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Apply Charging
In mathematics and computer science, apply is a function that applies a function to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages. It has a role in the study of the denotational semantics of computer programs, because it is a continuous function on complete partial orders. Apply is also a continuous function in homotopy theory, and, indeed underpins the entire theory: it allows a homotopy deformation to be viewed as a continuous path in the space of functions. Likewise, valid mutations (refactorings) of computer programs can be seen as those that are "continuous" in the Scott topology. The most general setting for apply is in category theory, where it is right adjoint to currying in closed monoidal categories. A special case of this are the Cartesian closed categories, whose internal language is simply typed lambda calculus. Programming In computer programming, apply applies a function ... [...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] |
Cartesian Closed Categories
In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with a morphism defined on one of the factors. These categories are particularly important in mathematical logic and the theory of programming, in that their internal language is the simply typed lambda calculus. They are generalized by closed monoidal categories, whose internal language, linear type systems, are suitable for both quantum and classical computation. Etymology Named after René Descartes (1596–1650), French philosopher, mathematician, and scientist, whose formulation of analytic geometry gave rise to the concept of Cartesian product, which was later generalized to the notion of categorical product. Definition The category C is called Cartesian closed iff it satisfies the following three properties: * It has a terminal object. * Any two objects ''X'' and ''Y'' of C have a product ''X'' ×''Y'' in C. * Any ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a General-purpose programming language, general-purpose, static typing, statically typed, purely functional programming, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research, and industrial applications, Haskell pioneered several programming language #Features, features such as type classes, which enable type safety, type-safe operator overloading, and Monad (functional programming), monadic input/output (IO). It is named after logician Haskell Curry. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). Haskell's Semantics (computer science), semantics are historically based on those of the Miranda (programming language), 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Go (programming Language)
Go is a high-level programming language, high-level general purpose programming language that is static typing, statically typed and compiled language, compiled. It is known for the simplicity of its syntax and the efficiency of development that it enables by the inclusion of a large standard library supplying many needs for common projects. It was designed at Google in 2007 by Robert Griesemer, Rob Pike, and Ken Thompson, and publicly announced in November of 2009. It is syntax (programming languages), syntactically similar to C (programming language), C, but also has memory safety, garbage collection (computer science), garbage collection, structural type system, structural typing, and communicating sequential processes, CSP-style concurrency (computer science), concurrency. It is often referred to as Golang to avoid ambiguity and because of its former domain name, golang.org, but its proper name is Go. There are two major implementations: * The original, Self-hosting (compi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflection (computer Science)
In computer science, reflective programming or reflection is the ability of a process to examine, introspect, and modify its own structure and behavior. Historical background The earliest computers were programmed in their native assembly languages, which were inherently reflective, as these original architectures could be programmed by defining instructions as data and using self-modifying code. As the bulk of programming moved to higher-level compiled languages such as ALGOL, COBOL, Fortran, Pascal, and C, this reflective ability largely disappeared until new programming languages with reflection built into their type systems appeared. Brian Cantwell Smith's 1982 doctoral dissertation introduced the notion of computational reflection in procedural programming languages and the notion of the meta-circular interpreter as a component of 3-Lisp. Uses Reflection helps programmers make generic software libraries to display data, process different formats of data, perform se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java (programming Language)
Java is a High-level programming language, high-level, General-purpose programming language, general-purpose, Memory safety, memory-safe, object-oriented programming, object-oriented programming language. It is intended to let programmers ''write once, run anywhere'' (Write once, run anywhere, WORA), meaning that compiler, compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are typically compiled to Java bytecode, bytecode that can run on any Java virtual machine (JVM) regardless of the underlying computer architecture. The syntax (programming languages), syntax of Java is similar to C (programming language), C and C++, but has fewer low-level programming language, low-level facilities than either of them. The Java runtime provides dynamic capabilities (such as Reflective programming, reflection and runtime code modification) that are typically not available in traditional compiled languages. Java gained popularity sh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C Sharp (programming Language)
