CppCon 2020 Template Metaprogramming: Type Traits Part 1 Jody Hagins jhagins@maystreet.com coachhagins@gmail.com ## CppCon 2020 Template Metaprogramming: Type Traits Introduction ## I ntended Audience Not necessarily beginner to C++, but beginner to traditional template metaprogramming techniques • Type traits part of standard library for ~10 years ## I ntended Audience • Beginner/Intermediate • Gentle Not 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 ## I

Abstract definitions - Built-ins - Coinduction - Copatterns - Core language - Coverage Checking - Cubical - Cumulativity - Data Types - Flat Modality - Foreign Function Interface - Mixfix Operators - Module System - Mutual Recursion ○ Pattern Synonyms ○ Positivity Checking ○ Postulates ○ Pragmas ○ Prop ○ Record Types ○ Reflection ○ Rewriting ○ Run-time Irrelevance Types ○ Sort System ○ Syntactic Sugar ○ Syntax Declarations ○ Telescopes ○ Termination Checking ○ Universe Levels ○ With-Abstraction ○ Without K • Tools - Automatic Proof Search

3.2 Built-ins 27 3.3 Coinduction 40 3.4 Copatterns 42 3.5 Core language 45 3.6 Coverage Checking 48 3.7 Cubical 51 3.8 Cumulativity 64 3.9 Data Types 66 3.10 Flat Modality 68 3.11 Foreign 3.24 Module System 112 3.25 Mutual Recursion 117 3.26 Pattern Synonyms 120 3.27 Positivity Checking 121 3.28 Postulates  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 manual

Getting Started o Prerequisites o Installation o Quick Guide to Editing, Type Checking and Compiling Agda Code Language Reference o Abstract definitions o Built-ins Operators o Module System o Mutual Recursion o Pattern Synonyms o Positivity Checking o Postulates o Pragmas o Record Types o Reflection o Rewriting o Safe Agda o Sized Types o Syntactic Sugar o Telescopes o Termination Checking o Universe Levels o With-Abstraction o Without K ## • Tools • Automatic Proof

Abstract definitions - Built-ins - Coinduction - Copatterns - Core language - Coverage Checking - Cubical - Cumulativity - Data Types - Flat Modality - Foreign Function Interface - Mixfix Operators - Module System - Mutual Recursion ○ Pattern Synonyms ○ Positivity Checking ○ Postulates ○ Pragmas ○ Prop ○ Record Types ○ Reflection ○ Rewriting ○ Run-time Irrelevance Types ○ Sort System ○ Syntactic Sugar ○ Syntax Declarations ○ Telescopes ○ Termination Checking ○ Universe Levels ○ With-Abstraction ○ Without K • Tools - Automatic Proof Search

3.2 Built-ins 27 3.3 Coinduction 40 3.4 Copatterns 42 3.5 Core language 45 3.6 Coverage Checking 48 3.7 Cubical 51 3.8 Cumulativity 64 3.9 Data Types 66 3.10 Flat Modality 69 3.11 Foreign 3.25 Module System 113 3.26 Mutual Recursion 118 3.27 Pattern Synonyms 121 3.28 Positivity Checking ..... 123 3.29 Postulates ..... 125 3.30 Pragmas ..... 126 3.31 Prop ..... 129 3.32 Record Sugar ..... 162 3.40 Syntax Declarations ..... 166 3.41 Telescopes ..... 167 3.42 Termination Checking ..... 168 3.43 Universe Levels ..... 170 3.44 With-Abstraction ..... 172 3.45 Without K .

3.18 Module System 53 3.19 Mutual Recursion 58 3.20 Pattern Synonyms 59 3.21 Positivity Checking 59 3.22 Postulates 61 3.23 Pragmas 62 3.24 Record Types 62 3.25 Reflection 68 3.26 Rewriting Rewriting 76 3.27 Safe Agda 76 3.28 Sized Types 77 3.29 Telescopes 80 3.30 Termination Checking 80 3.31 Universe Levels 81 3.32 With-Abstraction ..... 81 3.33 Without K ..... 90 4 Tools 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 tools. A description of the Agda language is given

Overview 2 Getting Started 2.1 Prerequisites 2.2 Installation 2.3 Quick Guide to Editing, Type Checking and Compiling Agda Code 3 Language Reference 3.1 Abstract definitions 3.2 Built-ins 3 Operators 3.18 Module System 3.19 Mutual Recursion 3.20 Pattern Synonyms 3.21 Positivity Checking 3.22 Postulates 3.23 Pragmas 3.24 Record Types 3.25 Reflection 3.26 Rewriting 3.27 Safe Safe Agda 3.28 Sized Types 3.29 Syntactic Sugar 3.30 Telescopes 98 3.31 Termination Checking 98 3.32 Universe Levels 99 3.33 With-Abstraction 99 3.34 Without K 109 4 Tools 111 4.1 Automatic

Overview 2 Getting Started 2.1 Prerequisites 2.2 Installation 2.3 Quick Guide to Editing, Type Checking and Compiling Agda Code 3 Language Reference 3.1 Abstract definitions 3.2 Built-ins 3 Operators 3.18 Module System 3.19 Mutual Recursion 3.20 Pattern Synonyms 3.21 Positivity Checking 3.22 Postulates 3.23 Pragmas 3.24 Record Types 3.25 Reflection 3.26 Rewriting 3.27 Safe Safe Agda 3.28 Sized Types 3.29 Syntactic Sugar 3.30 Telescopes 98 3.31 Termination Checking 98 3.32 Universe Levels 99 3.33 With-Abstraction 99 3.34 Without K 109 4 Tools 111 4.1 Automatic

definitions • Built-ins • Coinduction • Copatterns • Core language • Coverage Checking • Cubical • Cubical compatible • Cumulativity • Data Types • Flat Modality Unification • Mixfix Operators Module System Mutual Recursion Pattern Synonyms Positivity Checking Postulates Pragmas Prop Record Types Reflection Rewriting Run-time Irrelevance Safe Types Sort System Syntactic Sugar Syntax Declarations Telescopes Termination Checking Two-Level Type Theory Universe Levels With-Abstraction Without K Tools Automatic Proof Search