http://leanprover.github.io Lean in Lean Leonardo de Moura - MSR - USA  Workshop Microsoft $ ^{®} $ Research ## Lean ## • Goals • proof/type checkers ## 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 ## Contents Contents 3 1 Overview 5 1 1.1 Perspectives on Lean 5 1.2 Where To Go From Here 12 2 Defining Objects in Lean 13 2.1 Some Basic Types 14 2.2 Defining Functions 17 2.3 Defining New Types 20 2.4 Records and and Structures 22 2.5 Nonconstructive Definitions 25 3 Programming in Lean 27 3.1 Evaluating Expressions 28 3.2 Recursive Definitions 30 3.3 Inhabited Types, Subtypes, and Option Types

http://leanprover.github.io  Lean 4 Leonardo de Moura - MSR - USA Sebastian Ullrich - KIT - Germany Microsoft $ ^{®} $ Research 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: ht https://leanprover-community.github.io/mathlib-overview.html • Lean 4 repository: https://github.com/leanprover/lean4 ## Mathlib The Lean mathematical library, mathlib, is a community-driven effort to

# Programming in Lean Release 3.4.2 Jeremy Avigad and Simon Hudon Apr 02, 2019 Powered by TCPDF (www.tcpdf.org) ## CONTENTS 1 Introduction 1 2 Types and Terms 3 2.1 Some Basic Types 3 2.2 Defining 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 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 : execute a single tactic with different options ( is a comma-separated list) ## Emacs Lean-mode commands ## Flycheck commands

0 码力 | 9 页 | 62.97 KB | 2 年前

3

# The Lean Reference Manual Release 3.3.0 Jeremy Avigad, Gabriel Ebner, and Sebastian Ullrich Sep 06, 2018 Powered by TCPDF (www.tcpdf.org) ## CONTENTS 1 Using Lean 1 1.1 Using Lean Online 1 1.2 2 Using Lean with VSCode 1 1.3 Using Lean with Emacs 2 1.4 Using the Package Manager 3 2 Lexical Structure 7 2.1 Symbols and Commands 7 2.2 Identifiers 7 2.3 String Literals 8 2.4 Char Literals 61 ## Bibliography # 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

# Theorem Proving in Lean Release 3.23.0 Jeremy Avigad, Leonardo de Moura, and Soonho Kong Apr 25, 2023 Powered by TCPDF (www.tcpdf.org) ## CONTENTS 1 Introduction 1.1 Computers and Theorem Proving Proving 1.2 About Lean 1.3 About this Book 1.4 Acknowledgments 2 Dependent Type Theory 2.1 Simple Type Theory 2.2 Types as Objects 2.3 Function Abstraction and Evaluation 2.4 Introducing Definitions Rewriting ..... 70 5.7 Using the Simplifier ..... 72 5.8 Exercises ..... 77 6 Interacting with Lean ..... 79 6.1 Importing Files ..... 79 6.2 More on Sections ..... 80 6.3 More on Namespaces

TuckAssuring QualityDec 2014Toby FlintLean Startup Book ReviewMark StaroskaStory PointsJason

(October 13, 2021)  lean-forward.github.io/ logical-verification/2021 ## Contents Contents iii Preface vii I Basics 2 Type Definitions 8 1.3 Function Definitions 13 1.4 Lemma Statements 16 1.5 Summary of New Lean Constructs 18 2 Backward Proofs 21 2.1 Tactic Mode 22 2.2 Basic Tactics 23 2.3 Reasoning about Mathematical Induction 31 2.7 Induction Tactic 33 2.8 Cleanup Tactics 33 2.9 Summary of New Lean Constructs 34 3 Forward Proofs 35 3.1 Structured Proofs 35 3.2 Structured Constructs 37 3

v=RXzurBazN-I ## Scaled Agile Framework (SAFe): Dean Leffingwell - Agile Software Requirements: Lean Requirements for Teams Programs and the Enterprise (2011) and Scaling Software Agility: Best Practices quality - can't scale crappy code • Program execution • Alignment • Transparency ## House of Lean: ## The Goal: Value #### Sustainable shortest lead time. Best quality and value to people and society Foundation: Management Support Management applies and teaches lean thinking, bases decisions on this long-term philosophy Eight Principles of Lean|Agile Leadership "We need to figure out a way to deliver