https://github.com/reynir/brainfuck

Brainfuck formalized in Coq
https://github.com/reynir/brainfuck

Last synced: 2 months ago
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Brainfuck formalized in Coq

• Host: GitHub
• URL: https://github.com/reynir/brainfuck
• Owner: reynir
• Created: 2013-09-17T21:55:39.000Z (over 11 years ago)
• Default Branch: master
• Last Pushed: 2022-03-29T10:54:51.000Z (almost 3 years ago)
• Last Synced: 2024-10-13T21:28:49.769Z (3 months ago)
• Language: Coq
• Homepage:
• Size: 29.3 KB
• Stars: 27
• Watchers: 5
• Forks: 2
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
Brainfuck

=========

This is a project where I try to formalize

[brainfuck](http://en.wikipedia.org/wiki/Brainfuck) in

[Coq](http://en.wikipedia.org/wiki/Coq).

Goal

---

The goal is to prove properties about brainfuck. I have implemented a compiler

from simple arithmetic expressions (addition, subtraction and multiplication) to

brainfuck. This is done by compiling to a stack machine subset of brainfuck.

Arithmetic expression compiler

------------------------------

A compiler from simple arithmetic expressions with addition, subtraction and

multiplication to brainfuck is included in `ae_compiler.v`. The correctness of

the compiler is proven as well. The idea in the proof is to develop a number of

stack primitives and show their correctness, and then compile down to those

stack primitives.

The hello world example

-----------------------

A `"Hello World!"` example is included in `bf_theorems.v`. It proves that the

given `"Hello World!"` program does output the string `Hello World!` (or rather

the ASCII values corresponding to said string - you have to verify that

yourself!). The proof is largely automated. Unfortunately it takes a while to

finish so it is recommended to comment out the theorem.

The time it takes to compile with the `hello_world` theorem:

    real    0m14.674s

    user    0m14.340s

    sys     0m0.230s

And when `hello_world` is commented out:

    real    0m2.485s

    user    0m2.313s

    sys     0m0.113s

The project's [Github page](https://github.com/reynir/Brainfuck/).