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Try doing some basic maths questions in the Lean Theorem Prover. Functions, real numbers, equivalence relations and groups. Click on README.md and then on "Open in CoCalc with one click".
License: APACHE
Creating a Lean project
Lean files are organized in projects called packages. The tool leanpkg
manages project creation and dependencies. We will now create a new project depending on mathlib. The following commands should be typed in a terminal.
If you have not logged in since you installed Lean and mathlib, then you need to first type
source ~/.profile
.Then go to a folder where you want to create a project in a subfolder
my_project
, and type:launch VScode, either through your application menu or by typing
code
On the main screen, or in the File menu, click "Open folder" (on a Mac, just "Open"), and choose the folder
my_project
(not one of its subfolders).Your Lean code should now be put inside files with extension
.lean
living inmy_project/src/
or a subfolder thereof. In the file explorer on the left-hand side of VScode, you can right-click onsrc
, chooseNew file
, and type a filename to create a file there.
If you want to make sure everything is working, you can start by creating, say my_project/src/test.lean
containing:
When the cursor is on the last line, the right hand part of VScode should display a "Lean messages" area saying: topological_space : Type u_1 → Type u_1
If, for some reason, you happen to loose the "Lean messages" area, you can get it back with "Ctrl-Shift-Enter". Also, you can get the Lean documentation inside VScode using "Ctrl-Shift-p" and then, inside the text field that appeared, type "lean doc" and hit Enter. Then click "Theorem proving in Lean" and enjoy.
Working on an existing package
Suppose you want to work on an existing project. As example, we will take the tutorial project. Open a terminal.
If you have not logged in since you installed Lean and mathlib, then you need to first type
source ~/.profile
.Go the the directory where you would like this package to live.
Run
git clone https://github.com/leanprover-community/tutorials.git
.This creates a directory named
tutorials
. Enter it withcd tutorials
.Type
leanpkg configure
to getleanpkg
ready for use in this project.Type
update-mathlib
to get mathlib ready for use in this project.Type
leanpkg build
to compile everything, this should only take a few seconds.launch VScode, either through your application menu or by typing
code
On the main screen, or in the File menu, click "Open folder" (just "Open" on a Mac), and choose the folder
tutorials
(not one of its subfolders).Using the file explorer on the left-hand side, explore everthing you want in
tutorials/src