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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-orie ... [...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 Mathematical object, object X in ''C'' to ... [...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 ... [...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 ... [...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 This declaration says that any instance of Functor must support a method fmap, which maps a function over the elements of the instance. Functors in Haskell should also obey the so-called ''functor laws'', which state that the mapping operation preserves the identity function and composition of functions: fmap id = id fmap (g . h) = (fmap g) . (fmap h) where . stands for function composition. In Scala a trait can instead be used: trait Functor comonads, all of which build atop a canonical functor structure. Functors are useful in modeling functional effects by values of parameterized data types. Modifiable computations are modeled by allo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Object
In computer programming, a function object is a construct allowing an object (computer science), object to be invoked or called as if it were an ordinary subroutine, function, usually with the same syntax (a function parameter that can also be a function). In some languages, particularly C++, function objects are often called functors (not related to Functor (functional programming), the functional programming concept). Description A typical use of a function object is in writing callback (computer science), callback functions. A callback in procedural programming, procedural languages, such as C (programming language), 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 facade pattern, façade for a full object, carrying its own state. Many modern (an ... [...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, High-level programming language, high-level, Comparison of multi-paradigm programming languages, 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 managerOPAM together with a composable build system for OCamlDune. OCaml was initially developed in the context of automated theorem proving, and is used in static program analysis, static analysis and formal methods software. Beyond these areas, it has found use in systems programming, web development, and specific financial utili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard ML
Standard ML (SML) is a General-purpose programming language, general-purpose, High-level programming language, high-level, Modular programming, modular, Functional programming, functional programming language with compile-time type checking and type inference. It is popular for writing compilers, for programming language research, and for developing automated theorem proving, theorem provers. Standard ML is a modern dialect of ML (programming language), 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 Expression (computer science), expressions in contrast to statements or commands, although some expressions of type Unit type, unit are only eva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
