proofs VS stoneknifeforth

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!

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.

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...

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...

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!

a problem that a lot of these series run into is that the author runs out of steam before they finish writing them. crenshaw's otherwise excellent series suffers from this, for example

so far the author of this one has only written the first chapter

i've written a few didactic compilers that are complete enough to compile themselves, though nothing else

https://github.com/kragen/stoneknifeforth (from a forth-like language to an i386 linux elf executable)

https://github.com/kragen/peg-bootstrap/blob/master/peg.md (from a peg language description with semantic actions to javascript)

http://canonical.org/~kragen/sw/urscheme (from a subset of scheme to at&t-syntax i386 assembly)

Look at how much room you have for data! I wonder what we can fit in there.

More seriously, a metacircular example to draw from would be: https://github.com/kragen/stoneknifeforth

i wasn't able to get a runnable forth to less than a couple of pages written in itself https://github.com/kragen/stoneknifeforth but schönfinkel's ski-combinators are maybe the simplest practical basis

    s f g x → f x (g x)

I've done all these things (except designing the hardware) and I agree that it can be very painful. I did some of them in 02008, for example: https://github.com/kragen/stoneknifeforth

The thing is, though, you can also not do all those things. You can use variables, and they don't even have to be allocated on a stack (unless you're writing a recursive function, which you usually aren't), and all the NIP TUCK ROT goes away, and with it all the Memory Championship tricks. You can test each definition interactively as you write it, and then the fact that the language is absurdly error-prone hardly matters. You can use metaprogramming so that your code is as DRY as a nun's pochola. You can use the interactivity of Forth to quickly validate your hypotheses about not just your code but also the hardware in a way you can't do with C. You can do it with GDB, but Forth is a lot faster than GDBscript, but that's not saying much because even Bash is a lot faster than GDBscript.

But Yossi was just using Forth as a programming language, like a C without local variables or type checking, not an embedded operating system. And, as I said, that's really not Forth's strength. Bash and Tcl aren't good programming languages, either. If you try to use Tcl as a substitute for C you will also be very sad. But the way they're used, that isn't that important.

I explained a more limited version of this 12 years ago: https://yosefk.com/blog/my-history-with-forth-stack-machines...

So, I don't think Forth is only useful when you have the freedom to change the problem, though programs in any language do become an awful lot easier when you have that freedom.

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 three-address RISC-like code (though using an unbounded number of registers). https://github.com/darius/parson/blob/master/eg_calc_to_rpn.... is a 16-line version that compiles the same language to a stack machine like your tutorial example.

In 66 lines of code in https://github.com/kragen/peg-bootstrap/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 λ-calculus 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 META-II, I wrote a compiler from grammar descriptions to an assembly code for a parsing-oriented 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 compiler-compiler 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 front-end; it can't, for example, do the kinds of RPN tricks we're talking about above.

Title effectively says it all. The only thing I have found is StoneKnife Forth (implementation is in tinyboot1.tbf1) but this file is implemented in the same dialect of forth it implements, which due to being minimal makes it difficult to read and comprehend efficiently (I also can't find the origin of some words such as 'byte' used in the code but not implemented by the interpreter). I would prefer something in the C family to look at but anything should do as long as it's clean enough that I could use it as a reference to reimplement the compiler without much difficulty. Thank you in advance for any help with what is seemingly quite a narrow request.

I'm pretty sure Linux ELF has always allowed you to specify the initial load address. When I first wrote StoneKnifeForth https://github.com/kragen/stoneknifeforth its load address was 0x1000, but at some point Linux stopped allowing load addresses lower than 0x10000 by default (vm.mmap_min_addr). I originally wrote it in 02008, using the lower load address, and fixed it in 02017. It's still not using 0x804800 like normal executables but 0x20000. ASLR does not affect this.

Maybe you mean that before ELF support, Linux a.out executables had to be loaded at a fixed virtual address? That's possible—I started using Linux daily in 01995, at which point a.out was already only supported for backward compatibility.