Topic: data type as a set of values and a set of operations

topics > computer science > data > Group: data type

program module

data type as a set of operations
data type as a set of values
object-oriented data types
object-oriented classes
object-oriented objects
representation data type
universal data type


A data type defines a set of values and a set of operations on those values. The operations defines an interpretation of the values. This works well at the concrete, value, or atomic type level. A data type protects the values by restricting the set of operations.

As noted under data type as a set of values, it becomes difficult to treat objects as values as they become more complex. An exception is object-oriented programming where the set of values is the instances of a class. It works here because everything is an object; there are no values.

Clusters are used to define a set of operations on a set of values defined by the representation type. In both cases, this combines the specification of behavior with the specification of representation. (cbb 1/90)

Subtopic: type as value and operations up

Quote: data and operations are the warp and weft of experience; state and process descriptions; e.g., integer and boolean have identical bit strings [»brinP_1973]
Quote: a concrete type or value type is like an 'int'; it does one thing well and efficiently without inheritance; e.g., 'date' [»koenA12_1995]
Quote: a 'hard' type is defined by the language with a representation, associated operations and values [»moffDV7_1981]
Quote: a data type indicates how something is measured, its set of possible values, and its set of possible operations [»handP_1981]
Quote: a data type is a set of values operated on by a set of operations [»berrDM4_1977]
Quote: in Algol languages, data types are sets of operations with an interpretation of values
Quote: in Russell, the meaning of a data type is the meaning of its operations over the universal domain of bit strings [»demeA_1978]
Quote: a data type is a set of operations specifying an interpretation of values of a universal value space [»demeA_1978]
Quote: data types interpret values of a universal space where any operation can apply to any value
Quote: an abstract data type is a representation type and a set of operations [»johnRI3_1976]
Quote: a data type is a set of data structures for discussing a set of operations on objects of that type [»scotD6_1972]
Quote: a programmer sees types as partitioning values into classes with common attributes and operations [»wegnP10_1986]
Quote: IBM 360 cells contain a value; arrays contain an ordered set of cells; operations are a mapping from operands to results [»wirtN1_1968]

Subtopic: type as fields and methods up

Quote: an object is a data record of fields and a method suite of procedures that accept the object as a first argument [»cardL_1991]

Subtopic: types as interpretation up

Quote: system programmers sees types as protection of bit strings from unintended interpretation [»wegnP10_1986]

Subtopic: concrete vs. abstract up

Quote: use concrete types for efficiency and abstract types for flexibility; neither are useful for inheritance

Related Topics up

Group: program module   (10 topics, 336 quotes)
Group: sets   (7 topics, 148 quotes)

Topic: data type as a set of operations (38 items)
Topic: data type as a set of values (20 items)
Topic: object-oriented data types (29 items)
Topic: object-oriented classes (67 items)
Topic: object-oriented objects (39 items)
Topic: representation data type (21 items)
Topic: universal data type
(18 items)

Updated barberCB 5/04
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