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Meta-circular Evaluator
In computing, a meta-circular evaluator (MCE) or meta-circular interpreter (MCI) is an interpreter which defines each feature of the interpreted language using a similar facility of the interpreter's host language. For example, interpreting a lambda application may be implemented using function application. Meta-circular evaluation is most prominent in the context of Lisp. A self-interpreter is a meta-circular interpreter where the interpreted language is nearly identical to the host language; the two terms are often used synonymously. History The dissertation of Corrado Böhm describes the design of a self-hosting compiler. Due to the difficulty of compiling higher-order functions, many languages were instead defined via interpreters, most prominently Lisp. The term itself was coined by John C. Reynolds, and popularized through its use in the book ''Structure and Interpretation of Computer Programs''. Self-interpreters A self-interpreter is a meta-circular interpreter wher ...
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Computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, engineering, mathematical, technological and social aspects. Major computing disciplines include computer engineering, computer science, cybersecurity, data science, information systems, information technology and software engineering. The term "computing" is also synonymous with counting and calculating. In earlier times, it was used in reference to the action performed by mechanical computing machines, and before that, to human computers. History The history of computing is longer than the history of computing hardware and includes the history of methods intended for pen and paper (or for chalk and slate) with or without the aid of tables. Computing is intimately tied to the representation of numbers, though mathematical conc ...
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System F
System F (also polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism of universal quantification over types. System F formalizes parametric polymorphism in programming languages, thus forming a theoretical basis for languages such as Haskell and ML. It was discovered independently by logician Jean-Yves Girard (1972) and computer scientist John C. Reynolds Whereas simply typed lambda calculus has variables ranging over terms, and binders for them, System F additionally has variables ranging over ''types'', and binders for them. As an example, the fact that the identity function can have any type of the form ''A'' → ''A'' would be formalized in System F as the judgement :\vdash \Lambda\alpha. \lambda x^\alpha.x: \forall\alpha.\alpha \to \alpha where \alpha is a type variable. The upper-case \Lambda is traditionally used to denote type-level functions, as opposed to the lower-case \la ...
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Prolog
Prolog is a logic programming language associated with artificial intelligence and computational linguistics. Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is intended primarily as a declarative programming language: the program logic is expressed in terms of relations, represented as facts and rules. A computation is initiated by running a ''query'' over these relations. The language was developed and implemented in Marseille, France, in 1972 by Alain Colmerauer with Philippe Roussel, based on Robert Kowalski's procedural interpretation of Horn clauses at University of Edinburgh. Prolog was one of the first logic programming languages and remains the most popular such language today, with several free and commercial implementations available. The language has been used for theorem proving, expert systems, term rewriting, type systems, and automated planning, as well as its original intended field of use, nat ...
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PostScript (programming Language)
PostScript (PS) is a page description language in the electronic publishing and desktop publishing realm. It is a dynamically typed, concatenative programming language. It was created at Adobe Systems by John Warnock, Charles Geschke, Doug Brotz, Ed Taft and Bill Paxton from 1982 to 1984. History The concepts of the PostScript language were seeded in 1976 by John Gaffney at Evans & Sutherland, a computer graphics company. At that time Gaffney and John Warnock were developing an interpreter for a large three-dimensional graphics database of New York Harbor. Concurrently, researchers at Xerox PARC had developed the first laser printer and had recognized the need for a standard means of defining page images. In 1975-76 Bob Sproull and William Newman developed the Press format, which was eventually used in the Xerox Star system to drive laser printers. But Press, a data format rather than a language, lacked flexibility, and PARC mounted the Interpress effort to create a succes ...
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Forth (programming Language)
Forth is a procedural, stack-oriented programming language and interactive environment designed by Charles H. "Chuck" Moore and first used by other programmers in 1970. Although not an acronym, the language's name in its early years was often spelled in all capital letters as ''FORTH''. The FORTH-79 and FORTH-83 implementations, which were not written by Moore, became de facto standards, and an official standardization of the language was published in 1994 as ANS Forth. A wide range of Forth derivatives existed before and after ANS Forth. Forth typically combines a compiler with an integrated command shell, where the user interacts via subroutines called ''words''. Words can be defined, tested, redefined, and debugged without recompiling or restarting the whole program. All syntactic elements, including variables and basic operators, are defined as words. A stack is used to pass parameters between words, leading to a Reverse Polish Notation style. For much of Forth's existe ...
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Clojure
Clojure (, like ''closure'') is a dynamic and functional dialect of the Lisp programming language on the Java platform. Like other Lisp dialects, Clojure treats code as data and has a Lisp macro system. The current development process is community-driven, overseen by Rich Hickey as its benevolent dictator for life (BDFL). Clojure advocates immutability and immutable data structures and encourages programmers to be explicit about managing identity and its states. This focus on programming with immutable values and explicit progression-of-time constructs is intended to facilitate developing more robust, especially concurrent, programs that are simple and fast. While its type system is entirely dynamic, recent efforts have also sought the implementation of a dependent type system. History and development process Rich Hickey is the creator of the Clojure language. Before Clojure, he developed dotLisp, a similar project based on the .NET platform, and three earlier attempts ...
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Pico (programming Language)
Pico is a programming language developed at the Software Languages Lab at Vrije Universiteit Brussel. The language was created to introduce the essentials of programming to non-computer science students. Pico can be seen as an effort to generate a palatable and enjoyable language for people who do not want to study hard for the elegance and power of a language. They have done it by adapting Scheme's semantics. While designing Pico, the Software Languages Lab was inspired by the Abelson and Sussman's book "Structure and Interpretation of Computer Programs". Furthermore, they were influenced by the teaching of programming at high school or academic level. Pico should be interpreted as 'small', the idea was to create a small language for educational purposes. Language elements Comments Comments are surrounded by backquotes ("`"). Variables Variables are dynamically typed; Pico uses static scope. var: value Functions Functions are first-class objects in Pico. They ca ...
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Scheme (programming Language)
Scheme is a dialect of the Lisp family of programming languages. Scheme was created during the 1970s at the MIT AI Lab and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers. It was the first dialect of Lisp to choose lexical scope and the first to require implementations to perform tail-call optimization, giving stronger support for functional programming and associated techniques such as recursive algorithms. It was also one of the first programming languages to support first-class continuations. It had a significant influence on the effort that led to the development of Common Lisp.Common LISP: The Language, 2nd Ed., Guy L. Steele Jr. Digital Press; 1981. . "Common Lisp is a new dialect of Lisp, a successor to MacLisp, influenced strongly by ZetaLisp and to some extent by Scheme and InterLisp." The Scheme language is standardized in the official IEEE standard1178-1990 (Reaff 2008) IEEE Standard for the S ...
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Diagonal Lemma
In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions. The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel's incompleteness theorems and Tarski's undefinability theorem. Background Let \mathbb be the set of natural numbers. A first-order theory T in the language of arithmetic ''represents'' the computable function f: \mathbb\rightarrow\mathbb if there exists a "graph" predicate \mathcal_f(x, y) in the language of T such that for each n \in \mathbb : \vdash_\,(\forall y) ^\circ f(n)=y) \Leftrightarrow \mathcal_f(^\circ n,\,y)/math> Here ^\circ n is the numeral corresponding to the natural number n, which is defined to be ...
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