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<link title="Extlib" rel="Chapter" href="Extlib.html"><link title="Polymorphic sets" rel="Section" href="#6_Polymorphicsets">
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<title>Batteries user guide : BatSet.PSet</title>
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<h1>Module <a href="type_BatSet.PSet.html">BatSet.PSet</a></h1>
<pre><span class="keyword">module</span> PSet: <code class="code"><span class="keyword">sig</span></code> <a href="BatSet.PSet.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><hr width="100%">
<br>
<h6 id="6_Polymorphicsets">Polymorphic sets</h6>
<p>
The definitions below describe the polymorphic set interface.
<p>
They are similar in functionality to the functorized
<a href="BatSet.Make.html"><code class="code"><span class="constructor">BatSet</span>.<span class="constructor">Make</span></code></a> module, but the compiler cannot ensure that sets
using different element ordering have different types: the
responsibility of not mixing non-sensical comparison functions
together is to the programmer. If you ever need a custom
comparison function, it is recommended to use the <a href="BatSet.Make.html"><code class="code"><span class="constructor">BatSet</span>.<span class="constructor">Make</span></code></a>
functor for additional safety.<br>
<pre><span id="TYPEt"><span class="keyword">type</span> <code class="type">'a</code> t</span> </pre>
<div class="info ">
The type of sets.<br>
</div>
<pre><span class="keyword">include</span> <a href="BatEnum.Enumerable.html">BatEnum.Enumerable</a></pre>
<pre><span class="keyword">include</span> <a href="BatInterfaces.Mappable.html">BatInterfaces.Mappable</a></pre>
<pre><span id="VALempty"><span class="keyword">val</span> empty</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
The empty set, using <code class="code">compare</code> as comparison function<br>
</div>
<pre><span id="VALcreate"><span class="keyword">val</span> create</span> : <code class="type">('a -> 'a -> int) -> 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
Creates a new empty set, using the provided function for key comparison.<br>
</div>
<pre><span id="VALis_empty"><span class="keyword">val</span> is_empty</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> bool</code></pre><div class="info ">
Test whether a set is empty or not.<br>
</div>
<pre><span id="VALsingleton"><span class="keyword">val</span> singleton</span> : <code class="type">?cmp:('a -> 'a -> int) -> 'a -> 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
Creates a new set with the single given element in it.<br>
</div>
<pre><span id="VALmem"><span class="keyword">val</span> mem</span> : <code class="type">'a -> 'a <a href="BatSet.PSet.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 id="VALadd"><span class="keyword">val</span> add</span> : <code class="type">'a -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.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 id="VALremove"><span class="keyword">val</span> remove</span> : <code class="type">'a -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.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 id="VALunion"><span class="keyword">val</span> union</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">union s t</code> returns the union of <code class="code">s</code> and <code class="code">t</code> - the set containing
all elements in either <code class="code">s</code> and <code class="code">t</code>. The returned set uses <code class="code">t</code>'s
comparison function. The current implementation works better for
small <code class="code">s</code>.<br>
</div>
<pre><span id="VALintersect"><span class="keyword">val</span> intersect</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">intersect s t</code> returns a new set of those elements that are in
both <code class="code">s</code> and <code class="code">t</code>. The returned set uses <code class="code">s</code>'s comparison function.<br>
</div>
<pre><span id="VALdiff"><span class="keyword">val</span> diff</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">diff s t</code> returns the set of all elements in <code class="code">s</code> but not in
<code class="code">t</code>. The returned set uses <code class="code">s</code>'s comparison function.<br>
</div>
<pre><span id="VALsym_diff"><span class="keyword">val</span> sym_diff</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">sym_diff s t</code> returns the set of all elements in <code class="code">s</code> or <code class="code">t</code> but not both.
This is the same as <code class="code">diff (union s t) (inter s t)</code>. The returned set uses
<code class="code">s</code>'s comparison function.<br>
</div>
<pre><span id="VALcompare"><span class="keyword">val</span> compare</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.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 id="VALequal"><span class="keyword">val</span> equal</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.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 id="VALsubset"><span class="keyword">val</span> subset</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> bool</code></pre><div class="info ">
<code class="code">subset a b</code> returns true if <code class="code">a</code> is a subset of <code class="code">b</code>. O(|a|).<br>
</div>
<pre><span id="VALdisjoint"><span class="keyword">val</span> disjoint</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> bool</code></pre><div class="info ">
<code class="code">disjoint s1 s2</code> tests whether the sets <code class="code">s1</code> and <code class="code">s2</code> contain no
shared elements. (i.e. <code class="code">inter s1 s2</code> is empty.)<br>
</div>
<pre><span id="VALiter"><span class="keyword">val</span> iter</span> : <code class="type">('a -> unit) -> 'a <a href="BatSet.PSet.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 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.<br>
</div>
<pre><span id="VALmap"><span class="keyword">val</span> map</span> : <code class="type">('a -> 'b) -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'b <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">map f x</code> creates a new set with elements <code class="code">f a0</code>,
<code class="code">f a1</code>... <code class="code">f aN</code>, where <code class="code">a0</code>, <code class="code">a1</code>, ..., <code class="code">aN</code> are the
values contained in <code class="code">x</code>
<p>
The resulting map uses the polymorphic <code class="code">compare</code> function to
order elements.<br>
</div>
<pre><span id="VALfilter"><span class="keyword">val</span> filter</span> : <code class="type">('a -> bool) -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.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 id="VALfilter_map"><span class="keyword">val</span> filter_map</span> : <code class="type">('a -> 'b option) -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'b <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">filter_map f m</code> combines the features of <code class="code">filter</code> and
<code class="code">map</code>. It calls calls <code class="code">f a0</code>, <code class="code">f a1</code>, <code class="code">f aN</code> where <code class="code">a0,a1..an</code>
are the elements of <code class="code">m</code> and returns the set of pairs <code class="code">bi</code>
such as <code class="code">f ai = <span class="constructor">Some</span> bi</code> (when <code class="code">f</code> returns <code class="code"><span class="constructor">None</span></code>, the
corresponding element of <code class="code">m</code> is discarded).
