Computer software, or just software, is a collection of computer programs and related data that provide the instructions for telling a computer what to do and how to do it. In other words, software is a conceptual entity which is a set of computer programs, procedures, and associated documentation concerned with the operation of a data processing system. We can also say software refers to one or more computer programs and data held in the storage of the computer for some purposes. In other words software is a set of programs, procedures, algorithms and its documentation. Program software performs the function of the program it implements, either by directly providing instructions to the computer hardware or by serving as input to another piece of software. The term was coined to contrast to the old term hardware (meaning physical devices). In contrast to hardware, software is intangible, meaning it "cannot be touched". Software is also sometimes used in a more narrow sense, meaning application software only. Sometimes the term includes data that has not traditionally been associated with computers, such as film, tapes, and records.

Examples of computer software include:

Application software includes end-user applications of computers such as word processors or video games, and ERP software for groups of users.

Middleware controls and co-ordinates distributed systems.

Programming languages define the syntax and semantics of computer programs. For example, many mature banking applications were written in the COBOL language, originally invented in 1959. Newer applications are often written in more modern programming languages.

System software includes operating systems, which govern computing resources. Today large applications running on remote machines such as Websites are considered to be system software, because the end-user interface is generally through a graphical user interface, such as a web browser. Teachware is any special breed of software or other means of product dedicated to education purposes in software engineering and beyond in general education.

Testware is any software for testing hardware or a software package.

Firmware is low-level software often stored on electrically programmable memory devices. Firmware is given its name because it is treated like hardware and run ("executed") by other software programs. Firmware often is not accessible for change by other entities but the developers' enterprises.

Shrinkware is the older name given to consumer-purchased software, because it was often sold in retail stores in a shrink-wrapped box.

Device drivers control parts of computers such as disk drives, printers, CD drives, or computer monitors.

Programming tools help conduct computing tasks in any category listed above. For programmers, these could be tools for debugging or reverse engineering older legacy systems in order to check source code compatibility.

History

The first theory about software was proposed by Alan Turing in his 1935 essay Computable numbers with an application to the Entscheidungsproblem (Decision problem). The term "software" was first used in print by John W. Tukey in 1958. Colloquially, the term is often used to mean application software. In computer science and software engineering, software is all information processed by computer system, programs and data. The academic fields studying software are computer science and software engineering.

The history of computer software is most often traced back to the first software bug in 1946. As more and more programs enter the realm of firmware, and the hardware itself becomes smaller, cheaper and faster as predicted by Moore's law, elements of computing first considered to be software, join the ranks of hardware. Most hardware companies today have more software programmers on the payroll than hardware designers, since software tools have automated many tasks of Printed circuit board engineers. Just like the Auto industry, the Software industry has grown from a few visionaries operating out of their garage with prototypes. Steve Jobs and Bill Gates were the Henry Ford and Louis Chevrolet of their times, who capitalized on ideas already commonly known before they started in the business. In the case of Software development, this moment is generally agreed to be the publication in the 1980s of the specifications for the IBM Personal Computer published by IBM employee Philip Don Estridge. Today his move would be seen as a type of crowd-sourcing.

Until that time, software was bundled with the hardware by Original equipment manufacturers (OEMs) such as Data General, Digital Equipment and IBM. When a customer bought a minicomputer, at that time the smallest computer on the market, the computer did not come with Pre-installed software, but needed to be installed by engineers employed by the OEM. Computer hardware companies not only bundled their software, they also placed demands on the location of the hardware in a refrigerated space called a computer room. Most companies had their software on the books for 0 dollars, unable to claim it as an asset (this is similar to financing of popular music in those days). When Data General introduced the Data General Nova, a company called Digidyne wanted to use its RDOS operating system on its own hardware clone. Data General refused to license their software (which was hard to do, since it was on the books as a free asset), and claimed their "bundling rights". The Supreme Court set a precedent called Digidyne v. Data General in 1985. The Supreme Court let a 9th circuit decision stand, and Data General was eventually forced into licensing the Operating System software because it was ruled that restricting the license to only DG hardware was an illegal tying arrangement. Soon after, IBM 'published' its DOS source for free, and Microsoft was born. Unable to sustain the loss from lawyer's fees, Data General ended up being taken over by EMC Corporation. The Supreme Court decision made it possible to value software, and also purchase Software patents. The move by IBM was almost a protest at the time. Few in the industry believed that anyone would profit from it other than IBM (through free publicity). Microsoft and Apple were able to thus cash in on 'soft' products. It is hard to imagine today that people once felt that software was worthless without a machine. There are many successful companies today that sell only software products, though there are still many common software licensing problems due to the complexity of designs and poor documentation, leading to patent trolls.