C# ( pronounced: C-sharp) ( ) is a general-purpose high-level programming language supporting multiple paradigms. C# encompasses static typing, strong typing, lexically scoped, imperative, declarative, functional, generic, object-oriented (class-based), and component-oriented programming disciplines. The principal inventors of the C# programming language were Anders Hejlsberg, Scott Wiltamuth, and Peter Golde from Microsoft. It was first widely distributed in July 2000 and was later approved as an international standard by Ecma (ECMA-334) in 2002 and ISO/ IEC (ISO/IEC 23270 and 20619) in 2003. Microsoft introduced C# along with .NET Framework and Microsoft Visual Studio, both of which are technically speaking, closed-source. At the time, Microsoft had no open-source products. Four years later, in 2004, a free and open-source project called Microsoft Mono began, providing a cross-platform compiler and runtime environment for the C# programming language. A decad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Lisp
Common Lisp (CL) is a dialect of the Lisp programming language, published in American National Standards Institute (ANSI) standard document ''ANSI INCITS 226-1994 (S2018)'' (formerly ''X3.226-1994 (R1999)''). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived from the ANSI Common Lisp standard. The Common Lisp language was developed as a standardized and improved successor of Maclisp. By the early 1980s several groups were already at work on diverse successors to MacLisp: Lisp Machine Lisp (aka ZetaLisp), Spice Lisp, NIL and S-1 Lisp. Common Lisp sought to unify, standardise, and extend the features of these MacLisp dialects. Common Lisp is not an implementation, but rather a language specification. Several implementations of the Common Lisp standard are available, including free and open-source software and proprietary products. Common Lisp is a general-purpose, multi-paradigm programming language. It supports a combination of procedural, functional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variadic Function
In mathematics and in computer programming, a variadic function is a function of indefinite arity, i.e., one which accepts a variable number of arguments. Support for variadic functions differs widely among programming languages. The term ''variadic'' is a neologism, dating back to 1936/1937. The term was not widely used until the 1970s. Overview There are many mathematical and logical operations that come across naturally as variadic functions. For instance, the summing of numbers or the concatenation of strings or other sequences are operations that can be thought of as applicable to any number of operands (even though formally in these cases the associative property is applied). Another operation that has been implemented as a variadic function in many languages is output formatting. The C function and the Common Lisp function are two such examples. Both take one argument that specifies the formatting of the output, and ''any number'' of arguments that provide the value ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta Reduction
In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computation based on function abstraction and application using variable Name binding, binding and Substitution (algebra), substitution. Untyped lambda calculus, the topic of this article, is a universal machine, a model of computation that can be used to simulate any Turing machine (and vice versa). It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. In 1936, Church found a formulation which was #History, logically consistent, and documented it in 1940. Lambda calculus consists of constructing #Lambda terms, lambda terms and performing #Reduction, reduction operations on them. A term is defined as any valid lambda calculus expression. In the simplest form of lambda calculus, terms are built using only the following rules: # x: A #validLambdaVar, variable is a character or string representing a pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structure And Interpretation Of Computer Programs
''Structure and Interpretation of Computer Programs'' (''SICP'') is a computer science textbook by Massachusetts Institute of Technology professors Harold Abelson and Gerald Jay Sussman with Julie Sussman. It is known as the "Wizard Book" in hacker culture. It teaches fundamental principles of computer programming, including recursion, abstraction, modularity, and programming language design and implementation. MIT Press published the first edition in 1984, and the second edition in 1996. It was used as the textbook for MIT's introductory course in computer science from 1984 to 2007. SICP focuses on discovering general patterns for solving specific problems, and building software systems that make use of those patterns. MIT Press published a JavaScript version of the book in 2022. Content The book describes computer science concepts using Scheme, a dialect of Lisp. It also uses a virtual register machine and assembler to implement Lisp interpreters and compilers. Topics i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
