854 lines
65 KiB
HTML
854 lines
65 KiB
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<title>Zapiski #1 srečanja programerskega bralnega krožka SICP</title>
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</head>
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<body>
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<div id="content" class="content">
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<h1 class="title">Zapiski #1 srečanja programerskega bralnega krožka SICP</h1>
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<div id="outline-container-org6c75ca4" class="outline-2">
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<h2 id="org6c75ca4">Zanimivi izseki</h2>
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<div class="outline-text-2" id="text-org6c75ca4">
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</div>
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<div id="outline-container-org5cec0f2" class="outline-3">
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<h3 id="org5cec0f2">str. 9</h3>
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<div class="outline-text-3" id="text-org5cec0f2">
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<blockquote>
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<p>
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Every reader should ask himself periodically "Toward what end, toward what end?" — but do not ask it too often lest you pass up the fun of programming for the constipation of bittersweet philosophy.
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</p>
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</blockquote>
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<blockquote>
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<p>
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Lisp is a survivor, having been in use for about a quarter of a century.
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</p>
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</blockquote>
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</div>
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</div>
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<div id="outline-container-org4adf256" class="outline-3">
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<h3 id="org4adf256">str. 11</h3>
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<div class="outline-text-3" id="text-org4adf256">
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<blockquote>
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<p>
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It is better to have 100 functions operate on one data structure than to have 10 functions operate on 10 data structures.
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</p>
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</blockquote>
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</div>
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</div>
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<div id="outline-container-org22673ad" class="outline-3">
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<h3 id="org22673ad">str. 18</h3>
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<div class="outline-text-3" id="text-org22673ad">
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<blockquote>
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<p>
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Thus, programs must be written for people to read, and only incidentally for machines to execute.
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</p>
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</blockquote>
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</div>
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</div>
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<div id="outline-container-orgdb0b647" class="outline-3">
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<h3 id="orgdb0b647">str. 19</h3>
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<div class="outline-text-3" id="text-orgdb0b647">
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<blockquote>
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<p>
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Underlying our approach to this subject is our conviction that "computer science" is not a science and that its significance has little to do with computers.
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</p>
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</blockquote>
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</div>
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</div>
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<div id="outline-container-org0baccf7" class="outline-3">
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<h3 id="org0baccf7">str. 27</h3>
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<div class="outline-text-3" id="text-org0baccf7">
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<blockquote>
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<p>
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Finally, we would like to acknowledge the support of the organizations that have encouraged this work over the years, including support from Hewlett-Packard, made possible by Ira Goldstein and Joel Birnbaum, and support from DARPA, made possible by Bob Kahn.
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</p>
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</blockquote>
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<p>
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Bob Kahn je mdr. soavtor protokolov TCP in IP, pionir omreževanja. V DARPA postal kasneje direktor IPTO (Informational Processing Techniques Office), kjer je ustanovil milijardo-dolarski projekt Strategic Copmuting Initiative, največjo investicijo ameriške federalne vlade v računalništvo ever ('83 do '93) - razvijali so proizvodnjo čipov in umetne inteligence. Ustrašili so se japoncev, podobno kot v 50ih sovjetov.
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</p>
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<p>
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Po DARPA ustanovil CNRI (corporation for national research initiatives), neprofitno organizacijo kjer je delal tudi guido van rossum (avtor pythona). Tam so izdali python verzije 1.3 do 1.6 ter GNU mailman.
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</p>
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<p>
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Preko očeta v sorodu s fizikom Hermanom Kahnom, ki je napisal knjigo o tem kako bi amerika lahko zmagala nuklearno vojno in postal inspiracija za dr. Strangelove-a v znanem Kubrickovem filmu. Ustanovil je Hudson institut, konzervativni think tank ki je začel pri premišljevanju hladnovojnih scenarijev in se razširil na polja ekonomije, zdravstva, šolstva in gemblanja. Delal je tudi v RAND korporaciji, močnem hladnovojnem inštitutu, vpletenem v vietnamsko vojno, iraško vojno, danes pa kuri "AI apokaliptični" scenarij.