With open software specifications and the possibility of software licensing, new opportunities arose for software tools that then became the de facto standard, such as DOS for operating systems, but also various proprietary word processing and spreadsheet programs. In a similar growth pattern, proprietary development methods became standard Software development methodology.

Overview

Software includes all the various forms and roles that digitally stored data may have and play in a computer (or similar system), regardless of whether the data is used as code for a CPU, or other interpreter, or whether it represents other kinds of information. Software thus encompasses a wide array of products that may be developed using different techniques such as ordinary programming languages, scripting languages, microcode, or an FPGA configuration.

The types of software include web pages developed in languages and frameworks like HTML, PHP, Perl, JSP, ASP.NET, XML, and desktop applications like OpenOffice.org, Microsoft Word developed in languages like C, C++, Objective-C, Java, C#, or Smalltalk. Application software usually runs on an underlying software operating systems such as Linux or Microsoft Windows. Software (or firmware) is also used in video games and for the configurable parts of the logic systems of automobiles, televisions, and other consumer electronics.

Computer software is so called to distinguish it from computer hardware, which encompasses the physical interconnections and devices required to store and execute (or run) the software. At the lowest level, executable code consists of machine language instructions specific to an individual processor. A machine language consists of groups of binary values signifying processor instructions that change the state of the computer from its preceding state. Programs are an ordered sequence of instructions for changing the state of the computer in a particular sequence. It is usually written in high-level programming languages that are easier and more efficient for humans to use (closer to natural language) than machine language. High-level languages are compiled or interpreted into machine language object code. Software may also be written in an assembly language, essentially, a mnemonic representation of a machine language using a natural language alphabet. Assembly language must be assembled into object code via an assembler.

Types of software

Practical computer systems divide software systems into three major classes: system software, programming software and application software, although the distinction is arbitrary, and often blurred.

System software

System software provides the basic functions for computer usage and helps run the computer hardware and system. It includes a combination of the following:

Device drivers

Operating systems

Servers

Utilities

Window systems

System software is responsible for managing a variety of independent hardware components, so that they can work together harmoniously. Its purpose is to unburden the application software programmer from the often complex details of the particular computer being used, including such accessories as communications devices, printers, device readers, displays and keyboards, and also to partition the computer's resources such as memory and processor time in a safe and stable manner.

Programming software

Programming software usually provides tools to assist a programmer in writing computer programs, and software using different programming languages in a more convenient way. The tools include:

Compilers

Debuggers

Interpreters

Linkers

Text editors

An Integrated development environment (IDE) is a single application that attempts to manage all these functions..

Application software

Application software is developed to aid in any task that benefits from computation. It is a broad category, and encompasses software of many kinds, including the internet browser being used to display this page. This category includes:

Business software

Computer-aided design

Databases

Decision making software

Educational software

Industrial automation

Mathematical software

Medical software

Molecular modeling software

Quantum chemistry and solid state physics software

Simulation software

Spreadsheets

Telecommunications (i.e., the Internet and everything that flows on it)

Video editing software

Video games

Word processing

Software topics

Architecture

Users often see things differently than programmers. People who use modern general purpose computers (as opposed to embedded systems, analog computers and supercomputers) usually see three layers of software performing a variety of tasks: platform, application, and user software.

Platform software: Platform includes the firmware, device drivers, an operating system, and typically a graphical user interface which, in total, allow a user to interact with the computer and its peripherals (associated equipment). Platform software often comes bundled with the computer. On a PC you will usually have the ability to change the platform software.

Application software: Application software or Applications are what most people think of when they think of software. Typical examples include office suites and video games. Application software is often purchased separately from computer hardware. Sometimes applications are bundled with the computer, but that does not change the fact that they run as independent applications. Applications are usually independent programs from the operating system, though they are often tailored for specific platforms. Most users think of compilers, databases, and other "system software" as applications.

User-written software: End-user development tailors systems to meet users' specific needs. User software include spreadsheet templates and word processor templates. Even email filters are a kind of user software. Users create this software themselves and often overlook how important it is. Depending on how competently the user-written software has been integrated into default application packages, many users may not be aware of the distinction between the original packages, and what has been added by co-workers.

