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From Wikipedia

Abstract type

This article discusses types with no direct members; see alsoAbstract data type.

In programming languages, an abstract type is a type in a nominative type system which is declared by the programmer. It may or may not include abstract methods or properties that contains members which are also shared members of some declared subtype. In many object oriented programming languages, abstract types are known as abstract base classes, interfaces,traits,mixins, flavors, or roles. Note that these names refer to different language constructs which are (or may be) used to implement abstract types.

Two overriding characteristics of abstract classes is that their use is a design issue in keeping with the best object oriented programming practices, and by their nature are unfinished.

Signifying abstract types

Abstract classes can be created, signified, or simulated in several ways:

  • By use of the explicit keywordabstract in the class definition, as in Java, D or C#.
  • By including, in the class definition, one or more methods (called purevirtual functionsinC++), which the class is declared to accept as part of its protocol, but for which no implementation is provided.
  • By inheriting from an abstract type, and not overriding all missing features necessary to complete the class definition.
  • In many dynamically typed languages such as Smalltalk, any class which sends a particular method to this, but doesn't implement that method, can be considered abstract. (However, in many such languages, the error is not detected until the class is used, and the message returns results in an exception error message such as "does Not Understand").

Example: abstract class demo { abstract void sum(int x,int y); }

Use of abstract types

Abstract types are an important feature in statically typed OO languages. They do not occur in languages without subtyping. Many dynamically typed languages have no equivalent feature (although the use of duck typing makes abstract types unnecessary); however traits are found in some modern dynamically-typed languages.

Some authors argue that classes should be leaf classes (have no subtypes), or else be abstract.

Abstract types are useful in that they can be used to define and enforce a protocol; a set of operations which all objects that implement the protocol must support.

Types of abstract types

There are several mechanisms for creating abstract types, which vary based on their capability.

  • Full abstract base classes are classes either explicitly declared to be abstract, or which contain abstract (unimplemented) methods. Except the instantiation capability, they have the same capabilities as a concrete class or type. Full abstract types were present in the earliest versions of C++; and the abstract base class remains the only language construct for generating abstract types in C++. A class having only pure virtual methods is often called a pure virtual class; it is necessarily abstract.
  • Java includes interfaces, an abstract type which may contain method signatures and constants (final variables), but no method implementations or non-final data members. Java classes may "implement" multiple interfaces. An abstract class in Java may implement interfaces and define some method signatures while keeping other methods abstract with the "abstract" keyword.
  • Traits are a more recent approach to the problem, found in Scala and Perl 6 (there known as roles), and proposed as an extension to Smalltalk (wherein the original implementation was developed). Traits are unrestricted in what they include in their definition, and multiple traits may be composed into a class definition. However, the composition rules for traits differ from standard inheritance, to avoid the semantic difficulties often associated with multiple inheritance.

Abstract algebra

Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and real or complex numbers, often now called elementary algebra. The distinction is rarely made in more recent writings.

Contemporary mathematics and mathematical physics make extensive use of abstract algebra; for example, theoretical physics draws on Lie algebras. Subject areas such as algebraic number theory, algebraic topology, and algebraic geometry apply algebraic methods to other areas of mathematics. Representation theory, roughly speaking, takes the 'abstract' out of 'abstract algebra', studying the concrete side of a given structure; see model theory.

Two mathematical subject areas that study the properties of algebraic structures viewed as a whole are universal algebra and category theory. Algebraic structures, together with the associated homomorphisms, form categories. Category theory is a powerful formalism for studying and comparing different algebraic structures.

History and examples

As in other parts of mathematics, concrete problems and examples have played important roles in the development of algebra. Through the end of the nineteenth century many, perhaps most of these problems were in some way related to the theory of algebraic equations. Among major themes we can mention:

Numerous textbooks in abstract algebra start with axiomatic definitions of various algebraic structures and then proceed to establish their properties, creating a false impression that somehow in algebra axioms had come first and then served as a motivation and as a basis of further study. The true order of historical development was almost exactly the opposite. For example, the hypercomplex numbers of the nineteenth century had kinematic and physical motivations but challenged comprehension. Most theories that we now recognize as parts of algebra started as collections of disparate facts from various branches of mathematics, acquired a common theme that served as a core around which various results were grouped, and finally became unified on a basis of a common set of concepts. An archetypical example of this progressive synthesis can be seen in the theory of groups.

Early group theory

There were several threads in the early development of group theory, in modern language loosely corresponding to number theory, theory of equations, and geometry, of which we concentrate on the first two.

