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goedel's Introduction

Goedel

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A proof in Coq of the Gödel-Rosser 1st incompleteness theorem, which says that any first order theory extending NN (which is PA without induction) that is complete is inconsistent.

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Building and installation instructions

The easiest way to install the latest released version of Goedel is via OPAM:

opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-goedel

To instead build and install manually, do:

git clone https://github.com/coq-community/goedel.git
cd goedel
make   # or make -j <number-of-cores-on-your-machine> 
make install

Documentation

More information about the project can be found at this website.

goedel's People

Contributors

casteran avatar herbelin avatar lessnessrandomness avatar letouzey avatar palmskog avatar ppedrot avatar zimmi48 avatar

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goedel's Issues

modificactions to goedel

@palmskog @Zimmi48

goedel is a great contribution, and is worth maintaining !

Nevertheless, if we want to use it also as a library of primitive recursive functions (for instance in coq-hydra-battles), there is a lot of work to be done.

  • add documentation (files of examples, coqdoc comments, text), especially for functions defined by interactive proofs.
  • add tactics
  • use "modern" coq style (bullets, implicit arguments, type classes, ...)

I created a branch new-stuff for these improvements (which may take a long time)

Release for 8.13

Given that there are changes planned upstream to the Ackermann library in hydra-battles (coq-community/hydra-battles#31), this could be a good time to make a timestamp/release of goedel that works with hydra-battles 0.4 and Coq 8.13 (and 8.12). After the release, we can restrict this project to 8.13+ like hydra-battles.

@Casteran what do you think? I can do the release if you think it's a good idea.

Compilation broken with Coq 8.14

FWIW, the compilation of Goedel fails with Coq 8.14 with the following error:

 File "./theories/chRem.v", line 257, characters 0-6:
Error: The reference double was not found in the current environment.

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