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Applicative Computing Systems
Applicative computing systems, or ACS are the systems of object calculi founded on combinatory logic and lambda calculus. The only essential notion which is under consideration in these systems is the representation of object. In combinatory logic the only metaoperator is application in a sense of applying one object to other. In lambda calculus two metaoperators are used: application – the same as in combinatory logic, and functional abstraction which binds the only variable in one object. Features The objects generated in these systems are the functional entities with the following features: # the number of argument places, or object arity is not fixed but is enabling step by step in interoperations with other objects; # in a process of generating the compound object one of its counterparts—function—is applied to other one—argument—but in other contexts they can change their roles, i.e. functions and arguments are considered on the equal rights; # the self-app ... [...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] |
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] |
Object (computer Science)
In computer science, an object can be a variable, a data structure, a function, or a method. As regions of memory, they contain value and are referenced by identifiers. In the object-oriented programming paradigm, ''object'' can be a combination of variables, functions, and data structures; in particular in class-based variations of the paradigm it refers to a particular instance of a class. In the relational model of database management, an object can be a table or column, or an association between data and a database entity (such as relating a person's age to a specific person). Object-based languages An important distinction in programming languages is the difference between an object-oriented language and an object-based language. A language is usually considered object-based if it includes the basic capabilities for an object: identity, properties, and attributes. A language is considered object-oriented if it is object-based and also has the capability of polymorphism, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Application
In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range. In this sense, function application can be thought of as the opposite of function abstraction. Representation Function application is usually depicted by juxtaposing the variable representing the function with its argument encompassed in parentheses. For example, the following expression represents the application of the function ''ƒ'' to its argument ''x''. :f(x) In some instances, a different notation is used where the parentheses aren't required, and function application can be expressed just by juxtaposition. For example, the following expression can be considered the same as the previous one: :f\; x The latter notation is especially useful in combination with the currying isomorphism. Given a function f : (X \times Y) \to Z, its application is represented as f(x, y) by the former notation and f\;(x,y) (or f \; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Abstraction
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(\la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applicative Programming Language
In the classification of programming languages, an applicative programming language is built out of functions applied to arguments. Applicative languages are functional, and applicative is often used as a synonym for functional. However, concatenative languages can be functional, while not being applicative. The semantics of applicative languages are based on beta reduction of terms, and side effects such as mutation of state are not permitted. Lisp and ML are applicative programming languages. See also * Applicative universal grammar * 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 A ... References {{Reflist Programming language classification Applicative computing systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applicative Programming Language
In the classification of programming languages, an applicative programming language is built out of functions applied to arguments. Applicative languages are functional, and applicative is often used as a synonym for functional. However, concatenative languages can be functional, while not being applicative. The semantics of applicative languages are based on beta reduction of terms, and side effects such as mutation of state are not permitted. Lisp and ML are applicative programming languages. See also * Applicative universal grammar * 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 A ... References {{Reflist Programming language classification Applicative computing systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Categorical Abstract Machine
The categorical abstract machine (CAM) is a model of computation for programs''Cousineau G., Curien P.-L., Mauny M.'' The categorical abstract machine. — LNCS, 201, Functional programming languages computer architecture.-- 1985, pp.~50-64. that preserves the abilities of applicative, functional, or compositional style. It is based on the techniques of applicative computing systems, applicative computing. Overview The notion of the categorical abstract machine arose in the mid-1980s. It took its place in computer science as a kind of theory of computation for programmers, represented by Cartesian closed category and embedded into the combinatory logic. CAM is a transparent and sound mathematical representation for the languages of functional programming. The machine code can be optimized using the equational form of a theory of computation. Using CAM, the various mechanisms of computation such as recursion or lazy evaluation can be emulated as well as parameter passing, such as ... [...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] |
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, ... [...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] |
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes reference books, serials and online products in the subject areas of: * Communications engineering * Economics * Environmental science * Finance * Food science and nutrition * Geophysics * Life sciences * Mathematics and statistics * Neuroscience * Physical sciences * Psychology Well-known products include the ''Methods in Enzymology'' series and encyclopedias such as ''The International Encyclopedia of Public Health'' and the ''Encyclopedia of Neuroscience''. See also * Akademische Verlagsgesellschaft (AVG) — the German predecessor, founded in 1906 by Leo Jolowicz (1868–1940), the father of Walter Jolowicz Walter may refer to: People * Walter (name), both a surname and a given name * Little Walter, American blues harmonica player Marion Wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |