gives a thought about types. That is something which he has tough of and learned as a child. I, on the contrary, developed so slowly that I did not begin to wonder about types until I was an adult.“ gives a thought about types. That is something which he has tough of and learned as a child. I, on the contrary, developed so slowly that I did not begin to wonder about types until I was an adult.“ informally: So, what is a type? Depends on who you ask. So called “dependent type”? 16What are types used for in programming? 17What are types used for in programming? • Similar to money and its roles: •

Back to Basics: Algebraic Data Types I also do C++ training! arthur.j.odwyer@gmail.com Arthur O’Dwyer 2020-09-16Outline ● Why the name “algebraic data types”? [3–18] ○ Memory layout diagrams. Why Questions? ● More about pair and tuple [57–69] Questions? 2What do I mean by algebraic types? pair C++98. The original algebraic data type. tuple C++11. optional C++17. variant tuple are product types To find the size of the domain of a pair or tuple type, we take the product of the sizes of its element types. Therefore pair and tuple are known as product types. 5 A A possible

EMBRACING USER DEFINED LITERALS SAFELY for Types that Behave as though Built-in Pablo Halpern phalpern@halpernwightsoftware.com CppCon 2021 This work by Pablo Halpern is licensed under a Creative Embracing User Defined Literals Safely for Types that Behave as though Built-in – Pablo Halpern, Tuesday 9am ■ Embracing (and also destroying) Variant Types Safely – Andrei Alexandrescu, Thursday 9am 10/26/21 Pablo Halpern, 2021 (CC BY 4.0) 10Minimizing the divide between builtin and user-defined types ■ Operator overloading allows the syntax for assigning, comparing, and streaming a std::string to

std::simd how to express inherent parallelism efficiently via data-parallel types Dr. Matthias Kretz GSI Helmholtz Center for Heavy Ion Research CppCon ’23 @mkretz@floss.social github.com/mattkretzMotivation ResearchMotivation std::simd Overview Example: Image Processing Programming Models Outlook Summary Data-Parallel Types One variable stores WT values. One operator signifies WT operations (element-wise). W for “width”; vectorizable type — all arithmetic types except bool or long double • simd_mask behaves like bool (element-wise) In contrast to bool, there are many different mask types: • storage: bit-masks vs. element-sized

. . . . . . . . . . . 3 2 Dependent Type Theory 5 2.1 Simple Type Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Types as Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.8 Dependent Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 and Proofs 23 3.1 Propositions as Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Working with Propositions as Types . . . . . . . . . . . . . . . .

. . . . . . . . . . 6 3 Types and Functions 7 3.1 Primitive Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 Dependent Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.8 Useful Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.9 More Expressions

. . . . . . . . . . 6 3 Types and Functions 7 3.1 Primitive Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 Dependent Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.8 Useful Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.9 More Expressions

Release 0.10.3 The Idris Community March 26, 2016 Contents 1 Introduction 3 2 Getting Started 5 3 Types and Functions 7 4 Interfaces 21 5 Modules and Namespaces 29 6 Packages 33 7 Testing Idris Packages conventional programming languages, there is a clear distinction between types and values. For example, in Haskell, the following are types, representing integers, characters, lists of characters, and lists of inhabitants of 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

Basic Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Defining Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Defining New Types . . . Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3 Inhabited Types, Subtypes, and Option Types . . . . . . . . . . . . . . . . 32 3.4 Monads . . . . . . . . . . . . . . . . . . 36 4 Theorem Proving in Lean 38 4.1 Assertions in Dependent Type Theory . . . . . . . . . . . . . . . . . . . . . 38 4.2 Propositions as Types . . . . . . . . . . . . . . . . . . . . . . . . . . .

Copatterns Core language Coverage Checking Cubical Cumulativity Data Types Flat Modality Foreign Function Interface Function Definitions Function Types Generalization of Declared Variables Guarded Cubical Implicit Pattern Synonyms Positivity Checking Postulates Pragmas Prop Record Types Reflection Rewriting Run-time Irrelevance Safe Agda Sized Types Sort System Syntactic Sugar Syntax Declarations Telescopes Termination compilation system can be used can be found in chapter Tools. Getting Started What is Agda? Dependent types Installation Installation from source Prebuilt Packages and System-Specific Instructions Installation