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

## Apache Ozone Erasure Coding(EC) The Modern Big Data Object Store with More Than 50% Storage Space Savings Uma Maheswara Rao Gangumalla Sr. Engineering Manager, Cloudera Inc Stephen O'Donnell Commit Key |Block|Value| |---|---| |Block 001|{ List of Chunks }| |Block 002|{ List of Chunks }| ## Erasure Coding Requirements ## ☐ Phase - I ☐ Enable EC at Cluster/Bucket Level ☐ Should be able to Write RS-X-Y-1024k ozone.server.default.replication.type EC ## Enabling at Bucket Level EC ➢ Users organize data with

contains(id); } }; ## What about runtime polymorphism? • Programmers make the virtual tables • Zoo type-erasure already generates virtual tables • The handles have the accessor to the virtual table *INDEX* Subtype handles inherit from the supertype handle ## What about resource managers? • For example a type that creates an std::ostream to a file: • Managed as special cases • That’s not something that can (currently) have a template argument for custom allocators. But std::optional can be of a std::vector type that would have a template argument for custom allocator, then, std::optional obstructs the custom

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