|
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] |
Tree As A Functor
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only plants that are usable as lumber, or only plants above a specified height. But wider definitions include taller palms, tree ferns, bananas, and bamboos. Trees are not a monophyletic taxonomic group but consist of a wide variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some trees reaching several thousand years old. Trees evolved around 400 million years ago, and it is estimated that there are around three trillion mature trees in the world currently. A tree typically has many secondary branches supported clear of t ... [...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, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Design Pattern
A design pattern is the re-usable form of a solution to a design problem. The idea was introduced by the architect Christopher Alexander and has been adapted for various other disciplines, particularly software engineering. The " Gang of Four" book. Details An organized collection of design patterns that relate to a particular field is called a pattern language. This language gives a common terminology for discussing the situations designers are faced with. Documenting a pattern requires explaining why a particular situation causes problems, and how the components of the pattern relate to each other to give the solution. Christopher Alexander describes common design problems as arising from "conflicting forces"—such as the conflict between wanting a room to be sunny and wanting it not to overheat on summer afternoons. A pattern would not tell the designer how many windows to put in the room; instead, it would propose a set of values to guide the designer toward a deci ... [...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] |
Function (mathematics)
In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. The set is called the Domain of a function, domain of the function and the set is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. History of the function concept, Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable function, differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generic Type
Generic programming is a style of computer programming in which algorithms are written in terms of data types ''to-be-specified-later'' that are then ''instantiated'' when needed for specific types provided as parameters. This approach, pioneered in the programming language ML in 1973, permits writing common functions or data types that differ only in the set of types on which they operate when used, thus reducing duplicate code. Generic programming was introduced to the mainstream with Ada in 1977. With templates in C++, generic programming became part of the repertoire of professional library design. The techniques were further improved and ''parameterized types'' were introduced in the influential 1994 book ''Design Patterns''. New techniques were introduced by Andrei Alexandrescu in his 2001 book ''Modern C++ Design: Generic Programming and Design Patterns Applied''. Subsequently, D implemented the same ideas. Such software entities are known as ''generics'' in Ada ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell
Haskell () is a general-purpose, statically typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research, and industrial applications, Haskell pioneered several programming language features such as type classes, which enable type-safe operator overloading, and monadic input/output (IO). It is named after logician Haskell Curry. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). Haskell's semantics are historically based on those of the Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in academia and industry. , Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Class
In computer science, a type class is a type system construct that supports ad hoc polymorphism. This is achieved by adding constraints to type variables in parametrically polymorphic types. Such a constraint typically involves a type class T and a type variable a, and means that a can only be instantiated to a type whose members support the overloaded operations associated with T. Type classes were first implemented in the Haskell programming language after first being proposed by Philip Wadler and Stephen Blott as an extension to "eqtypes" in Standard ML, and were originally conceived as a way of implementing overloaded arithmetic and equality operators in a principled fashion. In contrast with the "eqtypes" of Standard ML, overloading the equality operator through the use of type classes in Haskell does not need extensive modification of the compiler frontend or the underlying type system. Overview Type classes are defined by specifying a set of function or constant na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Composition
In mathematics, the composition operator \circ takes two function (mathematics), functions, f and g, and returns a new function h(x) := (g \circ f) (x) = g(f(x)). Thus, the function is function application, applied after applying to . (g \circ f) is pronounced "the composition of and ". Reverse composition, sometimes denoted f \mapsto g , applies the operation in the opposite order, applying f first and g second. Intuitively, reverse composition is a chaining process in which the output of function feeds the input of function . The composition of functions is a special case of the composition of relations, sometimes also denoted by \circ. As a result, all properties of composition of relations are true of composition of functions, such as #Properties, associativity. Examples * Composition of functions on a finite set (mathematics), set: If , and , then , as shown in the figure. * Composition of functions on an infinite set: If (where is the set of all real numbers) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scala (programming Language)
Scala ( ) is a strongly statically typed high-level general-purpose programming language that supports both object-oriented programming and functional programming. Designed to be concise, many of Scala's design decisions are intended to address criticisms of Java. Scala source code can be compiled to Java bytecode and run on a Java virtual machine (JVM). Scala can also be transpiled to JavaScript to run in a browser, or compiled directly to a native executable. When running on the JVM, Scala provides language interoperability with Java so that libraries written in either language may be referenced directly in Scala or Java code. Like Java, Scala is object-oriented, and uses a syntax termed '' curly-brace'' which is similar to the language C. Since Scala 3, there is also an option to use the off-side rule (indenting) to structure blocks, and its use is advised. Martin Odersky has said that this turned out to be the most productive change introduced in Scala 3. Unlike J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trait (computer Programming)
In computer programming, a trait is a language concept that represents a set of methods that can be used to extend the functionality of a class. Rationale In object-oriented programming, behavior is sometimes shared between classes which are not related to each other. For example, many unrelated classes may have methods to serialize objects to JSON. Historically, there have been several approaches to solve this without duplicating the code in every class needing the behavior. Other approaches include multiple inheritance and mixins, but these have drawbacks: the behavior of the code may unexpectedly change if the order in which the mixins are applied is altered, or if new methods are added to the parent classes or mixins. Traits solve these problems by allowing classes to use the trait and get the desired behavior. If a class uses more than one trait, the order in which the traits are used does not matter. The methods provided by the traits have direct access to the data of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applicative Functor
In functional programming, an applicative functor, or an applicative for short, is an intermediate structure between functors and monads. In category theory they are calleclosed monoidal functors Applicative functors allow for functorial computations to be sequenced (unlike plain functors), but don't allow using results from prior computations in the definition of subsequent ones (unlike monads). Applicative functors are the programming equivalent of lax monoidal functors with tensorial strength in category theory. Applicative functors were introduced in 2008 by Conor McBride and Ross Paterson in their paper ''Applicative programming with effects''. Applicative functors first appeared as a library feature in Haskell, but have since spread to other languages such as Idris, Agda, OCaml, Scala, and F#. Glasgow Haskell, Idris, and F# offer language features designed to ease programming with applicative functors. In Haskell, applicative functors are implemented in the Applicativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
