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Subtyping
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 , , or ) 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 su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substitutability
The Liskov substitution principle (LSP) is a particular definition of a subtyping relation, called strong behavioral subtyping, that was initially introduced by Barbara Liskov in a 1988 conference keynote address titled ''Data abstraction and hierarchy''. It is based on the concept of "substitutability" a principle in object-oriented programming stating that an object (such as a class) may be replaced by a sub-object (such as a class that extends the first class) without breaking the program. It is a semantic rather than merely syntactic relation, because it intends to guarantee semantic interoperability of types in a hierarchy, object types in particular. Barbara Liskov and Jeannette Wing described the principle succinctly in a 1994 paper as follows: ''Subtype Requirement'': Let be a property provable about objects of type . Then should be true for objects of type where is a subtype of . Symbolically: :S <: T \to (\forall xT) \phi(x) \to (\forall yS) \phi(y) Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liskov Substitution Principle
The Liskov substitution principle (LSP) is a particular definition of a subtyping relation, called strong behavioral subtyping, that was initially introduced by Barbara Liskov in a 1988 conference keynote address titled ''Data abstraction and hierarchy''. It is based on the concept of "substitutability" a principle in object-oriented programming stating that an object (such as a class) may be replaced by a sub-object (such as a class that extends the first class) without breaking the program. It is a semantic rather than merely syntactic relation, because it intends to guarantee semantic interoperability of types in a hierarchy, object types in particular. Barbara Liskov and Jeannette Wing described the principle succinctly in a 1994 paper as follows: ''Subtype Requirement'': Let be a property provable about objects of type . Then should be true for objects of type where is a subtype of . Symbolically: :S <: T \to (\forall xT) \phi(x) \to (\forall yS) \phi(y) T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inheritance (computer Science)
In object-oriented programming, inheritance is the mechanism of basing an object or class upon another object ( prototype-based inheritance) or class ( class-based inheritance), retaining similar implementation. Also defined as deriving new classes ( sub classes) from existing ones such as super class or base class and then forming them into a hierarchy of classes. In most class-based object-oriented languages, an object created through inheritance, a "child object", acquires all the properties and behaviors of the "parent object" , with the exception of: constructors, destructor, overloaded operators and friend functions of the base class. Inheritance allows programmers to create classes that are built upon existing classes, to specify a new implementation while maintaining the same behaviors ( realizing an interface), to reuse code and to independently extend original software via public classes and interfaces. The relationships of objects or classes through inheritance gi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymorphism (computer Science)
In programming language theory and type theory, polymorphism is the provision of a single interface to entities of different types or the use of a single symbol to represent multiple different types.: "Polymorphic types are types whose operations are applicable to values of more than one type." The concept is borrowed from a principle in biology where an organism or species can have many different forms or stages. The most commonly recognized major classes of polymorphism are: * '' Ad hoc polymorphism'': defines a common interface for an arbitrary set of individually specified types. * '' Parametric polymorphism'': not specifying concrete types and instead use abstract symbols that can substitute for any type. * ''Subtyping'' (also called ''subtype polymorphism'' or ''inclusion polymorphism''): when a name denotes instances of many different classes related by some common superclass. History Interest in polymorphic type systems developed significantly in the 1960s, with practica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barbara Liskov
Barbara Liskov (born November 7, 1939 as Barbara Jane Huberman) is an American computer scientist who has made pioneering contributions to programming languages and distributed computing. Her notable work includes the development of the Liskov substitution principle which describes the fundamental nature of data abstraction, and is used in type theory (see subtyping) and in object-oriented programming (see inheritance). Her work was recognized with the 2008 Turing Award, the highest distinction in computer science. Liskov is one of the earliest women to have been granted a doctorate in computer science in the United States, and the second woman to receive the Turing award. She is currently an Institute Professor and Ford Professor of Engineering at the Massachusetts Institute of Technology.Barbara Liskov Programming Methodology Group, MIT. < ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type System
In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term. Type systems formalize and enforce the otherwise implicit categories the programmer uses for algebraic data types, data structures, or other components (e.g. "string", "array of float", "function returning boolean"). Type systems are often specified as part of programming languages and built into interpreters and compilers, although the type system of a language can be extended by optional tools that perform added checks using the language's original type syntax and grammar. The main purpose of a type system in a programming langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object-oriented Programming