Documentation

Most software has software documentation so that the end user can understand the program, what it does, and how to use it. Without clear documentation, software can be hard to use—especially if it is very specialized and relatively complex like Photoshop or AutoCAD.

Developer documentation may also exist, either with the code as comments and/or as separate files, detailing how the programs works and can be modified.

Library

An executable is almost always not sufficiently complete for direct execution. Software libraries include collections of functions and functionality that may be embedded in other applications. Operating systems include many standard Software libraries, and applications are often distributed with their own libraries.

Standard

Since software can be designed using many different programming languages and in many different operating systems and operating environments, software standard is needed so that different software can understand and exchange information between each other. For instance, an email sent from a Microsoft Outlook should be readable from Yahoo! Mail and vice versa.

Execution

Computer software has to be "loaded" into the computer's storage (such as the hard drive or memory). Once the software has loaded, the computer is able to execute the software. This involves passing instructions from the application software, through the system software, to the hardware which ultimately receives the instruction as machine code. Each instruction causes the computer to carry out an operation – moving data, carrying out a computation, or altering the control flow of instructions.

Data movement is typically from one place in memory to another. Sometimes it involves moving data between memory and registers which enable high-speed data access in the CPU. Moving data, especially large amounts of it, can be costly. So, this is sometimes avoided by using "pointers" to data instead. Computations include simple operations such as incrementing the value of a variable data element. More complex computations may involve many operations and data elements together.

Quality and reliability

Software quality is very important, especially for commercial and system software like Microsoft Office, Microsoft Windows and Linux. If software is faulty (buggy), it can delete a person's work, crash the computer and do other unexpected things. Faults and errors are called "bugs." Many bugs are discovered and eliminated (debugged) through software testing. However, software testing rarely – if ever – eliminates every bug; some programmers say that "every program has at least one more bug" (Lubarsky's Law). All major software companies, such as Microsoft, Novell and Sun Microsystems, have their own software testing departments with the specific goal of just testing. Software can be tested through unit testing, regression testing and other methods, which are done manually, or most commonly, automatically, since the amount of code to be tested can be quite large. For instance, NASA has extremely rigorous software testing procedures for many operating systems and communication functions. Many NASA based operations interact and identify each other through command programs called software. This enables many people who work at NASA to check and evaluate functional systems overall. Programs containing command software enable hardware engineering and system operations to function much easier together.

License

The software's license gives the user the right to use the software in the licensed environment. Some software comes with the license when purchased off the shelf, or an OEM license when bundled with hardware. Other software comes with a free software license, granting the recipient the rights to modify and redistribute the software. Software can also be in the form of freeware or shareware.

Patents

Software can be patented in some but not all countries; however, software patents can be controversial in the software industry with many people holding different views about it. The controversy over software patents is about specific algorithms or techniques that the software contains, which may not be duplicated by others and considered intellectual property and copyright infringement depending on the severity.

Design and implementation

Design and implementation of software varies depending on the complexity of the software. For instance, design and creation of Microsoft Word software will take much more time than designing and developing Microsoft Notepad because of the difference in functionalities in each one.

Software is usually designed and created (coded/written/programmed) in integrated development environments (IDE) like Eclipse, Emacs and Microsoft Visual Studio that can simplify the process and compile the program. As noted in different section, software is usually created on top of existing software and the application programming interface (API) that the underlying software provides like GTK+, JavaBeans or Swing. Libraries (APIs) are categorized for different purposes. For instance, JavaBeans library is used for designing enterprise applications, Windows Forms library is used for designing graphical user interface (GUI) applications like Microsoft Word, and Windows Communication Foundation is used for designing web services. Underlying computer programming concepts like quicksort, hashtable, array, and binary tree can be useful to creating software. When a program is designed, it relies on the API. For instance, if a user is designing a Microsoft Windows desktop application, he/she might use the .NET Windows Forms library to design the desktop application and call its APIs like Form1.Close() and Form1.Show() to close or open the application and write the additional operations him/herself that it need to have. Without these APIs, the programmer needs to write these APIs him/herself. Companies like Sun Microsystems, Novell, and Microsoft provide their own APIs so that many applications are written using their software libraries that usually have numerous APIs in them.

Computer software has special economic characteristics that make its design, creation, and distribution different from most other economic goods. A person who creates software is called a programmer, software engineer, software developer, or code monkey, terms that all have a similar meaning.

Industry and organizations

A great variety of software companies and programmers in the world comprise a software industry. Software can be quite a profitable industry: Bill Gates, the founder of Microsoft was the richest person in the world in 2009 largely by selling the Microsoft Windows and Microsoft Office software products. The same goes for Larry Ellison, largely through his Oracle database software. Through time the software industry has become increasingly specialized.

