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In formal language theory, the empty string, or empty word, is the unique string of length zero. Formal theory Formally, a string is a finite, ordered sequence of characters such as letters, digits or spaces. The empty string is the special case where the sequence has length zero, so there are no symbols in the string. There is only one empty string, because two strings are only different if they have different lengths or a different sequence of symbols. In formal treatments, the empty string is denoted with ε or sometimes Λ or λ. The empty string should not be confused with the empty language ∅, which is a formal language (i.e. a set of strings) that contains no strings, not even the empty string. The empty string has several properties: * , ε, = 0. Its string length is zero. * ε ⋅ s = s ⋅ ε = s. The empty string is the identity element of the concatenation operation. The set of all strings forms a free monoid with respect to ⋅ and ε. * εR = ε. Reversal of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Monoid
In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identity element. The free monoid on a set ''A'' is usually denoted ''A''∗. The free semigroup on ''A'' is the subsemigroup of ''A''∗ containing all elements except the empty string. It is usually denoted ''A''+./ref> More generally, an abstract monoid (or semigroup) ''S'' is described as free if it is isomorphic to the free monoid (or semigroup) on some set. As the name implies, free monoids and semigroups are those objects which satisfy the usual universal property defining free objects, in the respective categories of monoids and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup). The study ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are of the form :A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be empty). A formal grammar is "context-free" if its production rules can be applied regardless of the context of a nonterminal. No matter which symbols surround it, the single nonterminal on the left hand side can always be replaced by the right hand side. This is what distinguishes it from a context-sensitive grammar. A formal grammar is essentially a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the first rule in the picture, :\langle\text\rangle \to \langle\text\rangle = \langle\text\rangle ; replaces \langle\text\rangle with \langle\text\rangle = \langle\text\rangle ;. There can be multiple replacement rules for a given nonterminal symbol. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
JavaScript
JavaScript (), often abbreviated as JS, is a programming language that is one of the core technologies of the World Wide Web, alongside HTML and CSS. As of 2022, 98% of Website, websites use JavaScript on the Client (computing), client side for Web page, webpage behavior, often incorporating third-party Library (computing), libraries. All major Web browser, web browsers have a dedicated JavaScript engine to execute the Source code, code on User (computing), users' devices. JavaScript is a High-level programming language, high-level, often Just-in-time compilation, just-in-time compiled language that conforms to the ECMAScript standard. It has dynamic typing, Prototype-based programming, prototype-based object-oriented programming, object-orientation, and first-class functions. It is Programming paradigm, multi-paradigm, supporting Event-driven programming, event-driven, functional programming, functional, and imperative programming, imperative programming paradigm, programmin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quotation Mark
Quotation marks (also known as quotes, quote marks, speech marks, inverted commas, or talking marks) are punctuation marks used in pairs in various writing systems to set off direct speech, a quotation, or a phrase. The pair consists of an opening quotation mark and a closing quotation mark, which may or may not be the same character. Quotation marks have a variety of forms in different languages and in different media. History The single quotation mark is traced to Ancient Greek practice, adopted and adapted by monastic copyists. Isidore of Seville, in his seventh century encyclopedia, , described their use of the Greek ''diplé'' (a chevron): 3⟩ Diplé. Our copyists place this sign in the books of the people of the Church, to separate or to indicate the quotations drawn from the Holy Scriptures. The double quotation mark derives from a marginal notation used in fifteenth-century manuscript annotations to indicate a passage of particular importance (not necessar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of technical limitations of computer systems at the time it was invented, ASCII has just 128 code points, of which only 95 are , which severely limited its scope. All modern computer systems instead use Unicode, which has millions of code points, but the first 128 of these are the same as the ASCII set. The Internet Assigned Numbers Authority (IANA) prefers the name US-ASCII for this character encoding. ASCII is one of the List of IEEE milestones, IEEE milestones. Overview ASCII was developed from telegraph code. Its first commercial use was as a seven-bit teleprinter code promoted by Bell data services. Work on the ASCII standard began in May 1961, with the first meeting of the American Standards Association's (ASA) (now the American Nat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Objective-C
