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Subtypes
In programming language theory, subtyping (also called subtype polymorphism or inclusion polymorphism) is a form of type polymorphism. 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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Datatype
In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains the possible values that an expression, such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers (which approximate real numbers), characters and Booleans. Concept A data type may be specified for many reasons: similarity, convenience, or to focus the attention. It is frequently a matter of good organization that aids the understanding of complex definitions. Almost all programming languages explicitly include the notion of data type, though the possible da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymorphism (computer Science)
In programming language theory and type theory, polymorphism is the use of one symbol to represent multiple different types.: "Polymorphic types are types whose operations are applicable to values of more than one type." In object-oriented programming, polymorphism is the provision of one Interface (object-oriented programming), interface to entities of different data types. 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 forms 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 ... [...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'' (for example, integer, floating point, string) to every '' term'' (a word, phrase, or other set of symbols). Usually the terms are various language 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 data types, such as "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 synta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations are: * Typed λ-calculus of Alonzo Church * Intuitionistic type theory of Per Martin-Löf Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid paradoxes in naive set theory and formal logic, such as Russell's paradox which demonstrates that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself. Between 1902 and 1908, Bertrand Russell proposed various solutions to this problem. By 1908, Russell arrive ... [...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 s supporting ( generics) such as |
Record (computer Science)
In computer science, a record (also called a structure, struct (C programming language), struct, or compound data type) is a composite data structure a collection of Field (computer science), fields, possibly of different data types, typically fixed in number and sequence. For example, a date could be stored as a record containing a Number, numeric year field, a month field represented as a string, and a numeric day-of-month field. A circle record might contain a numeric radius and a center that is a point record containing x and y coordinates. Notable applications include the programming language ''record type'' and for row-based storage, data organized as a sequence of records, such as a database table, spreadsheet or comma-separated values (CSV) file. In general, a record type value is stored in main memory, memory and row-based storage is in mass storage. A ''record type'' is a data type that describes such values and variables. Most modern programming languages allow the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Language
A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually defined by a formal language. Languages usually provide features such as a type system, Variable (computer science), variables, and mechanisms for Exception handling (programming), error handling. An Programming language implementation, implementation of a programming language is required in order to Execution (computing), execute programs, namely an Interpreter (computing), interpreter or a compiler. An interpreter directly executes the source code, while a compiler produces an executable program. Computer architecture has strongly influenced the design of programming languages, with the most common type (imperative languages—which implement operations in a specified order) developed to perform well on the popular von Neumann architecture. ... [...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 inte ... [...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] |
Inheritance (object-oriented Programming)
In object-oriented programming, inheritance is the mechanism of basing an Object (computer science), object or Class (computer programming), class upon another object (Prototype-based programming, prototype-based inheritance) or class (Class-based programming, class-based inheritance), retaining similar implementation. Also defined as deriving new classes (#Subclasses and superclasses, sub classes) from existing ones such as super class or Fragile base class, base class and then forming them into a hierarchy of classes. In most class-based object-oriented languages like C++, an object created through inheritance, a "child object", acquires all the properties and behaviors of the "parent object", with the exception of: Constructor (object-oriented programming), constructors, destructors, operator overloading, 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 implementat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Category Theory
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory is used in most areas of mathematics. In particular, many constructions of new mathematical objects from previous ones that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient space (other), quotient spaces, direct products, completion, and duality (mathematics), duality. Many areas of computer science also rely on category theory, such as functional programming and Semantics (computer science), semantics. A category (mathematics), category is formed by two sorts of mathematical object, objects: the object (category theory), objects of the category, and the morphisms, which relate two objects called the ''source'' and the ''target'' of the morphism. Metapho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John C
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died ), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (died ), one of the twelve apostles of Jesus Christ * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope John ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
