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title="Set">Up</a> </div> <h1>Module type <a href="type_Set.S.html">Set.S</a></h1> <pre><span id="MODULETYPES"><span class="keyword">module type</span> S</span> = <code class="code"><span class="keyword">sig</span></code> <a href="Set.S.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><div class="info modtype top"> <div class="info-desc"> <p>Output signature of the functor <a href="Set.Make.html"><code class="code"><span class="constructor">Set</span>.<span class="constructor">Make</span></code></a>.</p> </div> </div> <hr width="100%"> <pre><span id="TYPEelt"><span class="keyword">type</span> <code class="type"></code>elt</span> </pre> <div class="info "> <div class="info-desc"> <p>The type of the set elements.</p> </div> </div> <pre><span id="TYPEt"><span class="keyword">type</span> <code class="type"></code>t</span> </pre> <div class="info "> <div class="info-desc"> <p>The type of sets.</p> </div> </div> <pre><span id="VALempty"><span class="keyword">val</span> empty</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p>The empty set.</p> </div> </div> <pre><span id="VALis_empty"><span class="keyword">val</span> is_empty</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> bool</code></pre><div class="info "> <div class="info-desc"> <p>Test whether a set is empty or not.</p> </div> </div> <pre><span id="VALmem"><span class="keyword">val</span> mem</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEt">t</a> -> bool</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">mem x s</code> tests whether <code class="code">x</code> belongs to the set <code class="code">s</code>.</p> </div> </div> <pre><span id="VALadd"><span class="keyword">val</span> add</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">add x s</code> returns a set containing all elements of <code class="code">s</code>, plus <code class="code">x</code>. If <code class="code">x</code> was already in <code class="code">s</code>, <code class="code">s</code> is returned unchanged (the result of the function is then physically equal to <code class="code">s</code>).</p> </div> <ul class="info-attributes"> <li><b>Before 4.03 </b> Physical equality was not ensured.</li> </ul> </div> <pre><span id="VALsingleton"><span class="keyword">val</span> singleton</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">singleton x</code> returns the one-element set containing only <code class="code">x</code>.</p> </div> </div> <pre><span id="VALremove"><span class="keyword">val</span> remove</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">remove x s</code> returns a set containing all elements of <code class="code">s</code>, except <code class="code">x</code>. If <code class="code">x</code> was not in <code class="code">s</code>, <code class="code">s</code> is returned unchanged (the result of the function is then physically equal to <code class="code">s</code>).</p> </div> <ul class="info-attributes"> <li><b>Before 4.03 </b> Physical equality was not ensured.</li> </ul> </div> <pre><span id="VALunion"><span class="keyword">val</span> union</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p>Set union.</p> </div> </div> <pre><span id="VALinter"><span class="keyword">val</span> inter</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p>Set intersection.</p> </div> </div> <pre><span id="VALdiff"><span class="keyword">val</span> diff</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p>Set difference.</p> </div> </div> <pre><span id="VALcompare"><span class="keyword">val</span> compare</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a> -> int</code></pre><div class="info "> <div class="info-desc"> <p>Total ordering between sets. Can be used as the ordering function for doing sets of sets.</p> </div> </div> <pre><span id="VALequal"><span class="keyword">val</span> equal</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a> -> bool</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">equal s1 s2</code> tests whether the sets <code class="code">s1</code> and <code class="code">s2</code> are equal, that is, contain equal elements.</p> </div> </div> <pre><span id="VALsubset"><span class="keyword">val</span> subset</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a> -> bool</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">subset s1 s2</code> tests whether the set <code class="code">s1</code> is a subset of the set <code class="code">s2</code>.</p> </div> </div> <pre><span id="VALiter"><span class="keyword">val</span> iter</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> unit) -> <a href="Set.S.html#TYPEt">t</a> -> unit</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">iter f s</code> applies <code class="code">f</code> in turn to all elements of <code class="code">s</code>. The elements of <code class="code">s</code> are presented to <code class="code">f</code> in increasing order with respect to the ordering over the type of the elements.</p> </div> </div> <pre><span id="VALmap"><span class="keyword">val</span> map</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEelt">elt</a>) -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">map f s</code> is the set whose elements are <code class="code">f a0</code>,<code class="code">f a1</code>... <code class="code">f<br> aN</code>, where <code class="code">a0</code>,<code class="code">a1</code>...<code class="code">aN</code> are the elements of <code class="code">s</code>.</p> <p>The elements are passed to <code class="code">f</code> in increasing order with respect to the ordering over the type of the elements.</p> <p>If no element of <code class="code">s</code> is changed by <code class="code">f</code>, <code class="code">s</code> is returned unchanged. (If each output of <code class="code">f</code> is physically equal to its input, the returned set is physically equal to <code class="code">s</code>.)</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.04.0</li> </ul> </div> <pre><span id="VALfold"><span class="keyword">val</span> fold</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> 'a -> 'a) -> <a href="Set.S.html#TYPEt">t</a> -> 'a -> 'a</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">fold f s a</code> computes <code class="code">(f xN ... (f x2 (f x1 a))...)