Objective-C is a general-purpose, object-oriented programming language that adds Smalltalk-style messaging to the C programming language. Originally developed by Brad Cox and Tom Love in the early 1980s, it was selected by NeXT for its NeXTSTEP operating system. Due to Apple macOS’s direct lineage from NeXTSTEP, Objective-C was the standard programming language used, supported, and promoted by Apple for developing macOS and iOS applications (via their respective APIs, Cocoa and Cocoa Touch) until the introduction of the Swift programming language in 2014. Objective-C programs developed for non-Apple operating systems or that are not dependent on Apple's APIs may also be compiled for any platform supported by GNU GCC or LLVM/Clang. Objective-C source code 'messaging/implementation' program files usually have filename extensions, while Objective-C 'header/interface' files have extensions, the same as C header files. Objective-C++ files are denoted with a file extension. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MUMPS
MUMPS ("Massachusetts General Hospital Utility Multi-Programming System"), or M, is an imperative, high-level programming language with an integrated transaction processing key–value database. It was originally developed at Massachusetts General Hospital for managing hospital laboratory information systems. MUMPS technology has since expanded as the predominant database for health information systems and electronic health records in the United States. MUMPS-based information systems run over 40% of the hospitals in the U.S., run across all of the U.S. federal hospitals and clinics, and provide health information services for over 54% of patients across the U.S. A unique feature of the MUMPS technology is its integrated database language, allowing direct, high-speed read-write access to permanent disk storage. This provides tight integration of unlimited applications within a single database, and provides extremely high performance and reliability as an online transaction pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lua (programming Language)
Lua ( ; from meaning ''moon'') is a lightweight, high-level, multi-paradigm programming language designed primarily for embedded use in applications. Lua is cross-platform, since the interpreter of compiled bytecode is written in ANSI C, and Lua has a relatively simple C API to embed it into applications. Lua originated in 1993 as a language for extending software applications to meet the increasing demand for customization at the time. It provided the basic facilities of most procedural programming languages, but more complicated or domain-specific features were not included; rather, it included mechanisms for extending the language, allowing programmers to implement such features. As Lua was intended to be a general embeddable extension language, the designers of Lua focused on improving its speed, portability, extensibility, and ease-of-use in development. History Lua was created in 1993 by Roberto Ierusalimschy, Luiz Henrique de Figueiredo, and Waldemar Celes, membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julia (programming Language)
Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic programming language; with multiple dispatch as its core programming paradigm. Julia supports concurrent, (composable) parallel and distributed computing (with or without using MPI or the built-in corresponding to "OpenMP-style" threads), and direct calling of C and Fortran libraries without glue code. Julia uses a just-in-time (JIT) compiler that is referred to as "just- ahead-of-time" (JAOT) in the Julia community, as Julia compiles all code (by default) to machine code before running it. Julia is garbage-collected, uses eager evaluation, and includes efficient libraries for floating-point calculations, linear algebra, random number generation, and regular expression matching. Many libraries are available, including some (e.g., for fast Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java (programming Language)
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers ''write once, run anywhere'' ( WORA), meaning that compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are typically compiled to bytecode that can run on any Java virtual machine (JVM) regardless of the underlying computer architecture. The syntax of Java is similar to C and C++, but has fewer low-level facilities than either of them. The Java runtime provides dynamic capabilities (such as reflection and runtime code modification) that are typically not available in traditional compiled languages. , Java was one of the most popular programming languages in use according to GitHub, particularly for client–server web applications, with a reported 9 million developers. Java was originally developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research and industrial applications, Haskell has pioneered a number of programming language features such as type classes, which enable type-safe operator overloading, and monadic IO. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). It is named after logician Haskell Curry. Haskell's semantics are historically based on those of the Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in academia and industry. , Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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