Leonhard Euler considered algebraic operations on numbers modulo an integer, modular arithmetic, proving his generalization of Fermat's little theorem. These investigations were taken much further by Carl Friedrich Gauss, who considered the structure of multiplicative groups of residues mod n and established many properties of cyclic and more general abelian groups that arise in this way. In his investigations of composition of binary quadratic forms, Gauss explicitly stated the associative law for the composition of forms, but like Euler before him, he seems to have been more interested in concrete results than in general theory. In 1870, Leopold Kronecker gave a definition of an abelian group in the context of ideal class groups of a number field, a far-reaching generalization of Gauss's work. It appears that he did not tie it with previous work on groups, in particular, permutation groups. In 1882 considering the same question, object which does not exist at any particular time or place, but rather exists as a type of thing (as an idea, or abstraction). In philosophy, an important distinction is whether an object is considered abstract or concrete. Abstract objects are sometimes called abstracta (sing. abstractum) and concrete objects are sometimes called concreta (sing. concretum).

In philosophy

The type-token distinction identifies that physical objects are tokens of a particular type of thing. The "type" that it is a part of itself is an abstract object. The abstract-concrete distinction is often introduced and initially understood in terms of paradigmatic examples of objects of each kind:

Abstract objects have often garnered the interest of philosophers because they are taken to raise problems for popular theories. In ontology, abstract objects are considered problematic for physicalism and naturalism. Historically, the most important ontological dispute about abstract objects has been the problem of universals. In epistemology, abstract objects are considered problematic for empiricism. If abstracta lack causal powers or spatial location, how do we know about them? It is hard to say how they can affect our sensory experiences, and yet we seem to agree on a wide range of claims about them. Some, such as Edward Zalta and arguably Plato (in his Theory of Forms), have held that abstract objects constitute the defining subject matter of metaphysics or philosophical inquiry more broadly. To the extent that philosophy is independent of empirical research, and to the extent that empirical questions do not inform questions about abstracta, philosophy would seem specially suited to answering these latter questions.

Abstract objects and causality

Another popular proposal for drawing the abstract-concrete distinction has it that an object is abstract if it lacks any causal powers. A causal power is an ability to affect something causally. Thus the empty set is abstract because it cannot act on other objects. One problem for this view is that it is not clear exactly what it is to have a causal power. For a more detailed exploration of the abstract-concrete distinction, follow the link below to the Stanford Encyclopedia article.

Concrete and abstract thinking

Jean Piaget uses the terms "concrete" and "formal" to describe the different types of learning. Concrete thinking involves facts and descriptions about everyday, tangible objects, while abstract (formal operational) thinking involves a mental process.


In language, abstract and concrete objects are often synonymous with concrete nouns and abstract nouns. In English, many abstract nouns are formed by adding noun-forming suffixes ("-ness", "-ity", "-tion") to adjectives or verbs. Examples are "happiness", "circulation" and "serenity".

From Yahoo Answers

Question:I am only posing the question not making a statement. This as been suggested by someone else. I am just probing for opinions. Please .... if you dont know the defintion of abstract thought, please look it up before answering. let me reiterate - Im not making the statement here. Im just posing the question. Levonna- you just defined abstraction. not exactly the same thing

Answers:No,but it can seem that way because in the U.S. most whites are "professional-level" meaning they have only very,very highly specialized educations. Worse,they make a lot of money,so they are always busy,busy,busy. These are not conditions that are conducive to learning to think well. Most whites just perform their specialized function and then run out to play; mostly upscale restaurants,etc. Learning to think involves giving yourself a lot of unstructured time. Most whites don't do that anymore. They work,they play hard. Think? Not unless it's part of their job. I'm white,middle-class,and it's definitely something you notice. Lack of common-sense,that's also getting to be a problem with the upscales. The country is essentially being run by experts who have no real ability to think in abstract terms at all. They just link facts,organize information. It's never integrated.

Question:i need to know the definition of abstract art... if anyone could help:) Thanks:D

Answers:A trend in painting and sculpture in the twentieth century. Abstract art seeks to break away from traditional representation of physical objects. It explores the relationships of forms and colors, whereas more traditional art represents the world in recognizable images.


Answers:well their inst really no definition [ i think but their is pictures] here are some pictures of natural abstraction http://naturalabstraction.com/flora1.html

Question:Would learning Discrete Mathematics, or rather - Set Theory - in particular, help me learn Modern/Abstract Algebra? I've gotten Fraleigh's Abstract Algebra and find it a bit too obscure due to the heavy set notation and wonder, have all readers of this book learned set theory beforehand or do they struggle but eventually pick up on it? Thanks :) _______________________________

Answers:Set theory is used, but is not that important, for abstract algebra. My suggestion: start with an easier book. Your university library should have some. IMHO the most important thing for learning abstract algebra is "mathematical maturity". This comes from taking classes such as calculus and linear algebra in which you get exposed to abstract thinking and proofs, especially proofs.

From Youtube

Photoshop CS5 - Abstract Shapes Effect - Tutorial :Photoshop Difficulty Level : 3.8/10.00 In this tutorial you will be learning how to create a abstract effect, out of shapes. Easy to follow High Definition I'm pretty sure this tutorial will work for previous versions of Adobe Photoshop too. Rate + Comment + Subscribe = More Tutorials

ABSTRACT/REALISM DEFINITION :what does abstract art and realism have in common