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<a href="./Home">MLton 20201002</a>
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<h1>Lazy</h1>
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<div class="paragraph"><p>In a lazy (or non-strict) language, the arguments to a function are
not evaluated before calling the function.  Instead, the arguments are
suspended and only evaluated by the function if needed.</p></div>
<div class="paragraph"><p><a href="StandardML">Standard ML</a> is an eager (or strict) language, not a lazy
language.  However, it is easy to delay evaluation of an expression in
SML by creating a <em>thunk</em>, which is a nullary function.  In SML, a
thunk is written <span class="monospaced">fn () =&gt; e</span>.  Another essential feature of laziness
is <em>memoization</em>, meaning that once a suspended argument is evaluated,
subsequent references look up the value.  We can express this in SML
with a function that maps a thunk to a memoized thunk.</p></div>
<div class="listingblock">
<div class="content"><div class="highlight"><pre><span></span><span class="k">signature</span><span class="w"> </span><span class="n">LAZY</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">sig</span><span class="w"></span>
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">lazy</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>
</pre></div></div></div>
<div class="paragraph"><p>This is easy to implement in SML.</p></div>
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<div class="content"><div class="highlight"><pre><span></span><span class="k">structure</span><span class="w"> </span><span class="n">Lazy</span><span class="p">:</span><span class="w"> </span><span class="n">LAZY</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">   </span><span class="k">struct</span><span class="w"></span>
<span class="w">      </span><span class="k">fun</span><span class="w"> </span><span class="n">lazy</span><span class="w"> </span><span class="p">(</span><span class="n">th</span><span class="p">:</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">):</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="p">=</span><span class="w"></span>
<span class="w">         </span><span class="k">let</span><span class="w"></span>
<span class="w">            </span><span class="k">datatype</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">lazy_result</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Unevaluated</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">(</span><span class="n">unit</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">&#39;a</span><span class="p">)</span><span class="w"></span>
<span class="w">                                    </span><span class="p">|</span><span class="w"> </span><span class="n">Evaluated</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"></span>
<span class="w">                                    </span><span class="p">|</span><span class="w"> </span><span class="n">Failed</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">exn</span><span class="w"></span>

<span class="w">            </span><span class="k">val</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ref</span><span class="w"> </span><span class="p">(</span><span class="n">Unevaluated</span><span class="w"> </span><span class="n">th</span><span class="p">)</span><span class="w"></span>
<span class="w">         </span><span class="k">in</span><span class="w"></span>
<span class="w">            </span><span class="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>
<span class="w">               </span><span class="k">case</span><span class="w"> </span><span class="n">!r</span><span class="w"> </span><span class="k">of</span><span class="w"></span>
<span class="w">                   </span><span class="n">Unevaluated</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">let</span><span class="w"></span>
<span class="w">                                       </span><span class="k">val</span><span class="w"> </span><span class="n">a</span><span class="w">  </span><span class="p">=</span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">()</span><span class="w"></span>
<span class="w">                                           </span><span class="k">handle</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="n">:=</span><span class="w"> </span><span class="n">Failed</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"></span>
<span class="w">                                       </span><span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w">         </span><span class="n">r</span><span class="w"> </span><span class="n">:=</span><span class="w"> </span><span class="n">Evaluated</span><span class="w"> </span><span class="n">a</span><span class="w"></span>
<span class="w">                                     </span><span class="k">in</span><span class="w"></span>
<span class="w">                                       </span><span class="n">a</span><span class="w"></span>
<span class="w">                                     </span><span class="k">end</span><span class="w"></span>
<span class="w">                 </span><span class="p">|</span><span class="w"> </span><span class="n">Evaluated</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">a</span><span class="w"></span>
<span class="w">                 </span><span class="p">|</span><span class="w"> </span><span class="n">Failed</span><span class="w"> </span><span class="n">x</span><span class="w">    </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="n">x</span><span class="w"></span>
<span class="w">         </span><span class="k">end</span><span class="w"></span>
<span class="w">   </span><span class="k">end</span><span class="w"></span>
</pre></div></div></div>
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