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</p>
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</div>
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</div>
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<div id="outline-container-orgc817fbe" class="outline-3">
|
||
|
|
<h3 id="orgc817fbe">str. 77</h3>
|
||
|
|
<div class="outline-text-3" id="text-orgc817fbe">
|
||
|
|
<p>
|
||
|
|
Stoy 1977
|
||
|
|
</p>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-orge562901" class="outline-2">
|
||
|
|
<h2 id="orge562901">Vaje</h2>
|
||
|
|
<div class="outline-text-2" id="text-orge562901">
|
||
|
|
</div>
|
||
|
|
<div id="outline-container-org6035a65" class="outline-3">
|
||
|
|
<h3 id="org6035a65">1.1 Kaj vrnejo izrazi?</h3>
|
||
|
|
<div class="outline-text-3" id="text-org6035a65">
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>+ 5 3 4<span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
10
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>- 9 1<span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
8
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>/ 6 2<span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
3
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>+ <span style="color: #b16286;">(</span>* 2 4<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>- 4 6<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
6
|
||
|
|
</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: #b57614;">a</span> 3<span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
#nil
|
||
|
|
</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: #b57614;">b</span> <span style="color: #b16286;">(</span>+ a 1<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
#nil
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>+ a b <span style="color: #b16286;">(</span>* a b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
19
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>= a b<span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
#f
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #9d0006;">if</span> <span style="color: #b16286;">(</span><span style="color: #9d0006;">and</span> <span style="color: #8ec07c;">(</span>> b a<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>< b <span style="color: #d65d0e;">(</span>* a b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
||
|
|
b
|
||
|
|
a<span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
4
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #9d0006;">cond</span> <span style="color: #b16286;">(</span><span style="color: #8ec07c;">(</span>= a 4<span style="color: #8ec07c;">)</span> 6<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #8ec07c;">(</span>= b 4<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>+ 6 7 a<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #9d0006;">else</span> 25<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
16
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>+ 2 <span style="color: #b16286;">(</span><span style="color: #9d0006;">if</span> <span style="color: #8ec07c;">(</span>> b a<span style="color: #8ec07c;">)</span> b a<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
6
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>* <span style="color: #b16286;">(</span><span style="color: #9d0006;">cond</span> <span style="color: #8ec07c;">(</span><span style="color: #d65d0e;">(</span>> a b<span style="color: #d65d0e;">)</span> a<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #d65d0e;">(</span>< a b<span style="color: #d65d0e;">)</span> b<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #9d0006;">else</span> -1<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>+ a 1<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
<p>
|
||
|
|
16
|
||
|
|
</p>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-orga3d30b3" class="outline-3">
|
||
|
|
<h3 id="orga3d30b3">1.2 Pretvori izraz v prefix obliko</h3>
|
||
|
|
<div class="outline-text-3" id="text-orga3d30b3">
|
||
|
|
\begin{equation}
|
||
|
|
\frac{5+4+(2-(3-(6+\frac{4}{5}))) }{3(6-2)(2-7)}
|
||
|
|
\end{equation}
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>/ <span style="color: #b16286;">(</span>+ 5 4
|
||
|
|
<span style="color: #8ec07c;">(</span>- 2
|
||
|
|
<span style="color: #d65d0e;">(</span>- 3
|
||
|
|
<span style="color: #458588;">(</span>+ 6
|
||
|
|
4/5<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>* 3
|
||
|
|
<span style="color: #8ec07c;">(</span>- 6 2<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>- 2 7<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<pre class="example">
|
||
|
|
-37/150
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org3889f6d" class="outline-3">
|
||
|
|
<h3 id="org3889f6d">1.3 določi postopek, ki prejme 3 števila kot argumente in vrne vsoto kvadratov večjih dveh</h3>
|
||
|
|
<div class="outline-text-3" id="text-org3889f6d">
|
||
|
|
