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Mapsto P
The maps to symbol, ↦, is a rightward arrow protruding from a vertical bar. It is used in mathematics and in computer science to denote functions. In Z notation, a specification language used in software development, this symbol is called the maplet arrow and the expression x ↦ y is called a maplet. In separation logic it denotes the contents of a specific cell of memory. In the Unicode Unicode or ''The Unicode Standard'' or TUS is a character encoding standard maintained by the Unicode Consortium designed to support the use of text in all of the world's writing systems that can be digitized. Version 16.0 defines 154,998 Char ... character set, the symbol is code point U+21A6. See also * Arrow notation – e.g., x\mapsto x+1, also known as ''map'' References {{navbox punctuation Mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. The set is called the Domain of a function, domain of the function and the set is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. History of the function concept, Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable function, differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z Notation
The Z notation is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and computer-based systems in general. History In 1974, Jean-Raymond Abrial published "Data Semantics". He used a notation that would later be taught in the University of Grenoble until the end of the 1980s. While at EDF ( Électricité de France), working with Bertrand Meyer, Abrial also worked on developing Z. The Z notation is used in the 1980 book ''Méthodes de programmation''. Z was originally proposed by Abrial in 1977 with the help of Steve Schuman and Bertrand Meyer. It was developed further at the Programming Research Group at Oxford University, where Abrial worked in the early 1980s, having arrived at Oxford in September 1979. Abrial has said that Z is so named "Because it is the ultimate language!" although the name " Zermelo" is also associated with the Z notation through its use of Zermelo–Frae ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specification Language
A specification language is a formal language in computer science used during systems analysis, requirements analysis, and systems design to describe a system at a much higher level than a programming language, which is used to produce the executable code for a system. Joseph Goguen "One, None, A Hundred Thousand Specification Languages" Invited Paper, IFIP Congress 1986 pp 995-1004 Overview Specification languages are generally not directly executed. They are meant to describe the ''what'', not the ''how''. It is considered an error if a requirement specification is cluttered with unnecessary implementation detail. A common fundamental assumption of many specification approaches is that programs are modelled as algebraic or model-theoretic structures that include a collection of sets of data values together with functions over those sets. This level of abstraction coincides with the view that the correctness of the input/output behaviour of a program takes precedence over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Separation Logic
In computer science, separation logic is an extension of Hoare logic, a way of reasoning about programs. It was developed by John C. Reynolds, Peter O'Hearn, Samin Ishtiaq and Hongseok Yang, drawing upon early work by Rod Burstall. The assertion language of separation logic is a special case of the logic of bunched implications (BI). A CACM review article by O'Hearn charts developments in the subject to early 2019. Overview Separation logic facilitates reasoning about: * programs that manipulate pointer data structures—including information hiding in the presence of pointers; * ''"transfer of ownership"'' (avoidance of semantic frame axioms); and * virtual separation (modular reasoning) between concurrent modules. Separation logic supports the developing field of research described by Peter O'Hearn and others as ''local reasoning'', whereby specifications and proofs of a program component mention only the portion of memory used by the component, and not the entire global ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unicode
Unicode or ''The Unicode Standard'' or TUS is a character encoding standard maintained by the Unicode Consortium designed to support the use of text in all of the world's writing systems that can be digitized. Version 16.0 defines 154,998 Character (computing), characters and 168 script (Unicode), scripts used in various ordinary, literary, academic, and technical contexts. Unicode has largely supplanted the previous environment of a myriad of incompatible character sets used within different locales and on different computer architectures. The entire repertoire of these sets, plus many additional characters, were merged into the single Unicode set. Unicode is used to encode the vast majority of text on the Internet, including most web pages, and relevant Unicode support has become a common consideration in contemporary software development. Unicode is ultimately capable of encoding more than 1.1 million characters. The Unicode character repertoire is synchronized with Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
