Composite data types | Type theory | Type systems | Polymorphism (computer science) | Data types
In type theory, an intersection type can be allocated to values that can be assigned both the type and the type . This value can be given the intersection type in an intersection type system.Generally, if the ranges of values of two types overlap, then a value belonging to the intersection of the two ranges can be assigned the intersection type of these two types. Such a value can be safely passed as argument to functions expecting either of the two types.For example, in Java the class Boolean implements both the Serializable and the Comparable interfaces. Therefore, an object of type Boolean can be safely passed to functions expecting an argument of type Serializable and to functions expecting an argument of type Comparable. Intersection types are composite data types. Similar to product types, they are used to assign several types to an object.However, product types are assigned to tuples, so that each tuple element is assigned a particular product type component. In comparison, underlying objects of intersection types are not necessarily composite. A restricted form of intersection types are refinement types. Intersection types are useful for describing overloaded functions. For example, if number => number is the type of function taking a number as an argument and returning a number, and string => string is the type of function taking a string as an argument and returning a string, then the intersection of these two types can be used to describe (overloaded) functions that do one or the other, based on what type of input they are given. Contemporary programming languages, including Ceylon, Flow, Java, Scala, TypeScript, and Whiley (see ), use intersection types to combine interface specifications and to express ad hoc polymorphism.Complementing parametric polymorphism, intersection types may be used to avoid class hierarchy pollution from cross-cutting concerns and reduce boilerplate code, as shown in the below. The type theoretic study of intersection types is referred to as the intersection type discipline.Remarkably, program termination can be precisely characterized using intersection types. (Wikipedia).
What is an Intersection? (Set Theory)
What is the intersection of sets? This is another video on set theory in which we discuss the intersection of a set and another set, using the classic example of A intersect B. We do not quite go over a formal definition of intersection of a set in this video, but we come very close! Be su
From playlist Set Theory
From playlist Intersection Theory
Identify the type of angle from a figure acute, right, obtuse, straight ex 1
👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
From playlist Angle Relationships
When do vector functions intersect?
Free ebook http://tinyurl.com/EngMathYT Example discussing intersection of curves of two vector functions on one variable.
From playlist Engineering Mathematics
Intersection of Planes on Geogebra
In this video, we look at a strategy for finding the intersection of planes on Geogebra.
From playlist Geogebra
Union vs Intersection (Set Theory)
What is A union B? What is the union of sets? What is the intersection of sets? I've talked about these topic before, but in this video we will look at unions and intersections of sets side by side. So get ready to learn about these very cool set operations! I hope you find this video he
From playlist Set Theory
Determining if two angles are adjacent or not
👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
From playlist Angle Relationships From a Figure
http://mathispower4u.wordpress.com/
From playlist Parallel and Perpendicular Lines
Geogebra Tutorial : Union and Intersection of Sets
Union and intersection of sets can be drawing with geogebra. Please see the video to start how drawing union and intersection of sets. more visit https://onwardono.com
From playlist SET
Connecting tropical intersection theory with polytope algebra in types A and B by Alex Fink
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Joel Hass - Lecture 3 - Algorithms and complexity in the theory of knots and manifolds - 20/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro
From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
[Rust] Advent of Code 2021 - Day 22
This is an archive copy of day 22 of Advent of Code 2021. Advent of Code (https://adventofcode.com/) is an Advent calendar of small programming puzzles for a variety of skill sets and skill levels that can be solved in any programming language you like. -- Watch live at https://www.twitc
From playlist Advent of Code 2021
Bruno Klingler - 4/4 Tame Geometry and Hodge Theory
Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic. On the other hand, according to both the Hodge conjecture and the Grothendie
From playlist Bruno Klingler - Tame Geometry and Hodge Theory
Rose Morris-Wright: Parabolic Subgroups of Infinite Type Artin Groups
Abstract : Parabolic subgroups are the fundamental building blocks of Artin groups. These subgroups are isomorphic copies of smaller Artin groups nested inside a given Artin group. In this talk, I will discuss questions surrounding how parabolic subgroups sit inside Artin groups and how th
From playlist Virtual Conference
Danny Calegari: Big Mapping Class Groups - lecture 1
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-h
From playlist Topology
Traffic management in dense urban areas is an extremely complex problem with a host of conflicting goals and challenges. One of the most fundamental of those challenges happens at an intersection, where multiple streams of traffic - including vehicles, bikes and pedestrians - need to safel
From playlist Civil Engineering
Mirror symmetry & Looijenga's conjecture - Philip Engel
Philip Engel Columbia University October 29, 2014 A cusp singularity is an isolated surface singularity whose minimal resolution is a cycle of smooth rational curves meeting transversely. Cusp singularities come in naturally dual pairs. In the 1980's Looijenga conjectured that a cusp sing
From playlist Mathematics
Hyperbolic 3-manifolds of bounded volume and trace field degre - Bogwang Jeon
Bogwang Jeon, Columbia Univ October 8, 2015 http://www.math.ias.edu/wgso3m/agenda 2015-2016 Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 aca
From playlist Workshop on Geometric Structures on 3-Manifolds
Determining two angles that are supplementary
👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
From playlist Angle Relationships From a Figure
Stanford Seminar - An Intersectional Approach to Designing for Disability
February 10, 2023 Robin Brewer of University of Michigan Recent reports show that nearly 1 in 4 people, globally, have at least one disability. These numbers increase with age and can be more common in non-Western contexts. In this talk, I argue for a departure from accessibility research
From playlist Stanford Seminars