting (and difficult) part. I feel like it should be possible to do this, but it's going to take some work and there's still lots of unknowns.
In technical terms, I'm interested in dependently typed module systems, multistage programming[1], graded modal type theory[2], elaborator reflection, and two level type theory[3]. These all sound pretty intimidating, but you can actually see glimmers of some of this stuff in how Zig handles type parameters and modules, for example, something that most programmers really like the first time they see it!
I do feel like there is the core of a simple, flexible, powerful systems language out there... but finding it, and making it approachable while maintaining a solid footing in the theory and being sensitive to the practical demands of systems programming is a nontrivial task, and many people will be understandably skeptical that this is even a good direction to pursue. Thankfully the barrier to entry for programming language designers to implementing languages in this style has reduced significantly in just the last number of years[4], so I have hope that we might see some interesting stuff in the coming decade or so. In the meantime we have Rust as well, which is still an excellent language. I'm just one of those people who's never content with the status quo, always wishing we can push the state of the art further. This is why I got excited by Rust in the first place! :)
[1]: https://github.com/metaocaml/metaocaml-bibliography
[2]: https://granule-project.github.io/
[3]: https://github.com/AndrasKovacs/staged
[4]: https://github.com/AndrasKovacs/elaboration-zoo/
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Reference Implementation for MLF
Another option is this algorithm by Andras Kovacs dubbed "Dynamic order elaboration": https://github.com/AndrasKovacs/elaboration-zoo/tree/master/06-first-class-poly . Basically if you are checking a term against a bare meta variable, then postpone the checking until the meta variable has a solution.
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purescript-backend-optimizer - A new optimization pipeline and modern-ES backend for PureScript.
Special shout out to /u/AndrasKovacs and elaboration-zoo (as well as their various NbE notes) which served as a primary inspiration for the architecture. Can't thank you enough for those resources!
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Barebones lambda cube in OCaml
Highly recommend checking the first part of elaboration-zoo to see how all this might be implemented, it clears a lot of things up.
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Peridot MVP
Pattern unification
milewski-ctfp-pdf
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reflect-cpp - Now with compile time extraction of field names from structs and enums using C++-20.
Category Theory for Programmers by Bartosz Milewski (https://github.com/hmemcpy/milewski-ctfp-pdf/releases)
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Category Theory for Programming
Strangely similar name to the well-known 'Category Theory for Programmers'
https://github.com/hmemcpy/milewski-ctfp-pdf
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Polynomial Functors: A Mathematical Theory of Interaction [pdf]
There's this, but the programmer doesn't have to be working:
https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
- Monads vs Classes
- 今天看到的,是真的离谱。
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Reading recomendations on Category Theory
Milewski's "Category Theory for Programmers".
- Ask HN: Math for Programmers?
- [Math] Category Theory for Programmers
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Some math topics get mentioned a bunch in functional programming articles and forums. Which ones have ever actually helped you in writing your programs?
(3) category theory. I was never advised to read any, but found that bartosz's introduction really good. https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/. Helps to rewire the brain.
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what is the relation of a class in programming and category theory?
It's also possible to model programming languages using category theory, but I know less about that. If you're interested in following this up, then Benjamin Pierce has what I'm told is a good introduction to category theory for computer scientists, and Bartosz Milweski has an online book (it might be available in hard copy as well, I'm not sure) called Category Theory for Programmers. I believe simple programming languages like the simply typed lambda calculus end up being modelled as Cartesian closed categories.
What are some alternatives?
StepULC - Efficient and single-steppable ULC evaluation algorithm
semantic-source - Parsing, analyzing, and comparing source code across many languages
pi-forall - A demo implementation of a simple dependently-typed language
web-dev-golang-anti-textbook - Learn how to write webapps without a framework in Go.
tinka
paip-lisp - Lisp code for the textbook "Paradigms of Artificial Intelligence Programming"
peridot - A fast functional language based on two level type theory
practicing-ruby-manuscripts - Collection of source manuscripts for publicly released Practicing Ruby articles
higher-order-unification - A small implementation of higher-order unification
owasp-masvs - The OWASP MASVS (Mobile Application Security Verification Standard) is the industry standard for mobile app security.
iterator_item - A syntax exploration of eventually stable Rust Iterator items
Yup - Dead simple Object schema validation