Topic: collection class
Topic: database queries, joins, and relational algebra
Topic: foreach and for all statements
Topic: quantified repetition
Topic: set data type
Topic: setoriented languages
 
Summary
Many operations have been defined on sets, usually based on mathematical usage. These include permutations, cross product, set difference, indirect product, reductions, intersection, union, membership, and powerset. An important part of set operations is defining set literals, the null set, and base types. Unordered, duplicatedelement sets can be implemented as sequences. Sets with a small basetype can be implemented by a bit string whose length matches the base type's size. (cbb 5/80)
Relational databases allow information processing on sets. (cbb 1/90)
Subtopic: add/remove
Quote: assigning to a set is adding a member; accessing a set is removing a member [»millHD2_1986]
 Subtopic: set operations
Quote: in CPL, convert a set into a sorted list
 Quote: ring operations to insert, remove, copy, foreach forward/backward; no special cases for empty and one member rings [»suthIE5_1963]
 QuoteRef: grayJC_1973 ;;169 also set size, component type, union, intersection, difference, append
 QuoteRef: schwJT_1973 ;;502 npow (k,a) set of all subsets of A having k elements
 QuoteRef: wellMB4_1964 ;;433 set difference by all x such that x=ab for a in A, b in B, and ab >= 0 [others do the same on any range i.e., bounded by high and low for the set.
 QuoteRef: wirtN1_1971 ;;38 operations on powersets  int, union, difference, membership
 QuoteRef: grayJC_1973 ;;169 permute (indexset '% set) e.g., [3 2]'%[a b c d] == [c b]
 QuoteRef: grayJC_1973 ;;170 indirect product of two sets: from all element is set A form a reduction in set B and check number of elements
 Subtopic: aggregate operator
Quote: aggregate operator much simpler than normal programming language; e.g., sum nectar of all flowers [»paneJF9_2002]
 Subtopic: implementation
Quote: set union, intersection, and universal qualifier can be unittime operations on the Connection Machine [»hillWD_1985]
 Quote: implement lattice operations in almost constant time by encoding the lattice in binary; greatest lower bound, l.u.b., and relative complement [»aitkH1_1989]

Related Topics
Topic: collection class (11 items)
Topic: database queries, joins, and relational algebra (34 items)
Topic: foreach and for all statements (16 items)
Topic: quantified repetition (11 items)
Topic: set data type (16 items)
Topic: setoriented languages (20 items)