Non-profit software organizations include the Free Software Foundation, GNU Project and Mozilla Foundation. Software standard organizations like the W3C, IETF develop software standards so that most software can interoperate through standards such as XML, HTML, HTTP or FTP.

Other well-known large software companies include Novell, SAP, Symantec, Adobe Systems, and Corel, while small companies often provide innovation.

See also

List of software

hardware

References

External links

Software Wikia

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In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. On the other hand, any monoid can be understood as a special sort of category, and so can any preorder. In general, the objects and arrows may be abstract entities of any kind, and the notion of category provides a fundamental and abstract way to describe mathematical entities and their relationships. This is the central idea of category theory, a branch of mathematics which seeks to generalize all of mathematics in terms of objects and arrows, independent of what the objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. For more extensive motivational background and historical notes, see category theory and the list of category theory topics.

Two categories are the same if they have the same collection of objects, the same collection of arrows, and the same associative method of composing any pair of arrows. Two categories may also be considered "equivalent" for purposes of category theory, even if they are not precisely the same.

Well-known categories are denoted by a short capitalized word or abbreviation in bold or italics: examples include Set, the category of sets and set functions; Ring, the category of rings and ring homomorphisms; and Top, category of topological spaces and continuous maps. All of the preceding categories have the identity map as identity arrow and composition as the associative operation on arrows.

The standard text on category theory is "Categories for the Working Mathematician" by Saunders Mac Lane. Other references are given in the References below. The basic definitions in this article are contained within the first few chapters of any of these books.

Definition

A category C consists of

a class ob(C) of objects

a class hom(C) of morphisms, or arrows, or maps, between the objects. Each morphism f has a unique source object a and target object b where a and b are in ob(C). We write f: a → b, and we say "f is a morphism from a to b". We write hom(a, b) (or hom_C(a, b) when there may be confusion about to which category hom(a, b) refers) to denote the hom-class of all morphisms from a to b. (Some authors write Mor(a, b) or simply C(a, b) instead.)

for every three objects a, b and c, a binary operation hom(a, b) × hom(b, c) → hom(a, c) called composition of morphisms; the composition of f : a → b and g : b → c is written as g o f or gf. (Some authors write fg or f;g.)

such that the following axioms hold:

(associativity) if f : a → b, g : b → c and h : c → d then h o (g o f) = (h o g) o f, and

(identity) for every object x, there exists a morphism 1_x : x → x (some authors write id_x) called the identity morphism for x, such that for every morphism f : a → b, we have 1_b o f = f = f o 1_a.

From these axioms, one can prove that there is exactly one identity morphism for every object. Some authors use a slight variation of the definition in which each object is identified with the corresponding identity morphism.

History

Category theory first appeared in a paper entitled "General Theory of Natural Equivalences", written by Samuel Eilenberg and Saunders Mac Lane in 1945.

Small and large categories

A category C is called small if both ob(C) and hom(C) are actually sets and not proper classes, and large otherwise. A locally small category is a category such that for all objects a and b, the hom-class hom(a, b) is a set, called a homset. Many important categories in mathematics (such as the category of sets), although not small, are at least locally small.

Examples

The class of all sets together with all functions between sets, where composition is the usual function composition, forms a large category, Set. It is the most basic and the most commonly used category in mathematics. The category Rel consists of all sets, with binary relations as morphisms. Abstracting from relations instead of functions yields allegories instead of categories.

Any class can be viewed as a category whose only morphisms are the identity morphisms. Such categories are called discrete. For any given set I, the discrete category on I is the small category that has the elements of I as objects and only the identity morphisms as morphisms. Discrete categories are the simplest kind of category.

Any preordered set (P, ≤) forms a small category, where the objects are the members of P, the morphisms are arrows pointing from x to y when x ≤ y. Between any two objects there can be at most one morphism. The existence of identity morphisms and the composability of the morphisms are guaranteed by the reflexivity and the transitivity of the preorder. By the same argument, any partially ordered set and any equivalence relation can be seen as a small category. Any ordinal number can be seen as a category when viewed as an ordered set.

Any monoid (any algebraic structure with a single associative binary operation and an identity element) forms a small category with a single object x. (Here, x is any fixed set.) The morphisms from x to x are precisely the elements of the monoid, the identity morphism of x is the identity of the monoid, and the categorical composition of morphisms is given by the monoid operation. Several definitions and theorems about monoids may be generalized for categories.

