Data types | Type theory | Polymorphism (computer science)
In programming language theory, subtyping (also subtype polymorphism or inclusion polymorphism) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements, typically subroutines or functions, written to operate on elements of the supertype can also operate on elements of the subtype. If S is a subtype of T, the subtyping relation (written as S <: T, S ⊑ T, or S ≤: T ) means that any term of type S can safely be used in any context where a term of type T is expected. The precise semantics of subtyping here crucially depends on the particulars of how "safely be used" and "any context" are defined by a given type formalism or programming language. The type system of a programming language essentially defines its own subtyping relation, which may well be trivial, should the language support no (or very little) conversion mechanisms. Due to the subtyping relation, a term may belong to more than one type. Subtyping is therefore a form of type polymorphism. In object-oriented programming the term 'polymorphism' is commonly used to refer solely to this subtype polymorphism, while the techniques of parametric polymorphism would be considered generic programming. Functional programming languages often allow the subtyping of records. Consequently, simply typed lambda calculus extended with record types is perhaps the simplest theoretical setting in which a useful notion of subtyping may be defined and studied. Because the resulting calculus allows terms to have more than one type, it is no longer a "simple" type theory. Since functional programming languages, by definition, support function literals, which can also be stored in records, records types with subtyping provide some of the features of object-oriented programming. Typically, functional programming languages also provide some, usually restricted, form of parametric polymorphism. In a theoretical setting, it is desirable to study the interaction of the two features; a common theoretical setting is system F<:. Various calculi that attempt to capture the theoretical properties of object-oriented programming may be derived from system F<:. The concept of subtyping is related to the linguistic notions of hyponymy and holonymy. It is also related to the concept of bounded quantification in mathematical logic (see Order-sorted logic). Subtyping should not be confused with the notion of (class or object) inheritance from object-oriented languages; subtyping is a relation between types (interfaces in object-oriented parlance) whereas inheritance is a relation between implementations stemming from a language feature that allows new objects to be created from existing ones. In a number of object-oriented languages, subtyping is called interface inheritance, with inheritance referred to as implementation inheritance. (Wikipedia).
01b Spatial Data Analytics: Subsurface Data
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From playlist Spatial Data Analytics and Modeling
01 Spatial Data Analytics: Subsurface Modeling
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From playlist Spatial Data Analytics and Modeling
An introduction to subtraction, the terms and concepts involved, and subtraction as the opposite of addition. Some example problems are carefully worked and explained. From the Prealgebra course by Derek Owens. This course is available online at http://www.LucidEducation.com.
From playlist Prealgebra Chapter 1 (Complete chapter)
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This video provides two examples of subtracting signed fractions. Complete Video Library at http://www.mathispower4u.com
From playlist Adding and Subtracting Fractions
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This video explains how to write an subtraction equation from a number line model. http://mathispower4u.com
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From playlist QTS Numeracy Skills
Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 12 | #cybersecurity
Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom
From playlist Comprehensive Subdomain Enumeration
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From playlist Software Development
How To Create Billing System In C# and ASP .NET | Session 13 | #programming
Don’t forget to subscribe! This project series will guide on how to create a billing system in C and ASP.NET This tutorial will cover all the details (resources, tools, languages etc) that are necessary to create a complete and operational web-based billing system in C# and ASP.NET. You
From playlist Create Billing System In C# and ASP .NET
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From playlist Mathematics
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From playlist Crust of Rust
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From playlist Stanford CEHG Speaker Playlist
How To Create Billing System In C# and ASP .NET | Session 04 | #programming
Don’t forget to subscribe! This project series will guide on how to create a billing system in C and ASP.NET This tutorial will cover all the details (resources, tools, languages etc) that are necessary to create a complete and operational web-based billing system in C# and ASP.NET. You
From playlist Create Billing System In C# and ASP .NET
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From playlist Modern History
Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 16 | #cybersecurity
Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom
From playlist Comprehensive Subdomain Enumeration
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Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 10 | #cybersecurity
Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom
From playlist Comprehensive Subdomain Enumeration
How To Create Billing System In C# and ASP .NET | Session 12 | #programming
Don’t forget to subscribe! This project series will guide on how to create a billing system in C and ASP.NET This tutorial will cover all the details (resources, tools, languages etc) that are necessary to create a complete and operational web-based billing system in C# and ASP.NET. You
From playlist Create Billing System In C# and ASP .NET
Ethical Hacking Tutorial | Comprehensive Subdomain Enumeration | Session 08 | #cybersecurity
Don’t forget to subscribe! This ethical hacking tutorial series is about comprehensive subdomain enumeration. Through this tutorial series, I will be demonstrating how to install, configure and use different tools for subdomain enumeration. We will try to go through the following subdom
From playlist Comprehensive Subdomain Enumeration
18. Disease Progression Modeling and Subtyping, Part 1
MIT 6.S897 Machine Learning for Healthcare, Spring 2019 Instructor: David Sontag View the complete course: https://ocw.mit.edu/6-S897S19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60B0PQXVQyGNdCyCTDU1Q5j Prof. Sontag discusses aspects of disease progression modelin
From playlist MIT 6.S897 Machine Learning for Healthcare, Spring 2019