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<link title="Weak" rel="Chapter" href="Weak.html"><title>Set.S</title>
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<center><h1>Module type <a href="type_Set.S.html">Set.S</a></h1></center>
<br>
<pre><span class="keyword">module type</span> S = <code class="type">sig end</code></pre><div class="info">
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>.<br>
</div>
<hr width="100%">
<br><code><span class="keyword">type</span> <a name="TYPEelt"></a>elt </code>
<div class="info">
The type of the set elements.<br>
</div>
<br>
<br><code><span class="keyword">type</span> <a name="TYPEt"></a>t </code>
<div class="info">
The type of sets.<br>
</div>
<br>
<pre><span class="keyword">val</span> <a name="VALempty"></a>empty : <code class="type"><a href="Set.S.html#TYPEt">t</a></code></pre><div class="info">
The empty set.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALis_empty"></a>is_empty : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> bool</code></pre><div class="info">
Test whether a set is empty or not.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALmem"></a>mem : <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">
<code class="code">mem x s</code> tests whether <code class="code">x</code> belongs to the set <code class="code">s</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALadd"></a>add : <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">
<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.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALsingleton"></a>singleton : <code class="type"><a href="Set.S.html#TYPEelt">elt</a> -> <a href="Set.S.html#TYPEt">t</a></code></pre><div class="info">
<code class="code">singleton x</code> returns the one-element set containing only <code class="code">x</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALremove"></a>remove : <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">
<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.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALunion"></a>union : <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">
Set union.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALinter"></a>inter : <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">
Set intersection.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALdiff"></a>diff : <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">
Set difference.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALcompare"></a>compare : <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">
Total ordering between sets. Can be used as the ordering function
for doing sets of sets.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALequal"></a>equal : <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">
<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.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALsubset"></a>subset : <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">
<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>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALiter"></a>iter : <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">
<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 order in which the elements of <code class="code">s</code> are presented to <code class="code">f</code>
is unspecified.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALfold"></a>fold : <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">
<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>.
The order in which elements of <code class="code">s</code> are presented to <code class="code">f</code> is
unspecified.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALfor_all"></a>for_all : <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">
<code class="code">for_all p s</code> checks if all elements of the set
satisfy the predicate <code class="code">p</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALexists"></a>exists : <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">
<code class="code">exists p s</code> checks if at least one element of
the set satisfies the predicate <code class="code">p</code>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALfilter"></a>filter : <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">
<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>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALpartition"></a>partition : <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">
<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>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALcardinal"></a>cardinal : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> int</code></pre><div class="info">
Return the number of elements of a set.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALelements"></a>elements : <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">
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>.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALmin_elt"></a>min_elt : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a></code></pre><div class="info">
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.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALmax_elt"></a>max_elt : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a></code></pre><div class="info">
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.<br>
</div>
<pre><span class="keyword">val</span> <a name="VALchoose"></a>choose : <code class="type"><a href="Set.S.html#TYPEt">t</a> -> <a href="Set.S.html#TYPEelt">elt</a></code></pre><div class="info">
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.<br>
</div>
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