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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] |
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, including only woody plants with secondary growth, plants that are usable as lumber or plants above a specified height. In wider definitions, the taller palms, tree ferns, bananas, and bamboos are also trees. Trees are not a taxonomic group but include a 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 reaching several thousand years old. Trees have been in existence for 370 million years. It is estimated that there are some three trillion mature trees in the world. A tree typically has many secondary branches supported clear of the ground by the trunk. This trunk typically co ... [...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] |
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 decisi ... [...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] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. 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. 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 (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...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 types ''to-be-specified-later'' that are then ''instantiated'' when needed for specific types provided as parameters. This approach, pioneered by the ML programming language in 1973, permits writing common functions or types that differ only in the set of types on which they operate when used, thus reducing duplication. Such software entities are known as ''generics'' in Ada, C#, Delphi, Eiffel, F#, Java, Nim, Python, Go, Rust, Swift, TypeScript and Visual Basic .NET. They are known as ''parametric polymorphism'' in ML, Scala, Julia, and Haskell (the Haskell community also uses the term "generic" for a related but somewhat different concept); ''templates'' in C++ and D; and ''parameterized types'' in the influential 1994 book ''Design Patterns''. The term "generic programming" was originally coined by David Musser and Alexander Stepanov in a more specific sense than th ... [...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 require extensive modification of the compiler frontend or the underlying type system. Overview Type classes are defined by specifying a set of function or constant name ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Composition
In mathematics, function composition is an operation that takes two functions and , and produces a function such that . In this operation, the function is applied to the result of applying the function to . That is, the functions and are composed to yield a function that maps in domain to in codomain . Intuitively, if is a function of , and is a function of , then is a function of . The resulting ''composite'' function is denoted , defined by for all in . The notation is read as " of ", " after ", " circle ", " round ", " about ", " composed with ", " following ", " then ", or " on ", or "the composition of and ". Intuitively, composing functions 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 the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scala (programming Language)
Scala ( ) is a strong statically typed general-purpose programming language that supports both object-oriented programming and functional programming. Designed to be concise, many of Scala's design decisions are aimed 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 compiled to JavaScript to run in a browser, or directly to a native executable. 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 Java, Scala has many features of functional prog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trait (computer Programming)
In computer programming, a trait is a concept used in object-oriented programming which 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 dire ... [...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. 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 as well, including 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 Applicative type class. Definition In Haskell, an applic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monad (functional Programming)
In functional programming, a monad is a software design pattern with a structure that combines program fragments (Function (computer programming), functions) and wraps their return values in a Type system, type with additional computation. In addition to defining a wrapping monadic type, monads define two Operator (computer programming), operators: one to wrap a value in the monad type, and another to compose together functions that output values of the monad type (these are known as monadic functions). General-purpose languages use monads to reduce boilerplate code needed for common operations (such as dealing with undefined values or fallible functions, or encapsulating bookkeeping code). Functional languages use monads to turn complicated sequences of functions into succinct pipelines that abstract away control flow, and side-effect (computer science), side-effects. Both the concept of a monad and the term originally come from category theory, where a monad is defined as a Func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
