proofs
parson
proofs  parson  

5  1  
286  57  
    
8.8  2.0  
17 days ago  11 months ago  
Coq  Python  
GNU General Public License v3.0 or later   
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proofs

A Taste of Coq and Correct Code by Construction
If you're already familiar with a functional programming language like Haskell or OCaml, you have the prerequisite knowledge to work through my Coq tutorial here: https://github.com/stepchowfun/proofs/tree/main/proofs/Tutor...
My goal with this tutorial was to introduce the core aspects of the language (dependent types, tactics, etc.) in a "straight to the point" kind of way for readers who are already motivated to learn it. If you've heard about proof assistants like Coq or Lean and you're fascinated by what they can do, and you just want the TL;DR of how they work, then this tutorial is written for you.
Any feedback is appreciated!

Thoughts on proof assistants?
Personally I treat Coq like an extension of my brain. Whenever I'm uncertain about something, I formalize it in Coq. I have a repository of proofs with GitHub Actions set up in such a way forbids me from pushing commits containing mathematical mistakes. I've formalized various aspects of category theory, type theory, domain theory, etc., and I've also verified a few programs, such as this sorting algorithm. Lately I've been experimenting with a few novel types of graphs, proving various properties about them with the aim of eventually developing a way to organize all of my data (files, notes, photos, passwords, etc.) in some kind of graph structure like that.

Formally Verifying Rust's Opaque Types
It's always a pleasant surprise to see people using Coq and other formal verification technology. We need more rigor in programming! If this article gave you a thirst for interactive theorem proving and you want to learn it from the ground up, I've recently written a Coq tutorial [1] which covers topics like programming with dependent types, writing proofs as data, and extracting verified code. That repository also contains a handy tactic called `eMagic` [1] (a variant of another useful tactic called `magic` which solve goals with existentials) which can automatically prove the theorem from the article.
[1] https://github.com/stepchowfun/proofs/tree/main/proofs/Tutor...
[2] https://github.com/stepchowfun/proofs/blob/56438c9752c414560...

A complete compiler and VM in 150 lines of code
For anyone who wants to learn Coq, I've just finished writing a tutorial [1] that is aimed at programmers (rather than, say, computer scientists). It covers topics like programming with dependent types, writing proofs as data, universes & other type theory stuff, and extracting verified code—with exercises. I hope people find it useful, and any feedback would be appreciated!
[1] https://github.com/stepchowfun/proofs/tree/main/proofs/Tutor...

New Coq tutorial
Hi all, Coq is a "proof assistant" that allows you to write both code and proofs in the same language (thanks to the Curry–Howard correspondence). Its uses range from pure math (e.g., the Feit–Thompson theorem was proven in Coq!) to reasoning about programming languages (e.g., proving the soundness of a type system) to writing verified code (e.g., this verified C compiler!). You can "extract" your code (without the proofs) to OCaml/Haskell/Scheme for running it in production. Coq is awesome, but it's known for having a steep learning curve (it's based on type theory, which is a foundational system of mathematics). It took me several years to become proficient in it. I wanted to help people pick it up faster than I did, so I wrote this introductory tutorial. Hope you find it useful!
parson

A complete compiler and VM in 150 lines of code
That's powerful enough to conveniently write, for example, a numerical root finding program for an arbitrary arithmetic expression.
But I think that within a complexity budget of 150 lines of code you can maybe be even more ambitious than that.
The example compiler in https://github.com/darius/parson/blob/master/eg_calc_compile... is a bit more stripped down than that, but in its 32 lines of code it compiles arithmetic assignment statements to a threeaddress RISClike code (though using an unbounded number of registers). https://github.com/darius/parson/blob/master/eg_calc_to_rpn.... is a 16line version that compiles the same language to a stack machine like your tutorial example.
In 66 lines of code in https://github.com/kragen/pegbootstrap/blob/master/peg.md I wrote an example compiler which compiles a PEG grammar into a JavaScript parser for that grammar. Admittedly those 66 lines do not include an implementation of JavaScript to run the code on. It compiles the language it's written in.
In 132 lines of code in https://github.com/kragen/stoneknifeforth/blob/master/tinybo... I wrote an example compiler which compiles a crippled Forth dialect into i386 machine code, including an ELF header so you can run the result. It also compiles the language it's written in. It also doesn't include an i386 emulator to run it on.
In 83 lines of code in http://canonical.org/~kragen/sw/dev3/neelcompiler.ml Neel Krishnaswami wrote a compiler from the untyped λcalculus to a simple assembly language for a register machine. It also doesn't include an implementation of the assembly language.
In 18 lines of code in http://canonical.org/~kragen/sw/dev3/meta5ix.m5, a simplification of METAII, I wrote a compiler from grammar descriptions to an assembly code for a parsingoriented virtual machine. It compiles the language it's written in. A Python interpreter for the machine is in http://canonical.org/~kragen/sw/dev3/meta5ixrun.py (109 lines of code) and a precompiled version of the compilercompiler for bootstrapping is in http://canonical.org/~kragen/sw/dev3/meta5ix.generated.m5asm.
A slightly incompatible variant of Meta5ix which instead compiles itself to C is in http://canonical.org/~kragen/sw/dev3/meta5ix2c.m5 (133 lines of code, depending on how you count). (No C compiler is included.) The precompiled C output for bootstrapping is in http://canonical.org/~kragen/sw/dev3/meta5ix2c.c.
Meta5ix is extremely weak and limited, really only enough for a compiler frontend; it can't, for example, do the kinds of RPN tricks we're talking about above.
What are some alternatives?
CompCert  The CompCert formallyverified C compiler
pegbootstrap  A PEG that compiles itself.
masterthesis
pyparsing  Python library for creating PEG parsers
hacspec  Please see https://github.com/hacspec/hax
stoneknifeforth  a tiny selfhosted Forth implementation
aneris  Program logic for developing and verifying distributed systems
kefir  🥛turkic morphology project
ccctalk  Correct Code by Construction talk's code
PEGTL  Parsing Expression Grammar Template Library
coqsimpleio  IO for Gallina
konbini  Parser library for Kotlin