<p>
The resulting map uses the polymorphic <code class="code">compare</code> function to
order elements.<br>
</div>
<pre><span id="VALfold"><span class="keyword">val</span> fold</span> : <code class="type">('a -> 'b -> 'b) -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'b -> 'b</code></pre><div class="info ">
<code class="code">fold f s a</code> computes <code class="code">(f xN ... (f x1 (f x0 a))...)</code>,
where <code class="code">x0,x1..xN</code> are the elements of <code class="code">s</code>, in increasing order.<br>
</div>
<pre><span id="VALexists"><span class="keyword">val</span> exists</span> : <code class="type">('a -> bool) -> 'a <a href="BatSet.PSet.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 id="VALfor_all"><span class="keyword">val</span> for_all</span> : <code class="type">('a -> bool) -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> bool</code></pre><div class="info ">
Returns whether the given predicate applies to all elements in the set<br>
</div>
<pre><span id="VALpartition"><span class="keyword">val</span> partition</span> : <code class="type">('a -> bool) -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> * 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
returns two disjoint subsets, those that satisfy the given
predicate and those that don't<br>
</div>
<pre><span id="VALsplit"><span class="keyword">val</span> split</span> : <code class="type">'a -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a> * bool * 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
<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>.<br>
</div>
<pre><span id="VALcardinal"><span class="keyword">val</span> cardinal</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> int</code></pre><div class="info ">
Return the number of elements of a set.<br>
</div>
<pre><span id="VALelements"><span class="keyword">val</span> elements</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> '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 of the given set.<br>
</div>
<pre><span id="VALmin_elt"><span class="keyword">val</span> min_elt</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a</code></pre><div class="info ">
returns the smallest element of the set.<br>
<b>Raises</b> <code>Invalid_argument</code> if given an empty set.<br>
</div>
<pre><span id="VALmax_elt"><span class="keyword">val</span> max_elt</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a</code></pre><div class="info ">
returns the largest element of the set.<br>
<b>Raises</b> <code>Invalid_argument</code> if given an empty set.<br>
</div>
<pre><span id="VALchoose"><span class="keyword">val</span> choose</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a</code></pre><div class="info ">
returns an arbitrary (but deterministic) element of the given set.<br>
<b>Raises</b> <code>Invalid_argument</code> if given an empty set.<br>
</div>
<pre><span id="VALpop"><span class="keyword">val</span> pop</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a * 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
returns one element of the set and the set without that element.<br>
<b>Raises</b> <code>Not_found</code> if given an empty set<br>
</div>
<pre><span id="VALenum"><span class="keyword">val</span> enum</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a <a href="BatEnum.html#TYPEt">BatEnum.t</a></code></pre><div class="info ">
Return an enumeration of all elements of the given set.
The returned enumeration is sorted in increasing order with respect
to the ordering of this set.<br>
</div>
<pre><span id="VALof_enum"><span class="keyword">val</span> of_enum</span> : <code class="type">'a <a href="BatEnum.html#TYPEt">BatEnum.t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre>
<pre><span id="VALof_enum_cmp"><span class="keyword">val</span> of_enum_cmp</span> : <code class="type">cmp:('a -> 'a -> int) -> 'a <a href="BatEnum.html#TYPEt">BatEnum.t</a> -> 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre>
<pre><span id="VALof_list"><span class="keyword">val</span> of_list</span> : <code class="type">'a list -> 'a <a href="BatSet.PSet.html#TYPEt">t</a></code></pre><div class="info ">
builds a set from the given list, using the default comparison
function<br>
</div>
<br>
<h6 id="6_Boilerplatecode">Boilerplate code</h6><br>
<br>
<div class="h7" id="7_Printing">Printing</div><br>
<pre><span id="VALprint"><span class="keyword">val</span> print</span> : <code class="type">?first:string -><br> ?last:string -><br> ?sep:string -><br> ('a <a href="BatInnerIO.html#TYPEoutput">BatInnerIO.output</a> -> 'c -> unit) -><br> 'a <a href="BatInnerIO.html#TYPEoutput">BatInnerIO.output</a> -> 'c <a href="BatSet.PSet.html#TYPEt">t</a> -> unit</code></pre>
<pre><span id="VALget_cmp"><span class="keyword">val</span> get_cmp</span> : <code class="type">'a <a href="BatSet.PSet.html#TYPEt">t</a> -> 'a -> 'a -> int</code></pre><div class="info ">
get the comparison function used for a polymorphic map<br>
</div>
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