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<!DOCTYPE html>
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<title>Generators — Lua Functional 0.1.3 documentation</title>
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<div class="header" role="banner"><img class="rightlogo" src="_static/logo.png" alt="Logo"/><h1 class="heading"><a href="index.html">
<span>Lua Functional 0.1.3 documentation</span></a></h1>
<h2 class="heading"><span>Generators</span></h2>
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<section id="generators">
<h1>Generators<a class="headerlink" href="#generators" title="Permalink to this headline">¶</a></h1>
<p>This section contains a number of useful generators modeled after Standard ML,
Haskell, Python, Ruby, JavaScript and other languages.</p>
<section id="finite-generators">
<h2>Finite Generators<a class="headerlink" href="#finite-generators" title="Permalink to this headline">¶</a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="fun.range">
<span class="sig-prename descclassname"><span class="pre">fun.</span></span><span class="sig-name descname"><span class="pre">range</span></span><span class="sig-paren">(</span><span class="optional">[</span><em class="sig-param"><span class="n"><span class="pre">start</span></span></em>, <span class="optional">]</span><em class="sig-param"><span class="n"><span class="pre">stop</span></span></em><span class="optional">[</span>, <em class="sig-param"><span class="n"><span class="pre">step</span></span></em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#fun.range" title="Permalink to this definition">¶</a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>start</strong> (<em>number</em>) – an endpoint of the interval (see below)</p></li>
<li><p><strong>stop</strong> (<em>number</em>) – an endpoint of the interval (see below)</p></li>
<li><p><strong>step</strong> (<em>number</em>) – a step</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>an iterator</p>
</dd>
</dl>
<p>The iterator to create arithmetic progressions. Iteration values are generated
within closed interval <code class="docutils literal notranslate"><span class="pre">[start,</span> <span class="pre">stop]</span></code> (i.e. <em>stop</em> is included).
If the <em>start</em> argument is omitted, it defaults to <code class="docutils literal notranslate"><span class="pre">1</span></code> (<em>stop</em> > 0) or
to <code class="docutils literal notranslate"><span class="pre">-1</span></code> (<em>stop</em> < 0). If the <em>step</em> argument is omitted, it defaults to
<code class="docutils literal notranslate"><span class="pre">1</span></code> (<em>start</em> <= <em>stop</em>) or to <code class="docutils literal notranslate"><span class="pre">-1</span></code> (<em>start</em> > <em>stop</em>). If <em>step</em> is
positive, the last element is the largest <code class="docutils literal notranslate"><span class="pre">start</span> <span class="pre">+</span> <span class="pre">i</span> <span class="pre">*</span> <span class="pre">step</span></code> less than or
equal to <em>stop</em>; if <em>step</em> is negative, the last element is the smallest
<code class="docutils literal notranslate"><span class="pre">start</span> <span class="pre">+</span> <span class="pre">i</span> <span class="pre">*</span> <span class="pre">step</span></code> greater than or equal to <em>stop</em>.
<em>step</em> must not be zero (or else an error is raised).
<code class="docutils literal notranslate"><span class="pre">range(0)</span></code> returns empty iterator.</p>
<p>Examples:</p>
<div class="highlight-lua notranslate"><div class="highlight"><pre><span></span><span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="mi">1</span>
<span class="mi">2</span>
<span class="mi">3</span>
<span class="mi">4</span>
<span class="mi">5</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="o">-</span><span class="mi">5</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="o">-</span><span class="mi">1</span>
<span class="o">-</span><span class="mi">2</span>
<span class="o">-</span><span class="mi">3</span>
<span class="o">-</span><span class="mi">4</span>
<span class="o">-</span><span class="mi">5</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="mi">1</span>
<span class="mi">2</span>
<span class="mi">3</span>
<span class="mi">4</span>
<span class="mi">5</span>
<span class="mi">6</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="mi">0</span>
<span class="mi">5</span>
<span class="mi">10</span>
<span class="mi">15</span>
<span class="mi">20</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="mi">0</span>
<span class="mi">3</span>
<span class="mi">6</span>
<span class="mi">9</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="mi">0</span>
<span class="mf">0.2</span>
<span class="mf">0.4</span>
<span class="mf">0.6</span>
<span class="mf">0.8</span>
<span class="mi">1</span>
<span class="mf">1.2</span>
<span class="mf">1.4</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="mi">1</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="mi">1</span>
<span class="mi">0</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">v</span> <span class="kr">in</span> <span class="n">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="kr">do</span> <span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="kr">end</span>
<span class="nb">error</span><span class="p">:</span> <span class="n">step</span> <span class="n">must</span> <span class="ow">not</span> <span class="n">be</span> <span class="n">zero</span>
</pre></div>
</div>
</dd></dl>
</section>
<section id="infinity-generators">
<h2>Infinity Generators<a class="headerlink" href="#infinity-generators" title="Permalink to this headline">¶</a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="fun.duplicate">
