Module type S
= sigend
Output signature of the functor Set.Make .
Setstypeelt
The type of the set elements.
typet
The type of sets.
valempty : t
The empty set.
valadd : elt->t->taddxs returns a set containing all elements of s , plus x . If x was already in s , s is returned
unchanged (the result of the function is then physically equal to s ).
Before4.03 Physical equality was not ensured.
valsingleton : elt->tsingletonx returns the one-element set containing only x .
valremove : elt->t->tremovexs returns a set containing all elements of s , except x . If x was not in s , s is returned
unchanged (the result of the function is then physically equal to s ).
Before4.03 Physical equality was not ensured.
valunion : t->t->t
Set union.
valinter : t->t->t
Set intersection.
valdisjoint : t->t->bool
Test if two sets are disjoint.
Since 4.08
valdiff : t->t->t
Set difference: diffs1s2 contains the elements of s1 that are not in s2 .
valcardinal : t->int
Return the number of elements of a set.
Elementsvalelements : t->eltlist
Return the list of all elements of the given set. The returned list is sorted in increasing order with
respect to the ordering Ord.compare , where Ord is the argument given to Set.Make .
valmin_elt : t->elt
Return the smallest element of the given set (with respect to the Ord.compare ordering), or raise
Not_found if the set is empty.
valmin_elt_opt : t->eltoption
Return the smallest element of the given set (with respect to the Ord.compare ordering), or None if the
set is empty.
Since 4.05
valmax_elt : t->elt
Same as Set.S.min_elt , but returns the largest element of the given set.
valmax_elt_opt : t->eltoption
Same as Set.S.min_elt_opt , but returns the largest element of the given set.
Since 4.05
valchoose : t->elt
Return one element of the given set, or raise Not_found if the set is empty. Which element is chosen is
unspecified, but equal elements will be chosen for equal sets.
valchoose_opt : t->eltoption
Return one element of the given set, or None if the set is empty. Which element is chosen is unspecified,
but equal elements will be chosen for equal sets.
Since 4.05
Searchingvalfind : elt->t->eltfindxs returns the element of s equal to x (according to Ord.compare ), or raise Not_found if no such
element exists.
Since 4.01
valfind_opt : elt->t->eltoptionfind_optxs returns the element of s equal to x (according to Ord.compare ), or None if no such element
exists.
Since 4.05
valfind_first : (elt->bool)->t->eltfind_firstfs , where f is a monotonically increasing function, returns the lowest element e of s such
that fe , or raises Not_found if no such element exists.
For example, find_first(fune->Ord.compareex>=0)s will return the first element e of s where
Ord.compareex>=0 (intuitively: e>=x ), or raise Not_found if x is greater than any element of s .
Since 4.05
valfind_first_opt : (elt->bool)->t->eltoptionfind_first_optfs , where f is a monotonically increasing function, returns an option containing the
lowest element e of s such that fe , or None if no such element exists.
Since 4.05
valfind_last : (elt->bool)->t->eltfind_lastfs , where f is a monotonically decreasing function, returns the highest element e of s such
that fe , or raises Not_found if no such element exists.
Since 4.05
valfind_last_opt : (elt->bool)->t->eltoptionfind_last_optfs , where f is a monotonically decreasing function, returns an option containing the
highest element e of s such that fe , or None if no such element exists.
Since 4.05
Traversingvaliter : (elt->unit)->t->unititerfs applies f in turn to all elements of s . The elements of s are presented to f in increasing
order with respect to the ordering over the type of the elements.
valfold : (elt->'acc->'acc)->t->'acc->'accfoldfsinit computes (fxN...(fx2(fx1init))...) , where x1...xN are the elements of s , in
increasing order.
Transformingvalmap : (elt->elt)->t->tmapfs is the set whose elements are fa0 , fa1 ... faN , where a0 , a1 ... aN are the elements of s .
The elements are passed to f in increasing order with respect to the ordering over the type of the
elements.
If no element of s is changed by f , s is returned unchanged. (If each output of f is physically equal to
its input, the returned set is physically equal to s .)
Since 4.04
valfilter : (elt->bool)->t->tfilterfs returns the set of all elements in s that satisfy predicate f . If f satisfies every element
in s , s is returned unchanged (the result of the function is then physically equal to s ).
Before4.03 Physical equality was not ensured.
valfilter_map : (elt->eltoption)->t->tfilter_mapfs returns the set of all v such that fx=Somev for some element x of s .
For example,
filter_map(funn->ifnmod2=0thenSome(n/2)elseNone)s
is the set of halves of the even elements of s .
If no element of s is changed or dropped by f (if fx=Somex for each element x ), then s is returned
unchanged: the result of the function is then physically equal to s .
Since 4.11
valpartition : (elt->bool)->t->t*tpartitionfs returns a pair of sets (s1,s2) , where s1 is the set of all the elements of s that satisfy
the predicate f , and s2 is the set of all the elements of s that do not satisfy f .
valsplit : elt->t->t*bool*tsplitxs returns a triple (l,present,r) , where l is the set of elements of s that are strictly less
than x ; r is the set of elements of s that are strictly greater than x ; present is false if s contains
no element equal to x , or true if s contains an element equal to x .
Predicatesandcomparisonsvalis_empty : t->bool
Test whether a set is empty or not.
valmem : elt->t->boolmemxs tests whether x belongs to the set s .
valequal : t->t->boolequals1s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.
valcompare : t->t->int
Total ordering between sets. Can be used as the ordering function for doing sets of sets.
valsubset : t->t->boolsubsets1s2 tests whether the set s1 is a subset of the set s2 .
valfor_all : (elt->bool)->t->boolfor_allfs checks if all elements of the set satisfy the predicate f .
valexists : (elt->bool)->t->boolexistsfs checks if at least one element of the set satisfies the predicate f .
Convertingvalto_list : t->eltlistto_lists is Set.S.elementss .
Since 5.1
valof_list : eltlist->tof_listl creates a set from a list of elements. This is usually more efficient than folding add over
the list, except perhaps for lists with many duplicated elements.
Since 4.02
valto_seq_from : elt->t->eltSeq.tto_seq_fromxs iterates on a subset of the elements of s in ascending order, from x or above.
Since 4.07
valto_seq : t->eltSeq.t
Iterate on the whole set, in ascending order
Since 4.07
valto_rev_seq : t->eltSeq.t
Iterate on the whole set, in descending order
Since 4.12
valadd_seq : eltSeq.t->t->t
Add the given elements to the set, in order.
Since 4.07
valof_seq : eltSeq.t->t
Build a set from the given bindings
Since 4.07
OCamldoc 2025-06-12 Set.S(3o)
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