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## Topic: set construction

topics > mathematics > Group: sets

Group:
sequences

Topic:
collection class
Topic:
database queries, joins, and relational algebra
Topic:
relational database
Topic:
sequence generators
Topic:
set data type
Topic:
set definition by extension or intension
Topic:
tuples

#### Summary

A predicate, such as equality, is used to partition a class into one or more sets. Adding an element to a concrete set depends on the definition and implementation of the set. This may include sorted entry, add to the beginning, or check for duplicated elements. (cbb 5/80)

The Connection machine used sets to control which processors executed which instructions. Pierce defined existential graphs. (cbb 4/98)

Subtopic: intentional vs. extensional set

 Quote: minimal set predicate: the set of things having relationship x to object y [»kentW_1978] QuoteRef: milgE_1972 ;;518 t values -- atomic (integers, object refs) and sets (explicit-enumerated and conceptual -- defined implicitly through predicate on t values)

Subtopic: set declaration

 QuoteRef: simscrip_1971 ;;77 define a set by describing it as a queue or stack or set, optional ranking attribute (s) without certain routings and attributes QuoteRef: buxtJN_1962 ;;195 set is an ordered list (queue) of class subscripts i.e., within a class

Subtopic: set operations -- cartesian product, etc.

 Quote: constructing new type like deriving new sets by cartesian product, mappings, list, union, subset, superset [»nordB3_1976, OK]

Subtopic: projection and reduction

 QuoteRef: grayJC_1973 ;;169 projection (component-name.param).(param//item-set) is a slice across the set by a component name QuoteRef: grayJC_1973 ;;169 reduction (parametric relationship).(param//set) is a slice based on a predicate (short form e.g., (age=50).parents)

Subtopic: grouping, partition

 QuoteRef: katzJH_1963 ;;2 bundling function: defines a set of lines over an area set QuoteRef: katzJH_1963 ;;2 glumping function: a partition of a set into "elements" made of points with equal values

Subtopic: graphical operations

 Quote: Pierce--existential graphs, e.g., negation as a cut in a sheet of assertion; like Brown's Laws of Form [»sowaJF_1984]

Subtopic: generators and filters

 Quote: comprehension syntax creates sets from generators and filters; e.g., Miranda and Wadler's formalization [»wongL9_2000] QuoteRef: morrJH8_1972 ;;761 build sets through for loops e.g., {x: x .memberOf. nbr .suchThat. odd(x)} is all odd x in nbr

Subtopic: file I/O

 QuoteRef: markHM_1963 ;;36 file variable In set done according to definition of set (also can get first, or delete) QuoteRef: simscrip_1971 ;;116 File to put entity into a set (how determined by set definition

Subtopic: membership by bit or tag

 Quote: in a Connection Machine can allocate one bit per cell to indicate set membership [»hillWD_1985] Quote: if sets are disjoint, can represent membership by a tag value identifying the cell's set [»hillWD_1985, OK] Quote: the domain of a xector; mark members of the set with bits, tags, or pointers [»hillWD_1985] Quote: on the Connection Machine, convert pointer-represented sets to bit representation by propagating a marker through the fanout cells [»hillWD_1985]

Subtopic: membership by links

 Quote: can represent a set by a root cell pointing to a few fanout cells that point to the set's members [»hillWD_1985] Quote: the Connection Machine uses trees and butterflies for collecting, combining, and spreading information, e.g., sets; need two-way pointers [»hillWD_1985]

Related Topics

Group: sequences   (7 topics, 97 quotes)

Topic: collection class (11 items)
Topic: database queries, joins, and relational algebra (34 items)
Topic: relational database (35 items)
Topic: sequence generators (16 items)
Topic: set data type (16 items)
Topic: set definition by extension or intension (18 items)
Topic: tuples
(17 items)

Updated barberCB 1/05