<span class="sig-prename descclassname"><span class="pre">fun.</span></span><span class="sig-name descname"><span class="pre">duplicate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">...</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#fun.duplicate" title="Permalink to this definition">¶</a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>...</strong> (<em>non nil</em>) – objects to duplicate</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>an iterator</p>
</dd>
</dl>
<p>The iterator returns values over and over again indefinitely. All values
that passed to the iterator are returned as-is during the iteration.</p>
<p>Examples:</p>
<div class="highlight-lua notranslate"><div class="highlight"><pre><span></span><span class="o">></span> <span class="n">each</span><span class="p">(</span><span class="nb">print</span><span class="p">,</span> <span class="n">take</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">duplicate</span><span class="p">(</span><span class="s1">'a'</span><span class="p">,</span> <span class="s1">'b'</span><span class="p">,</span> <span class="s1">'c'</span><span class="p">)))</span>
<span class="n">a</span> <span class="n">b</span> <span class="n">c</span>
<span class="n">a</span> <span class="n">b</span> <span class="n">c</span>
<span class="o">></span> <span class="n">each</span><span class="p">(</span><span class="nb">print</span><span class="p">,</span> <span class="n">take</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">duplicate</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)))</span>
<span class="n">x</span>
<span class="n">x</span>
<span class="n">x</span>
<span class="o">></span> <span class="kr">for</span> <span class="n">_it</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span><span class="p">,</span> <span class="n">e</span> <span class="kr">in</span> <span class="n">take</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">duplicate</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="s1">'a'</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="s1">'b'</span><span class="p">))</span> <span class="kr">do</span>
<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span><span class="p">,</span> <span class="n">e</span><span class="p">)</span>
<span class="o">>></span> <span class="kr">end</span>
<span class="mi">1</span> <span class="mi">2</span> <span class="n">a</span> <span class="mi">3</span> <span class="n">b</span>
<span class="mi">1</span> <span class="mi">2</span> <span class="n">a</span> <span class="mi">3</span> <span class="n">b</span>
<span class="mi">1</span> <span class="mi">2</span> <span class="n">a</span> <span class="mi">3</span> <span class="n">b</span>
</pre></div>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="fun.xrepeat">
<span class="sig-prename descclassname"><span class="pre">fun.</span></span><span class="sig-name descname"><span class="pre">xrepeat</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">...</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#fun.xrepeat" title="Permalink to this definition">¶</a></dt>
<dd><p>An alias for <a class="reference internal" href="#fun.duplicate" title="fun.duplicate"><code class="xref py py-func docutils literal notranslate"><span class="pre">duplicate()</span></code></a>.</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="fun.replicate">
<span class="sig-prename descclassname"><span class="pre">fun.</span></span><span class="sig-name descname"><span class="pre">replicate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">...</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#fun.replicate" title="Permalink to this definition">¶</a></dt>
<dd><p>An alias for <a class="reference internal" href="#fun.duplicate" title="fun.duplicate"><code class="xref py py-func docutils literal notranslate"><span class="pre">duplicate()</span></code></a>.</p>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="fun.tabulate">
<span class="sig-prename descclassname"><span class="pre">fun.</span></span><span class="sig-name descname"><span class="pre">tabulate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">fun</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#fun.tabulate" title="Permalink to this definition">¶</a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>fun</strong> (<em>function</em><em>(</em><em>n: uint</em><em>) </em><em>-> </em><em>...</em>) – an unary generating function</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>an iterator</p>
</dd>
</dl>
<p>The iterator that returns <code class="docutils literal notranslate"><span class="pre">fun(0)</span></code>, <code class="docutils literal notranslate"><span class="pre">fun(1)</span></code>, <code class="docutils literal notranslate"><span class="pre">fun(2)</span></code>, <code class="docutils literal notranslate"><span class="pre">...</span></code> values
indefinitely.</p>
<p>Examples:</p>
<div class="highlight-lua notranslate"><div class="highlight"><pre><span></span><span class="o">></span> <span class="n">each</span><span class="p">(</span><span class="nb">print</span><span class="p">,</span> <span class="n">take</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="n">tabulate</span><span class="p">(</span><span class="kr">function</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="kr">return</span> <span class="s1">'a'</span><span class="p">,</span> <span class="s1">'b'</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span> <span class="kr">end</span><span class="p">)))</span>
<span class="n">a</span> <span class="n">b</span> <span class="mi">0</span>
<span class="n">a</span> <span class="n">b</span> <span class="mi">2</span>
<span class="n">a</span> <span class="n">b</span> <span class="mi">4</span>
<span class="n">a</span> <span class="n">b</span> <span class="mi">6</span>
<span class="n">a</span> <span class="n">b</span> <span class="mi">8</span>
<span class="o">></span> <span class="n">each</span><span class="p">(</span><span class="nb">print</span><span class="p">,</span> <span class="n">take</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="n">tabulate</span><span class="p">(</span><span class="kr">function</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="kr">return</span> <span class="n">x</span><span class="o">^</span><span class="mi">2</span> <span class="kr">end</span><span class="p">)))</span>
