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See also Abstract type

abstract data type (ADT) - A mathematical model for data types in which a data type is defined by its behavior (semantics) from the point of view of a user of the data, specifically in terms of possible values, possible operations on data of this type, and the behavior of these operations. This contrasts with data structures, which are concrete representations of data from the point of view of an implementer rather than a user.

abstract data type “A *data type that is defined solely in terms of the operations that apply to objects of the type without commitment as to how the value of such an object is to be represented (see data abstraction).” (Fair Use ODCS)

“An abstract data type strictly is a triple (D,F,A) consisting of a set of domains D, a set of functions F each with range and domain in D, and a set of axioms A, which specify the properties of the functions in F. By distinguishing one of the domains d in D, a precise characterization is obtained of the *data structure that the abstract data type imposes on d.” (Fair Use ODCS)

“For example, the natural numbers comprise an abstract data type, where the domain d is and there is an auxiliary domain. The functions or operations are ZERO, ISZERO, SUCC, and ADD and the axioms are: These axioms specify precisely the laws that must hold for any implementation of the natural numbers. (Note that a practical implementation could not fulfil the axioms because of word length and overflow.) Such precise characterization is invaluable both to the user and the implementer. Sometimes the concept of function is extended to procedures with multiple results.” (Fair Use ODCS)

Snippet from Wikipedia: Abstract data type

In computer science, an abstract data type (ADT) is a mathematical model for data types, defined by its behavior (semantics) from the point of view of a user of the data, specifically in terms of possible values, possible operations on data of this type, and the behavior of these operations. This mathematical model contrasts with data structures, which are concrete representations of data, and are the point of view of an implementer, not a user. For example, a stack has push/pop operations that follow a Last-In-First-Out rule, and can be concretely implemented using either a list or an array. Another example is a set which stores values, without any particular order, and no repeated values. Values themselves are not retrieved from sets, rather one tests a value for membership to obtain a Boolean "in" or "not in".

ADTs are a theoretical concept, used in formal semantics and program verification and, less strictly, in the design and analysis of algorithms, data structures, and software systems. Most mainstream computer languages do not directly support formally specifying ADTs. However, various language features correspond to certain aspects of implementing ADTs, and are easily confused with ADTs proper; these include abstract types, opaque data types, protocols, and design by contract. For example, in modular programming, the module declares procedures that correspond to the ADT operations, often with comments that describe the constraints. This information hiding strategy allows the implementation of the module to be changed without disturbing the client programs, but the module only informally defines an ADT. The notion of abstract data types is related to the concept of data abstraction, important in object-oriented programming and design by contract methodologies for software engineering.

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