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
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 is `older' 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.
- is_ordset(@Term) is semidet
- 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
- ord_empty(?List) is semidet
- True when List is the empty ordered set. Simply unifies list
with the empty list. Not part of Quintus.
- ord_seteq(+Set1, +Set2) is semidet
- True if Set1 and Set2 have the same elements. As both are
canonical sorted lists, this is the same as ==/2.
- - sicstus
- list_to_ord_set(+List, -OrdSet) is det
- Transform a list into an ordered set. This is the same as
sorting the list.
- ord_intersect(+Set1, +Set2) is semidet
- True if both ordered sets have a non-empty intersection.
- ord_disjoint(+Set1, +Set2) is semidet
- 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.
- - Use ord_intersection/3
- ord_intersection(+PowerSet, -Intersection) is semidet
- Intersection of a powerset. True when Intersection is an ordered set
holding all elements common to all sets in PowerSet. Fails if
PowerSet is an empty list.
- - sicstus
- ord_intersection(+Set1, +Set2, -Intersection) is det
- Intersection holds the common elements of Set1 and Set2. Uses
ord_disjoint/2 if Intersection is bound to
 on entry.
- ord_intersection(+Set1, +Set2, ?Intersection, ?Difference) is det
- 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.
- ord_add_element(+Set1, +Element, ?Set2) is det
- Insert an element into the set. This is the same as
ord_union(Set1, [Element], Set2).
- ord_del_element(+Set, +Element, -NewSet) is det
- Delete an element from an ordered set. This is the same as
ord_subtract(Set, [Element], NewSet).
- ord_selectchk(+Item, ?Set1, ?Set2) is semidet
- 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) & \+
- - Richard O'Keefe
- ord_memberchk(+Element, +OrdSet) is semidet
- True if Element is a member of OrdSet, compared using ==. Note
that enumerating elements of an ordered set can be done using
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
- - Richard O'Keefe
- ord_subset(+Sub, +Super) is semidet
- Is true if all elements of Sub are in Super
- ord_subtract(+InOSet, +NotInOSet, -Diff) is det
- Diff is the set holding all elements of InOSet that are not in
- ord_union(+SetOfSets, -Union) is det
- 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.
- - Copied from YAP, probably originally by Richard O'Keefe.
- ord_union(+Set1, +Set2, -Union) is det
- Union is the union of Set1 and Set2
- ord_union(+Set1, +Set2, -Union, -New) is det
- True iff
ord_union(Set1, Set2, Union) and
ord_subtract(Set2, Set1, New).
- ord_symdiff(+Set1, +Set2, ?Difference) is det
- 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
ord_union(Set1, Set2, Union),
ord_intersection(Set1, Set2, Intersection),
ord_subtract(Union, Intersection, Difference).
?- ord_symdiff([1,2], [2,3], X).
X = [1,3].