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 can be used without giving a label to the hypothesis. The corresponding element of the context can 2 then be referred to using the keyword this until another anonymous element is introduced, or by enclosing 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

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

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Using the Package Manager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Lexical Structure 7 2.1 Symbols and Commands

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Dependent Type Theory 5 2.1 Simple Type Theory

Adventures in SIMD Thinking (Part 2 of 2) Bob Steagall CppCon 2020 K E W B C O M P U T I N GCopyright © 2020 Bob Steagall K E W B C O M P U T I N G Agenda • Learn a little about Intel's SIMD facilities Faster (?) UTF-8 to UTF-32 conversion (with AVX2) • No heavy code, but lots of pictures • Thinking "vertically" CppCon 2020 - Adventures in SIMD Thinking 2Copyright © 2020 Bob Steagall Small-Kernel Convolution S = s0 s1 s2 s3 s4 s5 s6 ... K = k0 k1 k2 r0 = ... r1 = s0k0 + s1k1 + s2k2 r2 = s1k0 + s2k1 + s3k2 r3 = s2k0 + s3k1 + s4k2 r4 =

Back to Basics Designing Classes (part 1 of 2) Klaus Iglberger, CppCon 2021 klaus.iglberger@gmx.de2 Klaus Iglberger C++ Trainer/Consultant Author of the C++ math library (Co-)Organizer (Co-)Organizer of the Munich C++ user group Chair of the CppCon B2B and SD tracks Email: klaus.iglberger@gmx.deContent 3 Back to Basics: Class Design (Part 1) The Challenge of Class Design Design Testability Implementation Guidelines Resource Management Back to Basics: Class Design (Part 2) Implementation Guidelines Data Member Initialization Implicit Conversions Order of Data Members

if (NOT TARGET Catch2) project(Catch2 CXX) set(CMAKE_CXX_STANDARD 11) add_library(${PROJECT_NAME} INTERFACE) target_include_directories(${PROJECT_NAME} INTERFACE ${CMAKE_CU ${CMAKE_CURRENT_SOURCE_DIR}/include) # Mimic the library names in Catch2's own CMake files: add_library(Catch2::Catch2 ALIAS Catch2) # This one is historical, left over from when ApprovalTests.cpp was first created. # We could encourage users to move away from it. add_library(catch2 ALIAS Catch2) endif ()