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Functor (other)
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A functor, in mathematics, is a map between categories. Functor may also refer to: * Predicate functor in logic, a basic concept of predicate functor logic * Function word in linguistics * In computer programming: ** Functor (functional programming) **Function object used to pass function pointers along with state information ** for use of the term in Prolog language, see Prolog syntax and semantics ** In OCaml and Standard ML, a functor is a higher-order module (a module parameterized by one or more other modules), often used to define type-safe abstracted algorithms and data structures. See also * Function (other) Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functor
In mathematics, specifically category theory, a functor is a Map (mathematics), mapping between Category (mathematics), categories. Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated to continuous function, continuous maps between spaces. Nowadays, functors are used throughout modern mathematics to relate various categories. Thus, functors are important in all areas within mathematics to which category theory is applied. The words ''category'' and ''functor'' were borrowed by mathematicians from the philosophers Aristotle and Rudolf Carnap, respectively. The latter used ''functor'' in a Linguistics, linguistic context; see function word. Definition Let ''C'' and ''D'' be category (mathematics), categories. A functor ''F'' from ''C'' to ''D'' is a mapping that * associates each object X in ''C'' to an object F(X) in ''D' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate Functor Logic
In mathematical logic, predicate functor logic (PFL) is one of several ways to express first-order logic (also known as predicate logic) by purely algebraic means, i.e., without quantified variables. PFL employs a small number of algebraic devices called predicate functors (or predicate modifiers) that operate on terms to yield terms. PFL is mostly the invention of the logician and philosopher Willard Quine. Motivation The source for this section, as well as for much of this entry, is Quine (1976). Quine proposed PFL as a way of algebraizing first-order logic in a manner analogous to how Boolean algebra algebraizes propositional logic. He designed PFL to have exactly the expressive power of first-order logic with identity. Hence the metamathematics of PFL are exactly those of first-order logic with no interpreted predicate letters: both logics are sound, complete, and undecidable. Most work Quine published on logic and mathematics in the last 30 years of his life touched on PFL in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Word
In linguistics, function words (also called functors) are words that have little lexical meaning or have ambiguous meaning and express grammatical relationships among other words within a sentence, or specify the attitude or mood of the speaker. They signal the structural relationships that words have to one another and are the glue that holds sentences together. Thus they form important elements in the structures of sentences. Words that are not function words are called ''content words'' (or open class words, ''lexical words,'' or ''autosemantic words'') and include nouns, most verbs, adjectives, and most adverbs although some adverbs are function words (like ''then'' and ''why''). Dictionaries define the specific meanings of content words but can describe only the general usages of function words. By contrast, grammars describe the use of function words in detail but treat lexical words only in general terms. Since it was first proposed in 1952 by C. C. Fries, the distinguis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functor (functional Programming)
In functional programming, a functor is a design pattern inspired by the definition from category theory that allows one to apply a function to values inside a generic type without changing the structure of the generic type. In Haskell this idea can be captured in a type class: class Functor f where fmap :: (a -> b) -> f a -> f b with conditions called ''functor laws'' (where . stands for function composition), fmap id = id fmap (g . h) = (fmap g) . (fmap h) In Scala a trait can be used: trait Functor Applicative_Functor,_[__ Functors_form_a_base_for_more_complex_abstractions_like_Applicative_functor">Applicative_Functor,_Monad_(functional_programming)">Monad,_and_Monad_(functional_programming)#Comonads.html" "title="Monad_(functional_programming).html" "title="Applicative_functor.html" ;"title="[_.html" ;"title="[_">[_ Functors form a base for more complex abstractions like Applicative functor">Applicative Functor, Monad (functional programming)">Monad, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Object
In computer programming, a function object is a construct allowing an object to be invoked or called as if it were an ordinary function, usually with the same syntax (a function parameter that can also be a function). Function objects are often called functors. Description A typical use of a function object is in writing callback functions. A callback in procedural languages, such as C, may be performed by using function pointers. However it can be difficult or awkward to pass a state into or out of the callback function. This restriction also inhibits more dynamic behavior of the function. A function object solves those problems since the function is really a façade for a full object, carrying its own state. Many modern (and some older) languages, e.g. C++, Eiffel, Groovy, Lisp, Smalltalk, Perl, PHP, Python, Ruby, Scala, and many others, support first-class function objects and may even make significant use of them. Functional programming languages additionally support clo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prolog Syntax And Semantics
The syntax and semantics of Prolog, a programming language, are the sets of rules that define how a Prolog program is written and how it is interpreted, respectively. The rules are laid out in ISO standard ISO/IEC 13211''ISO/IEC 13211: Information technology — Programming languages — Prolog''. International Organization for Standardization, Geneva. although there are differences in the Prolog implementations. Data types Prolog is dynamically typed. It has a single data type, the ''term'', which has several subtypes: ''atoms'', ''numbers'', ''variables'' and ''compound terms''. An atom is a general-purpose name with no inherent meaning. It is composed of a sequence of characters that is parsed by the Prolog reader as a single unit. Atoms are usually bare words in Prolog code, written with no special syntax. However, atoms containing spaces or certain other special characters must be surrounded by single quotes. Atoms beginning with a capital letter must also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OCaml
OCaml ( , formerly Objective Caml) is a general-purpose programming language, general-purpose, multi-paradigm programming language which extends the Caml dialect of ML (programming language), ML with object-oriented programming, object-oriented features. OCaml was created in 1996 by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez, and others. The OCaml toolchain includes an interactive top-level Interpreter (computing), interpreter, a bytecode compiler, an optimizing native code compiler, a reversible debugger, and a package manager (OPAM). OCaml was initially developed in the context of automated theorem proving, and has an outsize presence in static program analysis, static analysis and formal methods software. Beyond these areas, it has found serious use in systems programming, web development, and financial engineering, among other application domains. The acronym ''CAML'' originally stood for ''Categorical Abstract Machine Language'', but O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard ML
Standard ML (SML) is a general-purpose, modular, functional programming language with compile-time type checking and type inference. It is popular among compiler writers and programming language researchers, as well as in the development of theorem provers. Standard ML is a modern dialect of ML, the language used in the Logic for Computable Functions (LCF) theorem-proving project. It is distinctive among widely used languages in that it has a formal specification, given as typing rules and operational semantics in ''The Definition of Standard ML''. Language Standard ML is a functional programming language with some impure features. Programs written in Standard ML consist of expressions as opposed to statements or commands, although some expressions of type unit are only evaluated for their side-effects. Functions Like all functional languages, a key feature of Standard ML is the function, which is used for abstraction. The factorial function can be expressed as follows: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
