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Unlambda
Unlambda is a minimal, "nearly pure" functional programming language invented by David Madore. It is based on combinatory logic, an expression system without the lambda operator or free variables. It relies mainly on two built-in functions (s and k) and an apply operator (written `, the backquote character). These alone make it Turing-complete, but there are also some input/output (I/O) functions to enable interacting with the user, some shortcut functions, and a lazy evaluation function. Variables are unsupported. Unlambda is free and open-source software distributed under a GNU General Public License (GPL) 2.0 or later. Basic principles As an esoteric programming language, Unlambda is meant as a demonstration of very pure functional programming rather than for practical use. Its main feature is the lack of conventional operators and data types—the only kind of data in the program are one-parameter functions. Data can nevertheless be simulated with appropriate functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Call With Current Continuation
In the Scheme computer programming language, the procedure call-with-current-continuation, abbreviated call/cc, is used as a control flow operator. It has been adopted by several other programming languages. Taking a function f as its only argument, (call/cc f) within an expression is applied to the current continuation of the expression. For example ((call/cc f) e2) is equivalent to applying f to the current continuation of the expression. The current continuation is given by replacing (call/cc f) by a variable c bound by a lambda abstraction, so the current continuation is (lambda (c) (c e2)). Applying the function f to it gives the final result (f (lambda (c) (c e2))). As a complementary example, in an expression (e1 (call/cc f)), the continuation for the sub-expression (call/cc f) is (lambda (c) (e1 c)), so the whole expression is equivalent to (f (lambda (c) (e1 c))). In other words it takes a "snapshot" of the current control context or control state of the program as an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Esoteric Programming Languages
An esoteric programming language (sometimes shortened to esolang) is a programming language designed to test the boundaries of computer programming language design, as a proof of concept, as software art, as a hacking interface to another language (particularly functional programming or procedural programming languages), or as a joke. The use of the word ''esoteric'' distinguishes them from languages that working developers use to write software. The creators of most esolangs do not intend them to be used for mainstream programming, although some esoteric features, such as visuospatial syntax, have inspired practical applications in the arts. Such languages are often popular among hackers and hobbyists. Usability is rarely a goal for designers of esoteric programming languages; often their design leads to quite the opposite. Their usual aim is to remove or replace conventional language features while still maintaining a language that is Turing-complete, or even one for which the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstraction Elimination
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators, which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in predicate logic. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments. In mathematics Combinatory logic was originally intended as a 'pre-logic' that would clarify the role of quantified variables in logic, essentially by eliminating them. Another way of eliminating quantified variables is Quine's predicate functor logic. While the expressive power of combinatory logic ty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatory Logic
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators, which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in predicate logic. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments. In mathematics Combinatory logic was originally intended as a 'pre-logic' that would clarify the role of quantified variables in logic, essentially by eliminating them. Another way of eliminating quantified variables is Quine's predicate functor logic. While the expressive power of combinatory logic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Esoteric Programming Language
An esoteric programming language (sometimes shortened to esolang) is a programming language designed to test the boundaries of computer programming language design, as a proof of concept, as software art, as a hacking interface to another language (particularly functional programming or procedural programming languages), or as a joke. The use of the word ''esoteric'' distinguishes them from languages that working developers use to write software. The creators of most esolangs do not intend them to be used for mainstream programming, although some esoteric features, such as visuospatial syntax, have inspired practical applications in the arts. Such languages are often popular among hackers and hobbyists. Usability is rarely a goal for designers of esoteric programming languages; often their design leads to quite the opposite. Their usual aim is to remove or replace conventional language features while still maintaining a language that is Turing-complete, or even one for which the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SKI Combinator Calculus
The SKI combinator calculus is a combinatory logic system and a computational system. It can be thought of as a computer programming language, though it is not convenient for writing software. Instead, it is important in the mathematical theory of algorithms because it is an extremely simple Turing complete language. It can be likened to a reduced version of the untyped lambda calculus. It was introduced by Moses Schönfinkel and Haskell Curry. All operations in lambda calculus can be encoded via abstraction elimination into the SKI calculus as binary trees whose leaves are one of the three symbols S, K, and I (called ''combinators''). Notation Although the most formal representation of the objects in this system requires binary trees, for simpler typesetting they are often represented as parenthesized expressions, as a shorthand for the tree they represent. Any subtrees may be parenthesized, but often only the right-side subtrees are parenthesized, with left associativity i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambda Calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. Lambda calculus consists of constructing § lambda terms and performing § reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules: * x – variable, a character or string representing a parameter or mathematical/logical value. * (\lambda x.M) – abstraction, function definition (M is a lambda term). The variable x becomes bound in the expression. * (M\ N) – application, applying a function M to an argument N. M and N are lambda terms. The reduction operations include: * (\lambda x.M \rightarrow(\l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambda Calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. Lambda calculus consists of constructing § lambda terms and performing § reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules: * x – variable, a character or string representing a parameter or mathematical/logical value. * (\lambda x.M) – abstraction, function definition (M is a lambda term). The variable x becomes bound in the expression. * (M\ N) – application, applying a function M to an argument N. M and N are lambda terms. The reduction operations include: * (\lambda x.M \rightarrow(\l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backquote
The backtick is a typographical mark used mainly in computing. It is also known as backquote, grave, or grave accent. The character was designed for typewriters to add a grave accent to a (lower-case) base letter, by overtyping it atop that letter. On early computer systems, however, this physical dead key+overtype function was rarely supported, being functionally replaced by precomposed characters. Consequently, this ASCII symbol was rarely (if ever) used in computer systems for its original aim and became repurposed for many unrelated uses in computer programming. The sign is located on the left-top of a US or UK layout keyboard, next to the key. On older keyboards the Escape key was at this location, and the backtick key was somewhere on the right side of the layout. Provision (if any) of the backtick on other keyboards varies by national keyboard layout and keyboard mapping. History Typewriters On typewriters designed for languages that routinely use diacritics (accent m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eager Evaluation
In a programming language, an evaluation strategy is a set of rules for evaluating expressions. The term is often used to refer to the more specific notion of a ''parameter-passing strategy'' that defines the kind of value that is passed to the function for each parameter (the ''binding strategy'') and whether to evaluate the parameters of a function call, and if so in what order (the ''evaluation order''). The notion of reduction strategy is distinct, although some authors conflate the two terms and the definition of each term is not widely agreed upon. To illustrate, executing a function call f(a,b) may first evaluate the arguments a and b, store the results in references or memory locations ref_a and ref_b, then evaluate the function's body with those references passed in. This gives the function the ability to look up the argument values, to modify them via assignment as if they were local variables, and to return values via the references. This is the call-by-reference evalu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fixed Point Combinator
In mathematics and computer science in general, a '' fixed point'' of a function is a value that is mapped to itself by the function. In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator) is a higher-order function \textsf that returns some fixed point of its argument function, if one exists. Formally, if the function ''f'' has one or more fixed points, then : \textsf\ f = f\ (\textsf\ f)\ , and hence, by repeated application, : \textsf\ f = f\ (f\ ( \ldots f\ (\textsf\ f) \ldots))\ . Y combinator In the classical untyped lambda calculus, every function has a fixed point. A particular implementation of fix is Curry's paradoxical combinator Y, represented by : \textsf = \lambda f. \ (\lambda x.f\ (x\ x))\ (\lambda x.f\ (x\ x))\ .Throughout this article, the syntax rules given in Lambda calculus#Notation are used, to save parentheses.For an arbitrary lambda term ''f'', the fixed-point property can be validated by beta reducing the left- an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Input/output
In computing, input/output (I/O, or informally io or IO) is the communication between an information processing system, such as a computer, and the outside world, possibly a human or another information processing system. Inputs are the signals or data received by the system and outputs are the signals or data sent from it. The term can also be used as part of an action; to "perform I/O" is to perform an input or output operation. are the pieces of hardware used by a human (or other system) to communicate with a computer. For instance, a keyboard or computer mouse is an input device for a computer, while monitors and printers are output devices. Devices for communication between computers, such as modems and network cards, typically perform both input and output operations. Any interaction with the system by a interactor is an input and the reaction the system responds is called the output. The designation of a device as either input or output depends on perspective. Mice a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
