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Cons
In computer programming, ( or ) is a fundamental function in most dialects of the Lisp programming language. ''constructs'' memory objects which hold two values or pointers to two values. These objects are referred to as (cons) cells, conses, non-atomic s-expressions ("NATSes"), or (cons) pairs. In Lisp jargon, the expression "to cons ''x'' onto ''y''" means to construct a new object with (cons ''x'' ''y''). The resulting pair has a left half, referred to as the (the first element, or '' contents of the address part of register''), and a right half, referred to as the (the second element, or '' contents of the decrement part of register''). It is loosely related to the object-oriented notion of a constructor, which creates a new object given arguments, and more closely related to the constructor function of an algebraic data type system. The word "cons" and expressions like "to cons onto" are also part of a more general functional programming jargon. Sometimes operato ...
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Elm (programming Language)
Elms are deciduous and semi-deciduous trees comprising the genus ''Ulmus'' in the family Ulmaceae. They are distributed over most of the Northern Hemisphere, inhabiting the temperate and tropical- montane regions of North America and Eurasia, presently ranging southward in the Middle East to Lebanon and Israel,Flora of Israel OnlineUlmus minor Mill. , Flora of Israel Online accessdate: July 28, 2020 and across the Equator in the Far East into Indonesia.Fu, L., Xin, Y. & Whittemore, A. (2002). Ulmaceae, in Wu, Z. & Raven, P. (eds) Flora of China'', Vol. 5 (Ulmaceae through Basellaceae). Science Press, Beijing, and Missouri Botanical Garden Press, St. Louis, US. Elms are components of many kinds of natural forests. Moreover, during the 19th and early 20th centuries, many species and cultivars were also planted as ornamental street, garden, and park trees in Europe, North America, and parts of the Southern Hemisphere, notably Australasia. Some individual elms reached great size ...
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Constructor (computer Science)
In class-based, object-oriented programming, a constructor (abbreviation: ctor) is a special type of function called to create an object. It prepares the new object for use, often accepting arguments that the constructor uses to set required member variables. A constructor resembles an instance method, but it differs from a method in that it has no explicit return type, it is not implicitly inherited and it usually has different rules for scope modifiers. Constructors often have the same name as the declaring class. They have the task of initializing the object's data members and of establishing the invariant of the class, failing if the invariant is invalid. A properly written constructor leaves the resulting object in a ''valid'' state. Immutable objects must be initialized in a constructor. Most languages allow overloading the constructor in that there can be more than one constructor for a class, with differing parameters. Some languages take consideration of s ...
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Algebraic Data Type
In computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite data type, i.e., a data type formed by combining other types. Two common classes of algebraic types are product types (i.e., tuples, and records) and sum types (i.e., tagged or disjoint unions, coproduct types or ''variant types''). The values of a product type typically contain several values, called ''fields''. All values of that type have the same combination of field types. The set of all possible values of a product type is the set-theoretic product, i.e., the Cartesian product, of the sets of all possible values of its field types. The values of a sum type are typically grouped into several classes, called ''variants''. A value of a variant type is usually created with a quasi-functional entity called a ''constructor''. Each variant has its own constructor, which takes a specified number of arguments with specified types. The set of all po ...
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Lisp (programming Language)
Lisp (historically LISP, an abbreviation of "list processing") is a family of programming languages with a long history and a distinctive, fully parenthesized prefix notation. Originally specified in the late 1950s, it is the second-oldest high-level programming language still in common use, after Fortran. Lisp has changed since its early days, and many dialects have existed over its history. Today, the best-known general-purpose Lisp dialects are Common Lisp, Scheme, Racket, and Clojure. Lisp was originally created as a practical mathematical notation for computer programs, influenced by (though not originally derived from) the notation of Alonzo Church's lambda calculus. It quickly became a favored programming language for artificial intelligence (AI) research. As one of the earliest programming languages, Lisp pioneered many ideas in computer science, including tree data structures, automatic storage management, dynamic typing, conditionals, higher-order function ...