Object-oriented programming (OOP) is a programming paradigm based on the concept of " objects", which can contain data and code. The data is in the form of fields (often known as attributes or ''properties''), and the code is in the form of procedures (often known as '' methods''). A common feature of objects is that procedures (or methods) are attached to them and can access and modify the object's data fields. In this brand of OOP, there is usually a special name such as or used to refer to the current object. In OOP, computer programs are designed by making them out of objects that interact with one another. OOP languages are diverse, but the most popular ones are class-based, meaning that objects are instances of classes, which also determine their types. Many of the most widely used programming languages (such as C++, Java, Python, etc.) are multi-paradigm and they support object-oriented programming to a greater or lesser degree, typically in combination with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics, logic, and computer science, a type theory is the formal system, formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a Foundations of mathematics, foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed lambda calculus, typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most proof assistant, computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of constructions, Calculus of Inductive Constructions. History Type theory was created to avoid a paradox in a mathematical foundation based on naive set theory and formal logic. Russell's paradox, which was discovered by Bertrand Russell, existed because a set could be defined using "all possible sets", which included itself. Between 1902 and 1908, Bertrand Russe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounded Quantification
In type theory, bounded quantification (also bounded polymorphism or constrained genericity) refers to universal or existential quantifiers which are restricted ("bounded") to range only over the subtypes of a particular type. Bounded quantification is an interaction of parametric polymorphism with subtyping. Bounded quantification has traditionally been studied in the functional setting of System F<:, but is available in modern object-oriented languages supporting () such as |
Record (computer Science)
In computer science, a record (also called a structure, struct, or compound data) is a basic data structure. Records in a database or spreadsheet are usually called "rows". A record is a collection of '' fields'', possibly of different data types, typically in a fixed number and sequence. The fields of a record may also be called ''members'', particularly in object-oriented programming; fields may also be called ''elements'', though this risks confusion with the elements of a collection. For example, a date could be stored as a record containing a numeric year field, a month field represented as a string, and a numeric day-of-month field. A personnel record might contain a name, a salary, and a rank. A Circle record might contain a center and a radius—in this instance, the center itself might be represented as a point record containing x and y coordinates. Records are distinguished from arrays by the fact that their number of fields is determined in the definition of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simula
Simula is the name of two simulation programming languages, Simula I and Simula 67, developed in the 1960s at the Norwegian Computing Center in Oslo, by Ole-Johan Dahl and Kristen Nygaard. Syntactically, it is an approximate superset of ALGOL 60, and was also influenced by the design of Simscript. Simula 67 introduced objects, classes, inheritance and subclasses, virtual procedures, coroutines, and discrete event simulation, and featured garbage collection. Other forms of subtyping (besides inheriting subclasses) were introduced in Simula derivatives. Simula is considered the first object-oriented programming language. As its name suggests, the first Simula version by 1962 was designed for doing simulations; Simula 67 though was designed to be a general-purpose programming language and provided the framework for many of the features of object-oriented languages today. Simula has been used in a wide range of applications such as simulating very-large-scale integ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order-sorted Logic
Many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects, but to partition it in a way that is similar to types in typeful programming. Both functional and assertive "parts of speech" in the language of the logic reflect this typeful partitioning of the universe, even on the syntax level: substitution and argument passing can be done only accordingly, respecting the "sorts". There are various ways to formalize the intention mentioned above; a ''many-sorted logic'' is any package of information which fulfils it. In most cases, the following are given: * a set of sorts, ''S'' * an appropriate generalization of the notion of ''signature'' to be able to handle the additional information that comes with the sorts. The domain of discourse of any structure of that signature is then fragmented into disjoint subsets, one for every sort. Example When reasoning about biological organisms, it is useful to distinguish two sorts: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