<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;">vsota-vecjih-kvadratov</span> a b c<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #9d0006;">cond</span> <span style="color: #8ec07c;">(</span><span style="color: #d65d0e;">(</span><= a b c<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>+ <span style="color: #458588;">(</span>* b b<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>* c c<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #d65d0e;">(</span><= b a c<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>+ <span style="color: #458588;">(</span>* a a<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>* c c<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #9d0006;">else</span> <span style="color: #d65d0e;">(</span>+ <span style="color: #458588;">(</span>* b b<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>* a a<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #a89984;">;; </span><span style="color: #a89984;">^ NAROBE! <= primerja vse tri stevilke, ne prvo z drugima dvema oz. ostalimi</span>
|
||
|
|
|
||
|
|
<span style="color: #458588;">(</span><span style="color: #9d0006;">define</span> <span style="color: #b16286;">(</span><span style="color: #b57614;">+kvadrat</span> a b<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>+ <span style="color: #8ec07c;">(</span>* a a<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>* b b<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;">vsota-vecjih-kvadratov2</span> a b c<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #9d0006;">if</span> <span style="color: #8ec07c;">(</span>>= a b<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #9d0006;">if</span> <span style="color: #d65d0e;">(</span>>= b c<span style="color: #d65d0e;">)</span>
|
||
|
|
<span style="color: #d65d0e;">(</span>+kvadrat a b<span style="color: #d65d0e;">)</span>
|
||
|
|
<span style="color: #d65d0e;">(</span>+kvadrat a c<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #9d0006;">if</span> <span style="color: #d65d0e;">(</span>>= a c<span style="color: #d65d0e;">)</span>
|
||
|
|
<span style="color: #d65d0e;">(</span>+kvadrat a b<span style="color: #d65d0e;">)</span>
|
||
|
|
<span style="color: #d65d0e;">(</span>+kvadrat b c<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>list
|
||
|
|
'<span style="color: #b16286;">(</span><span style="color: #79740e;">"Pričakovano"</span> 85 41 164 89<span style="color: #b16286;">)</span>
|
||
|
|
|
||
|
|
<span style="color: #b16286;">(</span>list <span style="color: #79740e;">"Funkcija1"</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>vsota-vecjih-kvadratov 6 1 7<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>vsota-vecjih-kvadratov 3 4 5<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>vsota-vecjih-kvadratov 8 10 2<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>vsota-vecjih-kvadratov 3 8 5<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
||
|
|
|
||
|
|
<span style="color: #b16286;">(</span>list <span style="color: #79740e;">"Funkcija2"</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>vsota-vecjih-kvadratov2 6 1 7<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>vsota-vecjih-kvadratov2 3 4 5<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>vsota-vecjih-kvadratov2 8 10 2<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>vsota-vecjih-kvadratov2 3 8 5<span style="color: #8ec07c;">)</span><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-left" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
|
||
|
|
<col class="org-right" />
|
||
|
|
</colgroup>
|
||
|
|
<tbody>
|
||
|
|
<tr>
|
||
|
|
<td class="org-left">Pričakovano</td>
|
||
|
|
<td class="org-right">85</td>
|
||
|
|
<td class="org-right">41</td>
|
||
|
|
<td class="org-right">164</td>
|
||
|
|
<td class="org-right">89</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-left">Funkcija1</td>
|
||
|
|
<td class="org-right">85</td>
|
||
|
|
<td class="org-right">41</td>
|
||
|
|
<td class="org-right">164</td>
|
||
|
|
<td class="org-right">73</td>
|
||
|
|
</tr>
|
||
|
|
|
||
|
|
<tr>
|
||
|
|
<td class="org-left">Funkcija2</td>
|
||
|
|
<td class="org-right">85</td>
|
||
|
|
<td class="org-right">41</td>
|
||
|
|
<td class="org-right">164</td>
|
||
|
|
<td class="org-right">89</td>
|
||
|
|
</tr>
|
||
|
|
</tbody>
|
||
|
|
</table>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org3946afc" class="outline-3">
|
||
|
|
<h3 id="org3946afc">1.4 Opis procedure</h3>
|
||
|
|
<div class="outline-text-3" id="text-org3946afc">
|
||
|
|
<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;">a-plus-abs-b</span> a b<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #8ec07c;">(</span><span style="color: #9d0006;">if</span> <span style="color: #d65d0e;">(</span>> b 0<span style="color: #d65d0e;">)</span> + -<span style="color: #8ec07c;">)</span> a b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Izraz <code>if</code> vrne funkcijo <code>+</code> ali <code>-</code> , glede na to, ali je argument <code>b</code> večji ali manjši od 0.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Če je <code>b</code> manjši od 0, ga odšteje od <code>a</code>, sicer pa ga prišeje. Zato je rezultat funkcije ekvivalenten vsoti <code>a</code> in absolutnega <code>b</code>.