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Church Encoding
In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this way. Terms that are usually considered primitive in other notations (such as integers, Booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding. The Church–Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding. In the untyped lambda calculus the only primitive data type is the function. Use A straightforward implementation of Church encoding slows some access operations from O(1) to O(n), where n is the size of the data structure, making Church encoding impractical. Research has shown that this can be addressed by targeted optimizations, but most functional programming languages instead expand their i ...
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Object-oriented Programming
Object-oriented programming (OOP) is a programming paradigm based on the concept of '' objects''. Objects can contain data (called fields, attributes or properties) and have actions they can perform (called procedures or methods and implemented in code). In OOP, computer programs are designed by making them out of objects that interact with one another. Many of the most widely used programming languages (such as C++, Java, and Python) support object-oriented programming to a greater or lesser degree, typically as part of multiple paradigms in combination with others such as imperative programming and declarative programming. Significant object-oriented languages include Ada, ActionScript, C++, Common Lisp, C#, Dart, Eiffel, Fortran 2003, Haxe, Java, JavaScript, Kotlin, Logo, MATLAB, Objective-C, Object Pascal, Perl, PHP, Python, R, Raku, Ruby, Scala, SIMSCRIPT, Simula, Smalltalk, Swift, Vala and Visual Basic.NET. History The idea of ...
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Subroutine
In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-defined interface and behavior and can be invoked multiple times. Callable units provide a powerful programming tool. The primary purpose is to allow for the decomposition of a large and/or complicated problem into chunks that have relatively low cognitive load and to assign the chunks meaningful names (unless they are anonymous). Judicious application can reduce the cost of developing and maintaining software, while increasing its quality and reliability. Callable units are present at multiple levels of abstraction in the programming environment. For example, a programmer may write a function in source code that is compiled to machine code that implements similar semantics. There is a callable unit in the source code and an associated one in the machine code, but they are different kinds of callable units with different impl ...
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Functional Programming
In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declarative programming paradigm in which function definitions are Tree (data structure), trees of Expression (computer science), expressions that map Value (computer science), values to other values, rather than a sequence of Imperative programming, imperative Statement (computer science), statements which update the State (computer science), running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local Identifier (computer languages), identifiers), passed as Parameter (computer programming), arguments, and Return value, returned from other functions, just as any other data type can. This allows programs to be written in a Declarative programming, d ...
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F Sharp (programming Language)
F# (pronounced F sharp) is a general-purpose, high-level, strongly typed, multi-paradigm programming language that encompasses functional, imperative, and object-oriented programming methods. It is most often used as a cross-platform Common Language Infrastructure (CLI) language on .NET, but can also generate JavaScript and graphics processing unit (GPU) code. F# is developed by the F# Software Foundation, Microsoft and open contributors. An open source, cross-platform compiler for F# is available from the F# Software Foundation. F# is a fully supported language in Visual Studio and JetBrains Rider. Plug-ins supporting F# exist for many widely used editors including Visual Studio Code, Vim, and Emacs. F# is a member of the ML language family and originated as a .NET Framework implementation of a core of the programming language OCaml. It has also been influenced by C#, Python, Haskell, Scala and Erlang. History Versions Language evolution F# uses an open deve ...
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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 Computer Science and Artificial Intelligence Laboratory (MIT CSAIL) 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 offic ...
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Coq (software)
The Rocq Prover (previously known as Coq) is an interactive theorem prover first released in 1989. It allows the expression of mathematical assertions, mechanical checking of proofs of these assertions, assists in finding formal proofs using proof automation routines and extraction of a certified program from the constructive proof of its formal specification. Rocq works within the theory of the ''calculus of inductive constructions'', a derivative of the '' calculus of constructions''. Rocq is not an automated theorem prover but includes automatic theorem proving tactics ( procedures) and various decision procedures. The Association for Computing Machinery awarded Thierry Coquand, Gérard Huet, Christine Paulin-Mohring, Bruno Barras, Jean-Christophe Filliâtre, Hugo Herbelin, Chetan Murthy, Yves Bertot, and Pierre Castéran with the 2013 ACM Software System Award for Rocq (when it was still named Coq). Overview When viewed as a programming language, Rocq implements a ...
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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 ...
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