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FP (programming Language)
FP (short for ''functional programming'') is a programming language created by John Backus to support the function-level programming paradigm. It allows building programs from a set of generally useful primitives and avoiding named variables (a style also called tacit programming or "point free"). It was heavily influenced by APL developed by Kenneth E. Iverson in the early 1960s. The FP language was introduced in Backus's 1977 Turing Award paper, "Can Programming Be Liberated from the von Neumann Style?", subtitled "a functional style and its algebra of programs." The paper sparked interest in functional programming research, eventually leading to modern functional languages, which are largely founded on the lambda calculus paradigm, and not the function-level paradigm Backus had hoped. In his Turing award paper, Backus described how the FP style is different: FP itself never found much use outside of academia. In the 1980s Backus created a successor language, FL as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function-level Programming
In computer science, function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on programs as mathematical objects, the other being value-level programming. In his 1977 Turing Award lecture, Backus set forth what he considered to be the need to switch to a different philosophy in programming language design: Programming languages appear to be in trouble. Each successive language incorporates, with a little cleaning up, all the features of its predecessors plus a few more. ..Each new language claims new and fashionable features... but the plain fact is that few languages make programming sufficiently cheaper or more reliable to justify the cost of producing and learning to use them. He designed FP to be the first programming language to specifically support the function-level programming style. A ''function-level'' program is variable-free (cf. ''point-free'' programming), since program variables, which ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set (abstract Data Type)
In computer science, a set is an abstract data type that can store unique values, without any particular sequence, order. It is a computer implementation of the mathematics, mathematical concept of a finite set. Unlike most other collection (abstract data type), collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed. Static sets allow only query operations on their elements — such as checking whether a given value is in the set, or enumerating the values in some arbitrary order. Other variants, called dynamic or mutable sets, allow also the insertion and deletion of elements from the set. A multiset is a special kind of set in which an element can appear multiple times in the set. Type theory In type theory, sets are generally identified with their indicator function (characteristic function): accord ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Programming Languages
An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of tertiary education. The name traces back to Plato's school of philosophy, founded approximately 386 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. The Royal Spanish Academy defines academy as scientific, literary or artistic society established with public authority and as a teaching establishment, public or private, of a professional, artistic, technical or simply practical nature. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, ''Akademos''. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed Under
In mathematics, a subset of a given set is closed under an operation on the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: is not a natural number, although both 1 and 2 are. Similarly, a subset is said to be closed under a ''collection'' of operations if it is closed under each of the operations individually. The closure of a subset is the result of a closure operator applied to the subset. The ''closure'' of a subset under some operations is the smallest superset that is closed under these operations. It is often called the ''span'' (for example linear span) or the ''generated set''. Definitions Let be a set equipped with one or several methods for producing elements of from other elements of . Operations and (partial) multivariate function are examples of such methods. If is a topological space, the limit of a sequence of eleme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lazy Evaluation
In programming language theory, lazy evaluation, or call-by-need, is an evaluation strategy which delays the evaluation of an Expression (computer science), expression until its value is needed (non-strict evaluation) and which avoids repeated evaluations (by the use of Sharing (computer science), sharing). The benefits of lazy evaluation include: * The ability to define control flow (structures) as abstractions instead of Language primitive, primitives. * The ability to define actual infinity, potentially infinite data structures. This allows for more straightforward implementation of some algorithms. * The ability to define partly-defined data structures where some elements are errors. This allows for rapid prototyping. Lazy evaluation is often combined with memoization, as described in Jon Bentley (computer scientist), Jon Bentley's ''Writing Efficient Programs''. After a function's value is computed for that Parameter (computer programming), parameter or set of parameters, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FL Programming Language
FL (short for "Function Level") is a programming language created at the IBM Almaden Research Center by John Backus, John Williams, and Edward Wimmers in the 1980s and documented in a report from 1989. FL was designed as a successor of Backus's earlier FP language, providing specific support for what Backus termed function-level programming. FL is a dynamically typed strict functional programming language with throw and catch exception semantics much like in ML. Each function has an implicit history argument which is used for doing things like strictly functional input/output In computing, input/output (I/O, i/o, or informally io or IO) is the communication between an information processing system, such as a computer, and the outside world, such as another computer system, peripherals, or a human operator. Inputs a ... (I/O), but is also used for linking to C code. For doing optimization, there exists a type-system which is an extension of Hindley–Milner type inference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combining Form
Neoclassical compounds are compound words composed from combining forms (which act as affixes or stems) derived from classical languages (classical Latin or ancient Greek) roots. Neo-Latin comprises many such words and is a substantial component of the technical and scientific lexicon of English and other languages, via international scientific vocabulary (ISV). For example, Greek '' bio-'' combines with ''-graphy'' to form ''biography'' ("life" + "writing/recording"). Source of international technical vocabulary Neoclassical compounds represent a significant source of Neo-Latin vocabulary. Moreover, since these words are composed from classical languages whose prestige is or was respected throughout the Western European culture, these words typically appear in many different languages. Their widespread use makes technical writing generally accessible to readers who may only have a smattering of the language in which it appears. Not all European languages have been equally re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter "M" first and "Y" last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be '' finite'', as in these examples, or '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expression (computer Science)
In computer science, an expression is a Syntax (programming languages), syntactic entity in a programming language that may be evaluated to determine its value (computer science), value. It is a combination of one or more Constant (programming), constants, variable (programming), variables, function (programming), functions, and operator (programming), operators that the programming language interprets (according to its particular Order of operations, rules of precedence and of Associative property, association) and computes to produce ("to return", in a state (computer science), stateful environment) another value. This process, for mathematical expressions, is called ''evaluation''. In simple settings, the return type, resulting value is usually one of various primitive data type, primitive types, such as string (computer science), string, boolean expression, boolean, or numerical (such as integer (computer science), integer, floating-point number, floating-point, or complex data t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strict Function
In computer science and computer programming, a function f is said to be strict if, when applied to a non-terminating expression, it also fails to terminate. A strict function in the denotational semantics of programming languages is a function ''f'' where f\left(\perp\right) = \perp. The entity \perp, called '' bottom'', denotes an expression that does not return a normal value, either because it loops endlessly or because it aborts due to an error such as division by zero. A function that is not strict is called non-strict. A strict programming language is one in which user-defined functions are always strict. Intuitively, non-strict functions correspond to control structures. Operationally, a strict function is one that always evaluates its argument; a non-strict function is one that might not evaluate some of its arguments. Functions having more than one parameter can be strict or non-strict in each parameter independently, as well as ''jointly strict'' in several parameter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closure (mathematics)
In mathematics, a subset of a given set (mathematics), set is closed under an Operation (mathematics), operation on the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: is not a natural number, although both 1 and 2 are. Similarly, a subset is said to be closed under a ''collection'' of operations if it is closed under each of the operations individually. The closure of a subset is the result of a closure operator applied to the subset. The ''closure'' of a subset under some operations is the smallest superset that is closed under these operations. It is often called the ''span'' (for example linear span) or the ''generated set''. Definitions Let be a set (mathematics), set equipped with one or several methods for producing elements of from other elements of .Operation (mathematics), Operations and (partial function, partial) multivar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambda Calculus
In mathematical logic, the lambda calculus (also written as ''λ''-calculus) is a formal system for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
