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

3.6 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 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 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

'a', "Hello world!", [2,3,4,5,6] In a language with dependent types, however, the distinction is less clear. Dependent types allow types to "depend" on values — in other words, types 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

it the most destructive type of work. It’s not really work at all, like the others. The others are what you planned on doing, allegedly because you needed to do it.” ## Theory of Constraints “Eliyahu “Eliyahu M. Goldratt, who created the Theory of Constraints, showed us how any improvements made anywhere besides the bottleneck are an illusion. Astonishing, but true! Any improvement made after the bottleneck even have what I need. It’s why I’ve stopped even putting in change requests.” “I have to manually type in hundreds of server names in one of the text boxes. Most of the time, there’s not enough room in

Functions 8 3.4 Dependent Types 10 3.5 I/O 12 3.6 "do" notation 13 3.7 Laziness 13 3.8 Useful Data Types 14 3.9 More Expressions 17 3.10 Dependent Records 18 4 Type Classes 21 4 ..... 39 8.1 Dependent pattern matching ..... 39 8.2 The with rule — matching intermediate values ..... 39 9 Theorem Proving ..... 41 9.1 Equality ..... 41 9.2 The Empty Type ..... 41 9.3 Simple conversions ..... 58 13.3 Literate programming ..... 58 13.4 Foreign function calls ..... 58 13.5 Type Providers ..... 60 13.6 C Target ..... 60 13.7 JavaScript Target ..... 61 13.8 Cumulativity

'a', "Hello world!", [2,3,4,5,6] In a language with dependent types, however, the distinction is less clear. Dependent types allow types to “depend” on values — in other words, types are 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

those types: • 42, ’a’, "Hello world!", [2,3,4,5,6] In a language with dependent types, however, the distinction is less clear. Dependent types allow types to “depend” on values — in other words, types are be manipulated like any other value. The standard example is the type of lists of a given length1, Vect n a, where a is the element type and n is the length of the list and can be an arbitrary term. When 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 1 Typically

'a', "Hello world!", [2,3,4,5,6] In a language with dependent types, however, the distinction is less clear. Dependent types allow types to “depend” on values — in other words, types are 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

learn it by heart and use it. The author of this paper being an example of this. Machine learning is a type of stochastic algorithms that try to find a solution based upon statistical data. A stochastic algorithm because the cards in each hand are hidden. Furthermore the shuffling and dealing of the deck is a type of random element, if done correctly $ ^{6} $ . ### 3.4 The Sprague-Grundy Theorem The Sprague-Grundy relevant, mostly those in use. $ ^{9} $ ### 4.1 Reinforcement learning Reinforcement learning is a type of machine learning where a program tries to find a solution for a problem, and is taught how to do

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