1Set.Make(3)                      OCaml library                     Set.Make(3)
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NAME

6       Set.Make  -  Functor  building  an  implementation of the set structure
7       given a totally ordered type.
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Module

10       Module   Set.Make
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Documentation

13       Module Make
14        : functor (Ord : OrderedType) -> sig end
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17       Functor building an implementation of the set structure given a totally
18       ordered type.
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22       Parameters:
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24       "Ord"
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26       Set.OrderedType
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34       type elt
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37       The type of the set elements.
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41       type t
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44       The type of sets.
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49       val empty : t
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51       The empty set.
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56       val is_empty : t -> bool
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58       Test whether a set is empty or not.
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63       val mem : elt -> t -> bool
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66       mem x s tests whether x belongs to the set s .
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71       val add : elt -> t -> t
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74       add  x s returns a set containing all elements of s , plus x . If x was
75       already in s , s is returned unchanged.
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80       val singleton : elt -> t
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83       singleton x returns the one-element set containing only x .
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88       val remove : elt -> t -> t
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91       remove x s returns a set containing all elements of s , except x . If x
92       was not in s , s is returned unchanged.
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97       val union : t -> t -> t
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99       Set union.
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104       val inter : t -> t -> t
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106       Set intersection.
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111       val diff : t -> t -> t
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113       Set difference.
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118       val compare : t -> t -> int
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120       Total  ordering  between sets. Can be used as the ordering function for
121       doing sets of sets.
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126       val equal : t -> t -> bool
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129       equal s1 s2 tests whether the sets s1 and s2 are equal, that  is,  con‐
130       tain equal elements.
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135       val subset : t -> t -> bool
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138       subset s1 s2 tests whether the set s1 is a subset of the set s2 .
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143       val iter : (elt -> unit) -> t -> unit
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146       iter  f  s  applies f in turn to all elements of s .  The elements of s
147       are presented to f in increasing order with  respect  to  the  ordering
148       over the type of the elements.
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153       val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
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156       fold  f  s  a computes (f xN ... (f x2 (f x1 a))...)  , where x1 ... xN
157       are the elements of s , in increasing order.
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162       val for_all : (elt -> bool) -> t -> bool
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165       for_all p s checks if all elements of the set satisfy the predicate p .
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170       val exists : (elt -> bool) -> t -> bool
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173       exists p s checks if at least one element  of  the  set  satisfies  the
174       predicate p .
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179       val filter : (elt -> bool) -> t -> t
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182       filter  p s returns the set of all elements in s that satisfy predicate
183       p .
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188       val partition : (elt -> bool) -> t -> t * t
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191       partition p s returns a pair of sets (s1, s2) , where s1 is the set  of
192       all  the elements of s that satisfy the predicate p , and s2 is the set
193       of all the elements of s that do not satisfy p .
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198       val cardinal : t -> int
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200       Return the number of elements of a set.
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205       val elements : t -> elt list
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207       Return the list of all elements of the given set.  The returned list is
208       sorted  in  increasing order with respect to the ordering Ord.compare ,
209       where Ord is the argument given to Set.Make .
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214       val min_elt : t -> elt
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216       Return the smallest element of the  given  set  (with  respect  to  the
217       Ord.compare ordering), or raise Not_found if the set is empty.
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222       val max_elt : t -> elt
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224       Same  as  Set.S.min_elt  , but returns the largest element of the given
225       set.
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230       val choose : t -> elt
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232       Return one element of the given set, or raise Not_found if the  set  is
233       empty.  Which element is chosen is unspecified, but equal elements will
234       be chosen for equal sets.
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239       val split : elt -> t -> t * bool * t
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242       split x s returns a triple (l, present, r) , where l is the set of ele‐
243       ments  of s that are strictly less than x ; r is the set of elements of
244       s that are strictly greater than x ; present is false if s contains  no
245       element equal to x , or true if s contains an element equal to x .
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252OCamldoc                          2017-03-22                       Set.Make(3)