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<div id="content" class="content">
<h1 class="title">Zapiski #3 srečanja programerskega bralnega krožka SICP</h1>
<div id="outline-container-org3870a64" class="outline-2">
<h2 id="org3870a64">Teme</h2>
<div class="outline-text-2" id="text-org3870a64">
</div>
<div id="outline-container-orga631c9e" class="outline-3">
<h3 id="orga631c9e">Funkcije višjega reda</h3>
</div>
</div>
<div id="outline-container-org9304723" class="outline-2">
<h2 id="org9304723">Vaje</h2>
<div class="outline-text-2" id="text-org9304723">
</div>
<div id="outline-container-org5904c5a" class="outline-3">
<h3 id="org5904c5a">1.29 Simpsonovo pravilo</h3>
<div class="outline-text-3" id="text-org5904c5a">
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #9d0006;">define</span><span style="color: #b16286;">(</span><span style="color: #b57614;">cube</span> x<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span>* x x x<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span><span style="color: #b16286;">(</span><span style="color: #b57614;">sum-integers</span> a b<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">if</span> <span style="color: #8ec07c;">(</span> &gt; a b<span style="color: #8ec07c;">)</span>
0
<span style="color: #8ec07c;">(</span>+ a <span style="color: #d65d0e;">(</span>sum-integers <span style="color: #458588;">(</span>+ a 1<span style="color: #458588;">)</span> b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span><span style="color: #b16286;">(</span><span style="color: #b57614;">sum-cubes</span> a b<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">if</span> <span style="color: #8ec07c;">(</span>&gt; a b<span style="color: #8ec07c;">)</span>
0
<span style="color: #8ec07c;">(</span>+ <span style="color: #d65d0e;">(</span>cube a<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>sum-cubes<span style="color: #458588;">(</span>+ a 1<span style="color: #458588;">)</span> b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">sum</span> term a next b<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">if</span> <span style="color: #8ec07c;">(</span>&gt; a b<span style="color: #8ec07c;">)</span>
0
<span style="color: #8ec07c;">(</span>+ <span style="color: #d65d0e;">(</span>term a<span style="color: #d65d0e;">)</span>
<span style="color: #d65d0e;">(</span>sum term <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> next b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">integral</span> f a b dx<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #b57614;">add-dx</span> x<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>+ x dx<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span>* <span style="color: #8ec07c;">(</span>sum f <span style="color: #d65d0e;">(</span>+ a <span style="color: #458588;">(</span>/ dx 2.0<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span> add-dx b<span style="color: #8ec07c;">)</span>
dx<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">simpson</span> f a b n<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b57614;">h</span> <span style="color: #8ec07c;">(</span>/ <span style="color: #d65d0e;">(</span>- b a<span style="color: #d65d0e;">)</span> n<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #b57614;">add-hh</span> a<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>+ a h h<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span>* <span style="color: #8ec07c;">(</span>+ <span style="color: #d65d0e;">(</span>- <span style="color: #458588;">(</span>f a<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
<span style="color: #d65d0e;">(</span>* 2 <span style="color: #458588;">(</span>sum f a add-hh b<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
<span style="color: #d65d0e;">(</span>* 4 <span style="color: #458588;">(</span>sum f <span style="color: #b16286;">(</span>+ a h<span style="color: #b16286;">)</span> add-hh b<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
<span style="color: #d65d0e;">(</span>- <span style="color: #458588;">(</span>f b<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
<span style="color: #8ec07c;">(</span>/ h 3.0<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span>list <span style="color: #b16286;">(</span>simpson cube 1 2 100<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span>simpson cube 1 2 1000<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-right" />
</colgroup>
<tbody>
<tr>
<td class="org-right">3.7500000000000004</td>
<td class="org-right">3.75</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org55533ea" class="outline-3">
<h3 id="org55533ea">1.30 linearen sum</h3>
<div class="outline-text-3" id="text-org55533ea">
<p>
Rekurzivne procedure:
</p>
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">sum</span> term a next b<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">if</span> <span style="color: #8ec07c;">(</span>&gt; a b<span style="color: #8ec07c;">)</span>
0
<span style="color: #8ec07c;">(</span>+ <span style="color: #d65d0e;">(</span>term a<span style="color: #d65d0e;">)</span>
<span style="color: #d65d0e;">(</span>sum term <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> next b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">cube</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* n n n<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">inc</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>+ n 1<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">sum-cubes</span> a b<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span>sum cube a inc b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span>sum-cubes 1 10<span style="color: #458588;">)</span>
</pre>
</div>
<pre class="example">
3025
</pre>
<p>
Iterativne procedure:
</p>
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">sum-iter</span> term a next b<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #b57614;">iter</span> a result<span style="color: #8ec07c;">)</span>
<span style="color: #8ec07c;">(</span><span style="color: #9d0006;">if</span> <span style="color: #d65d0e;">(</span>&gt; a b<span style="color: #d65d0e;">)</span>
result
<span style="color: #d65d0e;">(</span>iter <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>+ result <span style="color: #b16286;">(</span>term a<span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span>iter a 0<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">cube</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* n n n<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">inc</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>+ n 1<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">sum-cubes-iter</span> a b<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span>sum-iter cube a inc b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span>sum-cubes-iter 1 10<span style="color: #458588;">)</span>
</pre>
</div>
<pre class="example">
3025
</pre>
</div>
</div>
<div id="outline-container-orgf8c5fef" class="outline-3">
<h3 id="orgf8c5fef">1.31 Produkt višjega reda</h3>
<div class="outline-text-3" id="text-orgf8c5fef">
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">prod-iter</span> term a next b<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #b57614;">iter</span> a result<span style="color: #8ec07c;">)</span>
<span style="color: #8ec07c;">(</span><span style="color: #9d0006;">if</span> <span style="color: #d65d0e;">(</span>&gt; a b<span style="color: #d65d0e;">)</span>
result
<span style="color: #d65d0e;">(</span>iter <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>* result <span style="color: #b16286;">(</span>term a<span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span>iter a 0<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">piblizek</span> n<span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span><span style="color: #9d0006;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #b57614;">stevec</span> n<span style="color: #8ec07c;">)</span>
<span style="color: #8ec07c;">(</span>+ n 2<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
<span style="color: #b16286;">(</span>* 4 <span style="color: #8ec07c;">(</span>/ <span style="color: #d65d0e;">(</span>prod-iter <span style="color: #458588;">(</span><span style="color: #9d0006;">lambda</span> <span style="color: #b16286;">(</span>n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* <span style="color: #8ec07c;">(</span>- n 1<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>+ n 1<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
3
stevec
n<span style="color: #d65d0e;">)</span>
<span style="color: #d65d0e;">(</span>prod-iter <span style="color: #458588;">(</span><span style="color: #9d0006;">lambda</span> <span style="color: #b16286;">(</span>n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* n n<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
3
stevec
n<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
<span style="color: #458588;">(</span>piblizek 10<span style="color: #458588;">)</span>
</pre>
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<p>
TODO popravi!
</p>
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