Any group can be seen as a category with a single object in which every morphism is invertible (for every morphism f there is a morphism g that is both left and right inverse to f under composition) by viewing the group as acting on itself by left multiplication. A morphism which is invertible in this sense is called an isomorphism.

A groupoid is a category in which every morphism is an isomorphism. Groupoids are generalizations of groups, group actions and equivalence relations.

Any directed graph generates a small category: the objects are the vertices of the graph, and the morphisms are the paths in the graph (augmented with loops as needed) where composition of morphisms is concatenation of paths. Such a category is called the free category generated by the graph.

The class of all preordered sets with monotonic functions as morphisms forms a category, Ord. It is a concrete category, i.e. a category obtained by adding some type of structure onto Set, and requiring that morphisms are functions that respect this added structure.

The class of all groups with group homomorphisms as morphisms and function composition as the composition operation forms a large category, Grp. Like Ord, Grp is a concrete category. The category Ab, consisting of all abelian groups and their group homomorphisms, is a full subcategory of Grp, and the prototype of an abelian category. Other examples of concrete categories are given by the following table.

!Category	!Objects	!Morphisms
		magma homomorphisms
	smooth manifolds	p-times continuously differentiable maps
	metric spaces	short maps
	R-Modules, where R is a Ring	module homomorphisms
		ring homomorphisms
	topological spaces
	uniform spaces	uniformly continuous functions
		K-linear maps

Fiber bundles with bundle maps between them form a concrete category.

The category Cat consists of all small categories, with functors between them as morphisms.

Construction of new categories

Dual category

Any category C can itself be considered as a new category in a different way: the objects are the same as those in the original category but the arrows are those of the original category reversed. This is called the dual or opposite category and is denoted C^op.

Product categories

If C and D are categories, one can form the product category C × D: the objects are pairs consisting of one object from C and one from D, and the morphisms are also pairs, consisting of one morphism in C and one in D. Such pairs can be composed componentwise.

Types of morphisms

A morphism f : a → b is called

a monomorphism (or monic) if fg₁ = fg₂ implies g₁ = g₂ for all morphisms g₁, g₂ : x → a.

an epimorphism (or epic) if g₁f = g₂f implies g₁ = g₂ for all morphisms g₁, g₂ : b → x.

a bimorphism if it is both a monomorphism and an epimorphism.

a retraction if it has a right inverse, i.e. if there exists a morphism g : b → a with fg = 1_b.

a section if it has a left inverse, i.e. if there exists a morphism g : b → a with gf = 1_a.

an isomorphism if it has an inverse, i.e. if there exists a morphism g : b → a with fg = 1_b and gf = 1_a.

an endomorphism if a = b. The class of endomorphisms of a is denoted end(a).

an automorphism if f is both an endomorphism and an isomorphism. The class of automorphisms of a is denoted aut(a).

Every retraction is an epimorphism. Every section is a monomorphism. The following three statements are equivalent:

f is a monomorphism and a retraction;

f is an epimorphism and a section;

f is an isomorphism.

Relations among morphisms (such as fg = h) can most conveniently be represented with commutative diagrams, where the objects are represented as points and the morphisms as arrows.

Types of categories

In many categories, e.g. Ab or Vect_K, the hom-sets hom(a, b) are not just sets but actually abelian groups, and the composition of morphisms is compatible with these group structures; i.e. is bilinear. Such a category is called preadditive. If, furthermore, the category has all finite products and coproducts, it is called an additive category. If all morphisms have a kernel and a cokernel, and all epimorphisms are cokernels and all monomorphisms are kernels, then we speak of an abelian category. A typical example of an abelian category is the category of abelian groups.

A category is called complete if all limits exist in it. The categories of sets, abelian groups and topological spaces are complete.

A category is called cartesian closed if it has finite direct products and a morphism defined on a finite product can always be represented by a morphism defined on just one of the factors. Examples include Set and CPO, the category of complete partial orders with Scott-continuous functions.

A topos is a certain type of cartesian closed category in which all of mathematics can be formulated (just like classically all of mathematics is formulated in the category of sets). A topos can also be used to represent a logical theory.

See also

Enriched category

Higher category theory

Table of mathematical symbols

Notes

References

(now free on-line edition, GNU FDL). . . (revised and corrected free online version of Grundlehren der mathematischen Wissenschaften (278) Springer-Verlag, 1983). . . . . . . .

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