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

Setting View Variables Setting View Options ■ Rendering a View Content Type Negotiation ■ Controller::addViewClasses(). Content Type Negotiation Fallbacks Using AjaxView ☐ Redirecting to Other Pages authentication or authorization rules, delegates data fetching or processing to the model, selects the type of presentational data that the clients are accepting, and finally delegates the rendering process download composer.phar from the Composer website [https://getcomposer.org/download/]. Then simply type the following line in your terminal from your installation directory to install the CakePHP application

of a certain type. The variable's type is called static type, the location's type is called dynamic type. If the static type is not the same as the dynamic type, it is a super-type or subtype of of the dynamic type. An identifier is a symbol declared as a name for a variable, type, procedure, etc. The region of the program over which a declaration applies is called the scope of the declaration mod nil not notin object of or out proc ptr raise ref return shl shr static template try tuple type using var when while xor yield Some keywords are unused; they are reserved for future developments

manipulated like any other value. The standard example is the type of lists of a given length $ ^{1} $ , Vect n a, where a is the element type and n is the length of the list and can be an arbitrary term contain values, and where those values describe properties, for example the length of a list, the type of a function can begin to describe its own properties. Take for example the concatenation of two list's length is the sum of the lengths of the two input lists. We can therefore give the following type to the app function, which concatenates vectors: app : Vect n a -> Vect m a -> Vect (n + m)

Tokens 19 1.3 Syntax grammar 23 1.4 Documentation comments 42 2 Type system 43 Glossary 43 Introduction 44 2.1 Type kinds 45 2.1.1 Built-in types 46 kotlin.Any 46 kotlin.Nothing 46 types 48 2.1.3 Type parameters ..... 50 Function type parameters ..... 51 Mixed-site variance ..... 51 Declaration-site variance ..... 52 Use-site variance ..... 54 2.1.4 Type capturing .... . 55 2.1.5 Type containment ..... 60 2.1.6 Function types ..... 61 Suspending function types ..... 62 2.1.7 Flexible types ..... 63 Dynamic type ..... 64 Platform types ..... 64 2.1.8 Nullable

Literals 70 8.13 Annotated Strings 70 9 Functions 72 9.1 Argument Passing Behavior 73 9.2 Argument-type declarations 74 9.3 The return Keyword 75 9.4 Operators Are Functions 77 9.5 Operators With Special Names Types 127 12.1 Type Declarations 128 12.2 Abstract Types 130 12.3 Primitive Types 132 12.4 Composite Types 133 12.5 Mutable Composite Types 135 CONTENTS 12.6 Declared Types 136 12.7 Type Unions 137 12 9 UnionAll Types 146 12.10 Singleton types 147 12.11 Types of functions 148 12.12 Type{T} type selectors 149 12.13 Type Aliases 150 12.14 Operations on Types 151 12.15 Custom pretty-printing 152 12.16 “Value

Annotated Strings 70 9 Functions 72 9.1 Argument Passing Behavior 73 9.2 Argument-type declarations 74 9.3 The return Keyword 75 9.4 Operators Are Functions 77 9.5 Operators With Special 127 12.1 Type Declarations 128 12.2 Abstract Types 130 12.3 Primitive Types 132 12.4 Composite Types 133 12.5 Mutable Composite Types 135 12.6 Declared Types ..... 136 12.7 Type Unions ... 12.10 Singleton types ..... 147 12.11 Types of functions ..... 148 12.12 Type{T} type selectors ..... 149 12.13 Type Aliases ..... 150 12.14 Operations on Types ..... 151 12.15 Custom pretty-printing

Annotated Strings 70 9 Functions 72 9.1 Argument Passing Behavior 73 9.2 Argument-type declarations 74 9.3 The return Keyword 75 9.4 Operators Are Functions 77 9.5 Operators With Special 127 12.1 Type Declarations 128 12.2 Abstract Types 130 12.3 Primitive Types 132 12.4 Composite Types 133 12.5 Mutable Composite Types 135 12.6 Declared Types ..... 136 12.7 Type Unions ... 12.10 Singleton types ..... 147 12.11 Types of functions ..... 148 12.12 Type{T} type selectors ..... 149 12.13 Type Aliases ..... 150 12.14 Operations on Types ..... 151 12.15 Custom pretty-printing

6 An Example: Abstract Syntax 36 4 Theorem Proving in Lean 38 4.1 Assertions in Dependent Type Theory 38 4.2 Propositions as Types 39 4.3 Induction and Calculation 42 4.4 Axioms 45 Lean is an implementation of a logical foundation known as dependent type theory. Specifically, it implements a version of dependent type theory known as the Calculus of Inductive Constructions. The CIC is 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

Overview 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 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 tools. A description of the Agda language is Instructions ☐ Installation of the Development Version Installation Flags • Quick Guide to Editing, Type Checking and Compiling Agda Code ☐ Introduction ○ Menus Writing mathematical symbols in source