Formality
anders
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Formality | anders | |
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29 | 3 | |
2,014 | 17 | |
- | - | |
9.9 | 9.0 | |
over 2 years ago | 26 days ago | |
JavaScript | OCaml | |
MIT License | GNU General Public License v3.0 or later |
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Formality
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A dependently typed language for proofs that you can implement in one day
Also, my current work is using Kind as a foundation, the purpose of this language is exactly what you have asked for, give a check on https://github.com/uwu-tech/Kind.
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Kind: A Modern Proof Language
Kind has a "how I learned to stop worrying and love the `Type:Type`" vibe. That doesn't make it invalid as a proof language. It just inverts the priority: instead of consistency being the default and expressivity being opt-in (as in Agda, with the `type-in-type` pragma), it is expressive by default, and consistency is an opt-in. I strongly believe that is the right way. We plan to add opt-in termination (thus consistency) checkers, it is just not an immediate priority, but the language is completely ready for that. About `Type in Type` specifically, keep in mind that there are consistent, interesting type theories that feature `Type in Type`. So it isn't problematic in itself, and removing it seems wrong.
About erasure, you can flag an argument as computationally irrelevant by writing `` instead of `(x: A)`. So, for example, in the [Vector/concat.kind](https://github.com/uwu-tech/Kind/blob/master/base/Vector/con...) file, `A`, `n` and `m` are erased. As such, the length of the vector doesn't affect the runtime. As a good practice, you may also write `f` instead of `f(x)` syntax for erased arguments, but that is optional.
> TL;DR -- I think the language looks nice, and the compile to JS (from what I read of the Formcore source) looks to be well done. Also, the docs that are present are well presented in a non-academic way that I find pretty readable.
Thanks for the kind words. We put a lot of effort on the compilers and, while there is still a lot to improve, I'm confident they're ahead of all the other languages, by far.
- Kind has an universal compiler that targets several back-ends. [...] For example, to generate a QuickSort function in JavaScript, just type kind List.quicksort --js. You may never write code in any other language! Available targets: --js, --scm.
- Kind - A modern proof language
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Kind-Lang: contributions are welcome!
Kind is a functional, general-purpose programming language featuring theorems and proofs. It has the smallest core, a pretty solid JavaScript and Scheme compiler (seriously, check how clean is the generated kind.js), and a syntax that is a middle ground between Haskell and TypeScript, in an attempt to make it more accessible.
I'm writing CONTRIBUTE.md right now.
- First-class modules with self types
anders
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Anders CCHM/HTS Theorem Prover
Anders is HoTT theorem prover based on: classical MLTT-80 with 0, 1, 2, W types; CCHM in CHM flavour as cubical type system with hcomp/trans Kan operations; HTS sctrict equality on pretypes; de Rham stack modality primitives. We tend not to touch HIT yet, instead we will try to express as much HIT as possible through Coequlizer and HubSpokes Disc in the style of HoTT/Coq homotopy library and Three-HIT theorem. Written in OCaml https://github.com/groupoid/anders
- Show HN: Anders CCHM/HTS Theorem Prover
What are some alternatives?
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cubicaltt - Experimental implementation of Cubical Type Theory
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cicada - An old-school bash-like Unix shell written in Rust
apalache - APALACHE: symbolic model checker for TLA+ and Quint
sml-redprl - The People's Refinement Logic
FormCoreJS - A minimal pure functional language based on self dependent types.
cicada - Cicada Language
plutus - The Plutus language implementation and tools
fathom - 🚧 (Alpha stage software) A declarative data definition language for formally specifying binary data formats. 🚧