Template Metaprogramming: Type Traits Part 1 CppCon 2020 1 Jody Hagins
 jhagins@maystreet.com 
 coachhagins@gmail.comTemplate Metaprogramming: Type Traits CppCon 2020 2 IntroductionIntended Audience necessarily beginner to C++, but beginner to traditional template metaprogramming techniques • Type traits part of standard library for ~10 years 3Intended Audience • Beginner/Intermediate • Gentle necessarily beginner to C++, but beginner to traditional template metaprogramming techniques • Type traits part of standard library for ~10 years • Fundamentals have been in use for ~20 years 3Intended

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Dependent Type Theory 5 2.1 Simple Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.8 Dependent Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 8.6 Dependent Pattern Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

. . . . . . . . . . . . . . . . . . 36 4 Theorem Proving in Lean 38 4.1 Assertions in Dependent Type Theory . . . . . . . . . . . . . . . . . . . . . 38 4.2 Propositions as Types . . . . . . . . . Lean is an implementation of a logical foundation known as dependent type theory. Specifi- cally, it implements a version of dependent type theory known as the Calculus of Inductive Constructions. The CIC expression has a type. The type of expression indicates what sort of object the expression denotes. For example, an expression may denote a mathematical object like a natural number, a data type, an assertion

Types Sort System Syntactic Sugar Syntax Declarations Telescopes Termination Checking Two-Level Type Theory Universe Levels With-Abstraction Without K Tools Automatic Proof Search (Auto) Command-line options Agda page [https://github.com/agda/agda]. This is the manual for the Agda programming language, its type checking, compilation and editing system and related resources/tools. The latest PDF version of this compilation system can be used can be found in chapter Tools. Getting Started What is Agda? Dependent types Installation Installation from source Prebuilt Packages and System-Specific Instructions

Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.16 Guarded Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.17 Implicit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 3.45 Two-Level Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 3.46 Universe request or issue on the GitHub Agda page. This is the manual for the Agda programming language, its type checking, compilation and editing system and related resources/tools. The latest PDF version of this

Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.16 Guarded Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.17 Implicit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 3.45 Two-Level Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 3.46 Universe request or issue on the GitHub Agda page. This is the manual for the Agda programming language, its type checking, compilation and editing system and related resources/tools. The latest PDF version of this

Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.16 Guarded Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.17 Implicit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 3.45 Two-Level Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 3.46 Universe request or issue on the GitHub Agda page. This is the manual for the Agda programming language, its type checking, compilation and editing system and related resources/tools. The latest PDF version of this

Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.16 Guarded Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.17 Implicit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 3.45 Two-Level Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 3.46 Universe request or issue on the GitHub Agda page. This is the manual for the Agda programming language, its type checking, compilation and editing system and related resources/tools. The latest PDF version of this

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 3.44 Two-Level Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 3.45 Universe request or issue on the GitHub Agda page. This is the manual for the Agda programming language, its type checking, compilation and editing system and related resources/tools. The latest PDF version of this is Agda? Agda is a dependently typed programming language. It is an extension of Martin-Löf’s type theory and is the latest in the tradition of languages developed in the programming logic group at Chalmers