Lean in Lean Leonardo de Moura - MSR - USA Workshop Programming Language http://leanprover.github.io Lean • Goals • Extensibility, Expressivity, Scalability, Proof stability • Functional Programming Language Lean Timeline • Lean 1 (2013) Leo and Soonho Kong • Almost useless • Brave (crazy?) users in 2014: Jeremy Avigad, Cody Roux and Floris van Doorn • Lean 2 (2015) Leo and Soonho the HoTT library for Lean • First Math library (Jeremy Avigad, Rob Lewis, and many others) • Lean 3 (2016) Leo, Daniel Selsam, Gabriel Ebner, Jared Roesch, Sebastian Ullrich • Lean is now a programming

An Introduction to Lean Jeremy Avigad Leonardo de Moura Gabriel Ebner and Sebastian Ullrich Version 1fc176a, updated at 2017-01-09 14:16:26 -0500 2 Contents Contents 3 1 Overview 5 1.1 Perspectives Perspectives on Lean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Where To Go From Here . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Defining Objects in Lean 13 2.1 Nonconstructive Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3 Programming in Lean 27 3.1 Evaluating Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2

Lean 4 Leonardo de Moura - MSR - USA Sebastian Ullrich - KIT - Germany Programming Language http://leanprover.github.io • Goals • Extensibility, Expressivity, Scalability, Proof stability io/theorem_proving_in_lean/ • Zulip channel: https://leanprover.zulipchat.com/ • Community website: https://leanprover-community.github.io/ • Maintainers of the official release (Lean 3) • Mathlib: https://leanprover-community.github.io/mathlib-overview.html • Lean 4 repository: https://github.com/leanprover/lean4 Programming Language Mathlib The Lean mathematical library, mathlib, is a community-driven

Programming in Lean Release 3.4.2 Jeremy Avigad and Simon Hudon Apr 02, 2019 CONTENTS 1 Introduction 1 2 Types and Terms 3 2.1 Some Basic Types . . . . . . . . . . . . . . . . . . . . . . . . . Theorem Proving in Lean, which presents Lean as a system for building mathematical libraries and stating and proving mathematical theorems. From that perspective, the point of Lean is to implement a formal framework in which one can define mathematical objects and reason about them. But expressions in Lean have a computational interpretation, which is to say, they can be evaluated. Any closed term of type

Lean 2 Quick Reference Jeremy Avigad, Leonardo de Moura, Soonho Kong Version d0dd6d0, updated at 2017-01-30 19:53:44 -0500 Quick Reference Note that this quick reference guide describes Lean 2 only intros : same as intro intro : let Lean choose a name intros : introduce variables as long as the goal reduces to a function type and let Lean choose the names rename : rename a variable comma-separated list) Emacs Lean-mode commands Flycheck commands 6 C-c ! n : next error C-c ! p : previous error C-c ! l : list errors C-c C-x : execute Lean (in stand-alone mode) Lean-specific commands C-c

The Lean Reference Manual Release 3.3.0 Jeremy Avigad, Gabriel Ebner, and Sebastian Ullrich Sep 06, 2018 CONTENTS 1 Using Lean 1 1.1 Using Lean Online . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Using Lean with VSCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Using Lean with Emacs . . . . . . . . . . . . . . . . . Bibliography 63 ii CHAPTER ONE USING LEAN 1.1 Using Lean Online You can run a Javascript version of Lean online in your browser. It is much slower than running a version of Lean installed on your computer, but

Theorem Proving in Lean Release 3.23.0 Jeremy Avigad, Leonardo de Moura, and Soonho Kong Apr 25, 2023 CONTENTS 1 Introduction 1 1.1 Computers and Theorem Proving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 About Lean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 About this Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6 Interacting with Lean 79 6.1 Importing Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Limperg The Hitchhiker’s Guide to Logical Verification 2021 Standard Edition (October 13, 2021) lean-forward.github.io/ logical-verification/2021 ii Contents Contents iii Preface vii I Basics 1 Lemma Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5 Summary of New Lean Constructs . . . . . . . . . . . . . . . . . . . . . 18 2 Backward Proofs 21 2.1 Tactic Mode . . Cleanup Tactics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.9 Summary of New Lean Constructs . . . . . . . . . . . . . . . . . . . . . 34 3 Forward Proofs 35 3.1 Structured Proofs

Agility By Mark Schwartz “Mark Schwartz is a rare combination: a deep thinker who has also applied lean, Agile, and DevOps principles at the highest level, leading an extraordinary Agile transformation simply says that we should empower small teams to inspect and adapt rather than stick to a plan. Lean thinking gives that small team ways to speed up its inspecting and adapting process to maximize its can optimize the whole – a term of art in lean thinking – and be empowered as a team to own the entire value delivery process. Brining Lean Principles to Software Development: Kanban

26 27 using UnityEngine; using System.Collections; using System.Collections.Generic; using Lean; public class TilingEngine : MonoBehaviour { public List TileSprites; public Alright, the properties on this one is fairly beefy. I’m sure you noticed a new using statement for Lean. That is because we are using an asset called LeanPool. It is a free asset in the asset store and object from within tiles. With each loop, lean pool is to despawn an object. Lean pool will despawn the tile container and the tile container is set to Lean pool to spawn the Tile container prefab.