Logic and Mechanized Reasoning

This repository is designed to accompany the course by the same name. See also:

• the textbook (in progress): https://avigad.github.io/lamr
• a PDF version of the textbook: https://avigad.github.io/lamr/logic_and_mechanized_reasoning.pdf
• the course home page: https://www.cs.cmu.edu/~mheule/15217-f21/

This repository contains a supporting library and files containing examples from the textbook that you can edit and experiment with.

The course requires the Lean 4 programming language and theorem prover, as well as three additional automated reasoning tools: CaDiCaL (a SAT solver), Z3 (an SMT solver), and Vampire (a resolution theorem prover).

There are three ways for you to use the software and supporting libraries.

Option 1: Use Gitpod and the source repository

This is the easiest option. Gitpod will give you 50 free hours every month to run a virtual workspace through your browser.

1. Register for Gitpod account at https://gitpod.io/login/.

2. Go to https://gitpod.io/#/https://github.com/avigad/lamr. In other words, preface the url of this repository with https://gitpod.io/#. This will start a new workspace based on this repository.

3. It may take a little while for the workspace to start, but when it does, you will be looking at a VS Code editor window with a terminal at the bottom and a file browser on the left. If you open the file User/Examples/hello_world.lean, you should see output in a Lean Infoview window. Also, hovering over the #eval commands with the blue squiggly lines underneath should show you the output of those commands.

4. The folder User/Examples contains a copy all the examples from the textbook. Feel free to edit these files and experiment. You can also create new files to your heart's content. You should not change anything in the Mathlib or LAMR directories; we recommend keeping all your own files in the User folder. There is an original copy of the Examples folder in the LAMR directory, so you can copy these to User/Examples if you wish to restore the original files.

5. When you are done, choose Stop workspace from the menu on the left. The workspace should also stop automatically 30 minutes after the last interaction or 3 minutes after closing the tab.

Every time you return to the link in Step 2, Gitpod will start a fresh workspace. To restart a previous workspace, go to https://gitpod.io/workspaces/. If you change the filter from Active to All, you will see all your recent workspaces. You can pin a workspace to keep it on the list of active ones.

With this method, you can save files on a virtual machine and start and stop it at will. There isn't an easy way to transfer files from the virtual machine to your own computer, but you can simply copy text from the editor in the browser and paste it anywhere you want.

We will update the repository, including the examples folder, as the course proceeds. To update the copy of the repository on an existing virtual machine, type git pull --no-rebase in the terminal window. You will then have to manually copy new files from the LAMR/Examples folder to the User/Examples folder. Alternatively, you can simply follow the instructions above to start a new workspace.

Option 2: Use Gitpod and a forked repository

Git is a powerful version control system and Github allows you to share repositories in the cloud. If you are familiar with these or willing to learn how to use them, you can fork this repository to your github account and use the fork as a file system for the virtual machine.

1. Create a fork of https://github.com/avigad/lamr by clicking the Fork button in the upper right corner.

2. Follow the instructions above to start a virtual machine on your copy of the repository.

You can merge updates from the master lamr repository clicking Fetch upstream from your repository page on Github. And now you can use the usual git commands from the terminal inside your virtual machine to synchronize with your copy of the repository. Use git pull to update the local copy in the virtual machine from your repository, and use git commit and git push to transfer changes from the virtual machine to your repository.

Option 3: Install Lean, the repository, and course software locally

It should not be too hard to install Lean and all the course software on your own computer, on Windows, OS/X, or Linux.

1. Install Lean and VS Code following the instructions here.

2. Clone this repository, using git clone or the Download ZIP option on the Code button above.

3. Inside the top folder of the repository, type leanpkg build to compile the library files. Also, copy the examples folder from the LAMR folder to the User folder.

4. Open the repository folder in VS Code.

From there, you should be able to use Lean and experiment with the example files as described in Option 1.

To use CaDiCaL, Z3, and Vampire, you will have to add them to manually to the folder LAMR/bin. There are instructions on how to obtain CaDiCaL here. We will later provide instructions for obtaining Z3 and Vampire.