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## Topic: set data type

topics > mathematics > Group: sets

Group:
data structures
Group:
derived data types

Topic:
collection class
Topic:
data type as a set of values
Topic:
database schema
Topic:
set construction
Topic:
set operations
Topic:
set-oriented languages

#### Summary

Sets are a universal data type with a strong mathematical foundation. They consist of a base type and a membership predicate. The base type restricts membership to certain objects, and the membership predicate defines which of those objects are actually in the set. Sets may be ordered (ranked) or unordered, with duplicated or unique elements. Sets may be operated upon or they may be used in universally quantified control structures such as "for each X in S do". (cbb 5/80)
Subtopic: what is a set

 Quote: a set is the barest notion of data storage, i.e., mere existence [»millHD2_1986]

Subtopic: ordered vs. unordered set

 QuoteRef: grayJC_1973 ;;168 sets unordered or indexed, fixed or free (conversions between types e.g., undex (set) QuoteRef: grayJC_1973 ;;168 unordered sets do not contain duplicates while lists may QuoteRef: simscrip_1971 ;;83 ranked sets always maintain order QuoteRef: hehnEC7_1975 ;;9 unordered sets by braces around a sequence of values

Subtopic: multi-set or bag

 Quote: a bag is an unordered collection that allows duplicates; as used in probability problems [»straC8_1967] QuoteRef: earlJ4_1974 ;;35 multi-sets (duplicates allowed) and ordered sets QuoteRef: bobrDG9_1974 ;;161 qlisp: a "bag" is an unordered tuple (i.e., may have duplicates e.g., tuple plus (bag 5 c d d) matches 5+c+d+d and d+5+c+d

Subtopic: set as bit array

 Quote: a Modula-3 set is represented by a packed bit array

Subtopic: geometric set

 QuoteRef: katzJH_1963 ;;2 area set: an ordered set of areas QuoteRef: katzJH_1963 ;;2 line: an order set of points where each point member of a corresponding area in an area set QuoteRef: katzJH_1963 ;;2 area: a set of points in a property space QuoteRef: wirtN1_1971 ;;47 sets have a base type, null set [.] ??

Subtopic: set ownership

 QuoteRef: markHM_1963 ;;36 sets can be owned by one or two entities (i.e., membership restricted)

Subtopic: problems with set data type

 Quote: associate persistence with values and separate type from extent; e.g., the integer extent is almost useless; may want multiple extents [»buneP5_1986] Quote: XML does not distinguish between data and sets of data [»boswA10_2005]

Related Topics

Group: data structures   (12 topics, 278 quotes)
Group: derived data types   (9 topics, 119 quotes)

Topic: collection class (11 items)
Topic: data type as a set of values (20 items)
Topic: database schema (29 items)
Topic: set construction (20 items)
Topic: set operations (12 items)
Topic: set-oriented languages
(20 items)

Updated barberCB 1/05