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library(ordsets): Ordered set manipulation |

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- library(ordsets): Ordered set manipulation
- is_ordset/1
- ord_empty/1
- ord_seteq/2
- list_to_ord_set/2
- ord_intersect/2
- ord_disjoint/2
- ord_intersect/3
- ord_intersection/2
- ord_intersection/3
- ord_intersection/4
- ord_add_element/3
- ord_del_element/3
- ord_selectchk/3
- ord_memberchk/2
- ord_subset/2
- ord_subtract/3
- ord_union/2
- ord_union/3
- ord_union/4
- ord_symdiff/3

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Ordered sets are lists with unique elements sorted to the standard
order of terms (see sort/2).
Exploiting ordering, many of the set operations can be expressed in
order N rather than N`^`

2 when dealing with unordered sets
that may contain duplicates. The `library(ordsets)`

is
available in a number of Prolog implementations. Our predicates are
designed to be compatible with common practice in the Prolog community.
The implementation is incomplete and relies partly on `library(oset)`

,
an older ordered set library distributed with SWI-Prolog. New
applications are advised to use `library(ordsets)`

.

Some of these predicates match directly to corresponding list operations. It is advised to use the versions from this library to make clear you are operating on ordered sets. An exception is member/2. See ord_memberchk/2.

The ordsets library is based on the standard order of terms. This
implies it can handle all Prolog terms, including variables. Note
however, that the ordering is not stable if a term inside the set is
further instantiated. Also note that variable ordering changes if
variables in the set are unified with each other or a variable in the
set is unified with a variable that isāolder' than the newest
variable in the set. In practice, this implies that it is allowed to use
`member(X, OrdSet)`

on an ordered set that holds variables
only if X is a fresh variable. In other cases one should cease using it
as an ordset because the order it relies on may have been changed.

- [semidet]
**is_ordset**(`@Term`) - True if
`Term`is an ordered set. All predicates in this library expect ordered sets as input arguments. Failing to fullfil this assumption results in undefined behaviour. Typically, ordered sets are created by predicates from this library, sort/2 or setof/3. - [semidet]
**ord_empty**(`?List`) - True when
`List`is the empty ordered set. Simply unifies list with the empty list. Not part of Quintus. - [semidet]
**ord_seteq**(`+Set1, +Set2`) - True if
`Set1`and`Set2`have the same elements. As both are canonical sorted lists, this is the same as ==/2.- Compatibility
- sicstus

- [det]
**list_to_ord_set**(`+List, -OrdSet`) - Transform a list into an ordered set. This is the same as sorting the list.
- [semidet]
**ord_intersect**(`+Set1, +Set2`) - True if both ordered sets have a non-empty intersection.
- [semidet]
**ord_disjoint**(`+Set1, +Set2`) - True if
`Set1`and`Set2`have no common elements. This is the negation of ord_intersect/2. **ord_intersect**(`+Set1, +Set2, -Intersection`)`Intersection`holds the common elements of`Set1`and`Set2`.- deprecated
- Use ord_intersection/3

**ord_intersection**(`+PowerSet, -Intersection`)`Intersection`of a powerset. True when`Intersection`is an ordered set holding all elements common to all sets in`PowerSet`.- Compatibility
- sicstus

- [det]
**ord_intersection**(`+Set1, +Set2, -Intersection`) `Intersection`holds the common elements of`Set1`and`Set2`. Uses ord_disjoint/2 if`Intersection`is bound to`[]`

on entry.- [det]
**ord_intersection**(`+Set1, +Set2, ?Intersection, ?Difference`) `Intersection`and difference between two ordered sets.`Intersection`is the intersection between`Set1`and`Set2`, while`Difference`is defined by`ord_subtract(Set2, Set1, Difference)`

.- See also
- ord_intersection/3 and ord_subtract/3.

- [det]
**ord_add_element**(`+Set1, +Element, ?Set2`) - Insert an element into the set. This is the same as
`ord_union(Set1, [Element], Set2)`

. - [det]
**ord_del_element**(`+Set, +Element, -NewSet`) - Delete an element from an ordered set. This is the same as
`ord_subtract(Set, [Element], NewSet)`

. - [semidet]
**ord_selectchk**(`+Item, ?Set1, ?Set2`) - Selectchk/3, specialised for ordered sets. Is true when
`select(Item, Set1, Set2)`

and`Set1`,`Set2`are both sorted lists without duplicates. This implementation is only expected to work for`Item`ground and either`Set1`or`Set2`ground. The "chk" suffix is meant to remind you of memberchk/2, which also expects its first argument to be ground.`ord_selectchk(X, S, T)`

`=>`

`ord_memberchk(X, S)`

&`\+`

`ord_memberchk(X, T)`

.- author
- Richard O'Keefe

- [semidet]
**ord_memberchk**(`+Element, +OrdSet`) - True if
`Element`is a member of`OrdSet`, compared using ==. Note that*enumerating*elements of an ordered set can be done using member/2.Some Prolog implementations also provide ord_member/2, with the same semantics as ord_memberchk/2. We believe that having a semidet ord_member/2 is unacceptably inconsistent with the *_chk convention. Portable code should use ord_memberchk/2 or member/2.

- author
- Richard O'Keefe

- [semidet]
**ord_subset**(`+Sub, +Super`) - Is true if all elements of
`Sub`are in`Super` - [det]
**ord_subtract**(`+InOSet, +NotInOSet, -Diff`) `Diff`is the set holding all elements of`InOSet`that are not in`NotInOSet`.- [det]
**ord_union**(`+SetOfSets, -Union`) - True if
`Union`is the union of all elements in the superset`SetOfSets`. Each member of`SetOfSets`must be an ordered set, the sets need not be ordered in any way.- author
- Copied from YAP, probably originally by Richard O'Keefe.

- [det]
**ord_union**(`+Set1, +Set2, -Union`) `Union`is the union of`Set1`and`Set2`- [det]
**ord_union**(`+Set1, +Set2, -Union, -New`) - True iff
`ord_union(Set1, Set2, Union)`

and`ord_subtract(Set2, Set1, New)`

. - [det]
**ord_symdiff**(`+Set1, +Set2, ?Difference`) - Is true when
`Difference`is the symmetric difference of`Set1`and`Set2`. I.e.,`Difference`contains all elements that are not in the intersection of`Set1`and`Set2`. The semantics is the same as the sequence below (but the actual implementation requires only a single scan).ord_union(Set1, Set2, Union), ord_intersection(Set1, Set2, Intersection), ord_subtract(Union, Intersection, Difference).

For example:

?- ord_symdiff([1,2], [2,3], X). X = [1,3].

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