</code>, where <code class="code">x1 ... xN</code> are the elements of <code class="code">s</code>, in increasing order.</p> </div> </div> <pre><span id="VALfor_all"><span class="keyword">val</span> for_all</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> bool) -> <a href="Set.S.html#TYPEt">t</a> -> bool</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">for_all p s</code> checks if all elements of the set satisfy the predicate <code class="code">p</code>.</p> </div> </div> <pre><span id="VALexists"><span class="keyword">val</span> exists</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> bool) -> <a href="Set.S.html#TYPEt">t</a> -> bool</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">exists p s</code> checks if at least one element of the set satisfies the predicate <code class="code">p</code>.</p> </div> </div> <pre><span id="VALfilter"><span class="keyword">val</span> filter</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> bool) -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">filter p s</code> returns the set of all elements in <code class="code">s</code> that satisfy predicate <code class="code">p</code>. If <code class="code">p</code> satisfies every element in <code class="code">s</code>, <code class="code">s</code> is returned unchanged (the result of the function is then physically equal to <code class="code">s</code>).</p> </div> <ul class="info-attributes"> <li><b>Before 4.03 </b> Physical equality was not ensured.</li> </ul> </div> <pre><span id="VALpartition"><span class="keyword">val</span> partition</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> bool) -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a> * <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">partition p s</code> returns a pair of sets <code class="code">(s1, s2)</code>, where <code class="code">s1</code> is the set of all the elements of <code class="code">s</code> that satisfy the predicate <code class="code">p</code>, and <code class="code">s2</code> is the set of all the elements of <code class="code">s</code> that do not satisfy <code class="code">p</code>.</p> </div> </div> <pre><span id="VALcardinal"><span class="keyword">val</span> cardinal</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> int</code></pre><div class="info "> <div class="info-desc"> <p>Return the number of elements of a set.</p> </div> </div> <pre><span id="VALelements"><span class="keyword">val</span> elements</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a> list</code></pre><div class="info "> <div class="info-desc"> <p>Return the list of all elements of the given set. The returned list is sorted in increasing order with respect to the ordering <code class="code"><span class="constructor">Ord</span>.compare</code>, where <code class="code"><span class="constructor">Ord</span></code> is the argument given to <a href="Set.Make.html"><code class="code"><span class="constructor">Set</span>.<span class="constructor">Make</span></code></a>.</p> </div> </div> <pre><span id="VALmin_elt"><span class="keyword">val</span> min_elt</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a></code></pre><div class="info "> <div class="info-desc"> <p>Return the smallest element of the given set (with respect to the <code class="code"><span class="constructor">Ord</span>.compare</code> ordering), or raise <code class="code"><span class="constructor">Not_found</span></code> if the set is empty.</p> </div> </div> <pre><span id="VALmin_elt_opt"><span class="keyword">val</span> min_elt_opt</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a> option</code></pre><div class="info "> <div class="info-desc"> <p>Return the smallest element of the given set (with respect to the <code class="code"><span class="constructor">Ord</span>.compare</code> ordering), or <code class="code"><span class="constructor">None</span></code> if the set is empty.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.05</li> </ul> </div> <pre><span id="VALmax_elt"><span class="keyword">val</span> max_elt</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a></code></pre><div class="info "> <div class="info-desc"> <p>Same as <a href="Set.S.html#VALmin_elt"><code class="code"><span class="constructor">Set</span>.<span class="constructor">S</span>.min_elt</code></a>, but returns the largest element of the given set.</p> </div> </div> <pre><span id="VALmax_elt_opt"><span class="keyword">val</span> max_elt_opt</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a> option</code></pre><div class="info "> <div class="info-desc"> <p>Same as <a href="Set.S.html#VALmin_elt_opt"><code class="code"><span class="constructor">Set</span>.<span class="constructor">S</span>.min_elt_opt</code></a>, but returns the largest element of the given set.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.05</li> </ul> </div> <pre><span id="VALchoose"><span class="keyword">val</span> choose</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a></code></pre><div class="info "> <div class="info-desc"> <p>Return one element of the given set, or raise <code class="code"><span class="constructor">Not_found</span></code> if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.</p> </div> </div> <pre><span id="VALchoose_opt"><span class="keyword">val</span> choose_opt</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a> option</code></pre><div class="info "> <div class="info-desc"> <p>Return one element of the given set, or <code class="code"><span class="constructor">None</span></code> if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.05</li> </ul> </div> <pre><span id="VALsplit"><span class="keyword">val</span> split</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a> * bool * <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">split x s</code> returns a triple <code class="code">(l, present, r)</code>, where <code class="code">l</code> is the set of elements of <code class="code">s</code> that are strictly less than <code class="code">x</code>; <code class="code">r</code> is the set of elements of <code class="code">s</code> that are strictly greater than <code class="code">x</code>; <code class="code">present</code> is <code class="code"><span class="keyword">false</span></code> if <code class="code">s</code> contains no element equal to <code class="code">x</code>, or <code class="code"><span class="keyword">true</span></code> if <code class="code">s</code> contains an element equal to <code class="code">x</code>.