<span class="mi">0</span>
<span class="mi">1</span>
<span class="mi">4</span>
<span class="mi">9</span>
<span class="mi">16</span>
</pre></div>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="fun.zeros">
<span class="sig-prename descclassname"><span class="pre">fun.</span></span><span class="sig-name descname"><span class="pre">zeros</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fun.zeros" title="Permalink to this definition">¶</a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>an iterator</p>
</dd>
</dl>
<p>The iterator returns <code class="docutils literal notranslate"><span class="pre">0</span></code> indefinitely.</p>
<p>Examples:</p>
<div class="highlight-lua notranslate"><div class="highlight"><pre><span></span><span class="o">></span> <span class="n">each</span><span class="p">(</span><span class="nb">print</span><span class="p">,</span> <span class="n">take</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="n">zeros</span><span class="p">()))</span>
<span class="mi">0</span>
<span class="mi">0</span>
<span class="mi">0</span>
<span class="mi">0</span>
<span class="mi">0</span>
</pre></div>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="fun.ones">
<span class="sig-prename descclassname"><span class="pre">fun.</span></span><span class="sig-name descname"><span class="pre">ones</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#fun.ones" title="Permalink to this definition">¶</a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>an iterator</p>
</dd>
</dl>
<p>The iterator that returns <code class="docutils literal notranslate"><span class="pre">1</span></code> indefinitely.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">></span> <span class="n">each</span><span class="p">(</span><span class="nb">print</span><span class="p">,</span> <span class="n">take</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="n">ones</span><span class="p">()))</span>
<span class="mi">1</span>
<span class="mi">1</span>
<span class="mi">1</span>
<span class="mi">1</span>
<span class="mi">1</span>
</pre></div>
</div>
</dd></dl>
</section>
<section id="random-sampling">
<h2>Random sampling<a class="headerlink" href="#random-sampling" title="Permalink to this headline">¶</a></h2>
<dl class="py function">
<dt class="sig sig-object py" id="fun.rands">
<span class="sig-prename descclassname"><span class="pre">fun.</span></span><span class="sig-name descname"><span class="pre">rands</span></span><span class="sig-paren">(</span><span class="optional">[</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="optional">[</span>, <em class="sig-param"><span class="n"><span class="pre">m</span></span></em><span class="optional">]</span><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#fun.rands" title="Permalink to this definition">¶</a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>n</strong> (<em>uint</em>) – an endpoint of the interval (see below)</p></li>
<li><p><strong>m</strong> (<em>uint</em>) – an endpoint of the interval (see below)</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>an iterator</p>
</dd>
</dl>
<p>The iterator returns random values using <code class="xref py py-func docutils literal notranslate"><span class="pre">math.random()</span></code>.
If the <strong>n</strong> and <strong>m</strong> are set then the iterator returns pseudo-random
integers in the <code class="docutils literal notranslate"><span class="pre">[n,</span> <span class="pre">m)</span></code> interval (i.e. <strong>m</strong> is not included).
If the <strong>m</strong> is not set then the iterator generates pseudo-random integers
in the <code class="docutils literal notranslate"><span class="pre">[0,</span> <span class="pre">n)</span></code> interval. When called without arguments returns
pseudo-random real numbers with uniform distribution in the
interval <code class="docutils literal notranslate"><span class="pre">[0,</span> <span class="pre">1)</span></code>.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>This iterator is not pure-functional and may not work as
expected with some library functions.</p>
</div>
<p>Examples:</p>
<div class="highlight-lua notranslate"><div class="highlight"><pre><span></span><span class="o">></span> <span class="n">each</span><span class="p">(</span><span class="nb">print</span><span class="p">,</span> <span class="n">take</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="n">rands</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">)))</span>
<span class="mi">19</span>
<span class="mi">17</span>
<span class="mi">11</span>
<span class="mi">19</span>
<span class="mi">12</span>
<span class="mi">13</span>
<span class="mi">14</span>
<span class="mi">16</span>
<span class="mi">10</span>
<span class="mi">11</span>
<span class="o">></span> <span class="n">each</span><span class="p">(</span><span class="nb">print</span><span class="p">,</span> <span class="n">take</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="n">rands</span><span class="p">(</span><span class="mi">10</span><span class="p">)))</span>
<span class="mi">7</span>
<span class="mi">6</span>
<span class="mi">5</span>
<span class="mi">9</span>
<span class="mi">0</span>
<span class="o">></span> <span class="n">each</span><span class="p">(</span><span class="nb">print</span><span class="p">,</span> <span class="n">take</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="n">rands</span><span class="p">()))</span>
<span class="mf">0.79420629243124</span>
<span class="mf">0.69885246563716</span>
<span class="mf">0.5901037417281</span>
<span class="mf">0.7532286166836</span>
<span class="mf">0.080971251199854</span>
</pre></div>
</div>
</dd></dl>
</section>
</section>
</div>
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