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 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 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 ntended

rewrite of Yii, adopting the latest technologies and protocols, including Composer, PSR, namespaces, traits, and so forth. Version 2.0 represents the current generation of the framework and will receive the framework. Yii 2.0 also makes use of the latest features of PHP, such as namespaces $ ^{2} $ and traits $ ^{3} $ . Understanding these concepts will help you more easily pick up Yii 2.0. #### 1.2 Upgrading classes and interfaces $ ^{7} $ . • Late Static Bindings $ ^{8} $ . • Date and Time $ ^{9} $ . • Traits $ ^{10} $ • intl $ ^{11} $ . Yii 2.0 makes use of the intl PHP extension to support internationalization

/path HTTP/1.1 Host: example.com foo=bar&baz=bat ## HTTP Response消息格式 HTTP/1.1 200 OK Content-Type: text/plain ## PSR 7 HTTP消息接口规范 PSR 7 规范定义了HTTP请求，响应，数据流的接口，以MessageInterface接口为例，响应和请求接口同时要继承这个接口。 "keywords": ["framework", "laravel"], "license": "MIT", "type": "project", "require": { "php": ">=5.5.9",

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 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

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 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

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 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