</p> </div> </div> <pre><span id="VALfind"><span class="keyword">val</span> find</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">find x s</code> returns the element of <code class="code">s</code> equal to <code class="code">x</code> (according to <code class="code"><span class="constructor">Ord</span>.compare</code>), or raise <code class="code"><span class="constructor">Not_found</span></code> if no such element exists.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.01.0</li> </ul> </div> <pre><span id="VALfind_opt"><span class="keyword">val</span> find_opt</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a> option</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">find_opt x s</code> returns the element of <code class="code">s</code> equal to <code class="code">x</code> (according to <code class="code"><span class="constructor">Ord</span>.compare</code>), or <code class="code"><span class="constructor">None</span></code> if no such element exists.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.05</li> </ul> </div> <pre><span id="VALfind_first"><span class="keyword">val</span> find_first</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> bool) -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">find_first f s</code>, where <code class="code">f</code> is a monotonically increasing function, returns the lowest element <code class="code">e</code> of <code class="code">s</code> such that <code class="code">f e</code>, or raises <code class="code"><span class="constructor">Not_found</span></code> if no such element exists.</p> <p>For example, <code class="code">find_first (<span class="keyword">fun</span> e <span class="keywordsign">-></span> <span class="constructor">Ord</span>.compare e x >= 0) s</code> will return the first element <code class="code">e</code> of <code class="code">s</code> where <code class="code"><span class="constructor">Ord</span>.compare e x >= 0</code> (intuitively: <code class="code">e >= x</code>), or raise <code class="code"><span class="constructor">Not_found</span></code> if <code class="code">x</code> is greater than any element of <code class="code">s</code>.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.05</li> </ul> </div> <pre><span id="VALfind_first_opt"><span class="keyword">val</span> find_first_opt</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> bool) -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a> option</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">find_first_opt f s</code>, where <code class="code">f</code> is a monotonically increasing function, returns an option containing the lowest element <code class="code">e</code> of <code class="code">s</code> such that <code class="code">f e</code>, or <code class="code"><span class="constructor">None</span></code> if no such element exists.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.05</li> </ul> </div> <pre><span id="VALfind_last"><span class="keyword">val</span> find_last</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> bool) -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">find_last f s</code>, where <code class="code">f</code> is a monotonically decreasing function, returns the highest element <code class="code">e</code> of <code class="code">s</code> such that <code class="code">f e</code>, or raises <code class="code"><span class="constructor">Not_found</span></code> if no such element exists.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.05</li> </ul> </div> <pre><span id="VALfind_last_opt"><span class="keyword">val</span> find_last_opt</span> : <code class="type">(<a href="Set.S.html#TYPEelt">elt</a> -> bool) -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a> option</code></pre><div class="info "> <div class="info-desc"> <p><code class="code">find_last_opt f s</code>, where <code class="code">f</code> is a monotonically decreasing function, returns an option containing the highest element <code class="code">e</code> of <code class="code">s</code> such that <code class="code">f e</code>, or <code class="code"><span class="constructor">None</span></code> if no such element exists.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.05</li> </ul> </div> <pre><span id="VALof_list"><span class="keyword">val</span> of_list</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> list -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">of_list l</code> creates a set from a list of elements. This is usually more efficient than folding <code class="code">add</code> over the list, except perhaps for lists with many duplicated elements.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.02.0</li> </ul> </div> <h7 id="6_Iterators">Iterators</h7> <pre><span id="VALto_seq_from"><span class="keyword">val</span> to_seq_from</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a> <a href="Seq.html#TYPEt">Seq.t</a></code></pre><div class="info "> <div class="info-desc"> <p><code class="code">to_seq_from x s</code> iterates on a subset of the elements of <code class="code">s</code> in ascending order, from <code class="code">x</code> or above.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.07</li> </ul> </div> <pre><span id="VALto_seq"><span class="keyword">val</span> to_seq</span> : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a> <a href="Seq.html#TYPEt">Seq.t</a></code></pre><div class="info "> <div class="info-desc"> <p>Iterate on the whole set, in ascending order</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.07</li> </ul> </div> <pre><span id="VALadd_seq"><span class="keyword">val</span> add_seq</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> <a href="Seq.html#TYPEt">Seq.t</a> -> <a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p>Add the given elements to the set, in order.</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.07</li> </ul> </div> <pre><span id="VALof_seq"><span class="keyword">val</span> of_seq</span> : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> <a href="Seq.html#TYPEt">Seq.t</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info "> <div class="info-desc"> <p>Build a set from the given bindings</p> </div> <ul class="info-attributes"> <li><b>Since</b> 4.07</li> </ul> </div> </body></html>