114 lines
4.3 KiB
Lean4
114 lines
4.3 KiB
Lean4
-- Here's the import to make Lean know about things called `Game`s
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import GameServer.Commands
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-- Here are the imports defining many worlds for the game `Game` (the natural number game,
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-- in this case). Each world consists of a finite number of levels, and levels
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-- are numbered 1,2,3,4... inside the level files.
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import Game.Levels.Tutorial
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import Game.Levels.Addition
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import Game.Levels.Multiplication
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import Game.Levels.Power
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import Game.Levels.Implication
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import Game.Levels.AdvAddition
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import Game.Levels.LessOrEqual
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--import Game.Levels.AdvMultiplication
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--import Game.Levels.EvenOdd
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--import Game.Levels.Prime
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--import Game.Levels.StrongInduction
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--import Game.Levels.Hard
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import Game.Levels.Algorithm
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-- Here's what we'll put on the title screen
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Title "Natural Number Game"
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Introduction
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"
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# Welcome to the Natural Number Game
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#### An introduction to mathematical proof.
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In this game, we will build the basic theory of the natural
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numbers `{0,1,2,3,4,...}` from scratch. Our first goal is to prove
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that `2 + 2 = 4`. Next we'll prove that `x + y = y + x`.
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And at the end we'll see if we can prove Fermat's Last Theorem.
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We'll do this by solving levels of a computer puzzle game called Lean.
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# Read this.
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Learning how to use an interactive theorem prover takes time.
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Tests show that the people who get the most out of this game are
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those who read the help texts like this one.
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To start, click on \"Tutorial World\".
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Note: this is a new Lean 4 version of the game containing several
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worlds which were not present in the old Lean 3 version. A new version
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of Advanced Multiplication World is in preparation, and worlds
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such as Prime Number World and more will be appearing during October and
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November 2023.
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## More
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Click on the three lines in the top right and select \"Game Info\" for resources,
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links, and ways to interact with the Lean community.
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"
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Info "
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*Game version: 4.2*
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*Recent additions: Inequality world, algorithm world*
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## Progress saving
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The game stores your progress in your local browser storage.
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If you delete it, your progress will be lost!
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Warning: In most browsers, deleting cookies will also clear the local storage
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(or \"local site data\"). Make sure to download your game progress first!
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## Credits
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* **Creators:** Kevin Buzzard, Jon Eugster
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* **Original Lean3-version:** Kevin Buzzard, Mohammad Pedramfar
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* **Game Engine:** Alexander Bentkamp, Jon Eugster, Patrick Massot
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* **Additional levels:** Sian Carey, Ivan Farabella, Archie Browne.
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* **Additional thanks:** All the student beta testers, all the schools
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who invited Kevin to speak, and all the schoolkids who asked him questions
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about the material.
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## Resources
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* The [Lean Zulip chat](https://leanprover.zulipchat.com/) forum
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* [Original Lean3 version](https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/) (no longer maintained)
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## Problems?
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Please ask any questions about this game in the
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[Lean Zulip chat](https://leanprover.zulipchat.com/) forum, for example in
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the stream \"New Members\". The community will happily help. Note that
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the Lean Zulip chat is a professional research forum.
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Please use your full real name there, stay on topic, and be nice. If you're
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looking for somewhere less formal (e.g. you want to post natural number
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game memes) then head on over to the [Lean Discord](https://discord.gg/WZ9bs9UCvx).
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Alternatively, if you experience issues / bugs you can also open github issues:
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* For issues with the game engine, please open an
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[issue at the lean4game](https://github.com/leanprover-community/lean4game/issues) repo.
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* For issues about the game's content, please open an
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[issue at the NNG](https://github.com/hhu-adam/NNG4/issues) repo.
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"
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-- Here's where we show how to glue the worlds together
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Dependency Addition → Multiplication → Power
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--Dependency Addition → AdvAddition → AdvMultiplication → Inequality → Prime → Hard
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--Dependency Multiplication → AdvMultiplication
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--Dependency AdvAddition → EvenOdd → Inequality → StrongInduction
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Dependency Addition → Implication → AdvAddition → LessOrEqual
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Dependency AdvAddition → Algorithm
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-- The game automatically computes connections between worlds based on introduced
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-- tactics and theorems, but for example it cannot detect introduced definitions
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-- Dependency Implication → Power -- `Power` uses `≠` which is introduced in `Implication`
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MakeGame
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