|
||
|
|
</p>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org4e9feb3" class="outline-3">
|
||
|
|
<h3 id="org4e9feb3">1.5 Aplikativni red in normalni red evalvacije</h3>
|
||
|
|
<div class="outline-text-3" id="text-org4e9feb3">
|
||
|
|
<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;">p</span><span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>p<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;">test</span> x y<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #9d0006;">if</span> <span style="color: #8ec07c;">(</span>= x 0<span style="color: #8ec07c;">)</span>
|
||
|
|
0
|
||
|
|
y<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
|
||
|
|
<span style="color: #a89984;">;; </span><span style="color: #a89984;">Evalvira:</span>
|
||
|
|
<span style="color: #458588;">(</span>test 0 <span style="color: #b16286;">(</span>p<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Če interpreter deluje po aplikativnem zaporedju, bo najprej evalviral argumente. Ker je drugi argument postopek, ki v neskončnost vrača vrednost klica samega sebe, se bo program zaciklal oz. zmrznil.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Če pa interpreter deluje po normalnem zaporedju, bo pa začel izvajat postopek pred evalvacijo argumentov, le-te pa šele ko jih potrebuje. Tako bo, <code>if</code> stavek prepoznal ekvivalenco <code>x</code> in <code>0</code> ter vrnil <code>0</code>.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Klic takšne funkcije torej preveri ali interpreter deluje po aplikativnem ali normalnem zaporedju.
|
||
|
|
Guile scheme deluje po aplikativnem redu (in se zacikla). Normalni red pa lahko "simuliramo", če proceduro definiramo kot macro, z <code>define-case</code>. Klic macroja se ne zacikla.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #9d0006;">define-macro</span> <span style="color: #b16286;">(</span><span style="color: #076678;">test-m</span> x y<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #9d0006;">if</span> <span style="color: #8ec07c;">(</span>= x 0<span style="color: #8ec07c;">)</span>
|
||
|
|
0
|
||
|
|
y<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
|
||
|
|
<span style="color: #458588;">(</span>test-m 0 <span style="color: #b16286;">(</span>p<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<pre class="example">
|
||
|
|
0
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org9791637" class="outline-3">
|
||
|
|
<h3 id="org9791637">1.6 Novi if</h3>
|
||
|
|
<div class="outline-text-3" id="text-org9791637">
|
||
|
|
<p>
|
||
|
|
Imamo nov <code>if</code>, <code>new-if</code>.
|
||
|
|
</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;">new-if</span> predicate then-clause else-clause<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #9d0006;">cond</span> <span style="color: #8ec07c;">(</span>predicate then-clause<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #9d0006;">else</span> else-clause<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Kaj se zgodi, če ga uporabimo za računanje kvadratnih korenov?
|
||
|
|
</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;">sqrt-iter</span> guess x<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>new-if <span style="color: #8ec07c;">(</span>good-enough? guess x<span style="color: #8ec07c;">)</span>
|
||
|
|
guess
|
||
|
|
<span style="color: #8ec07c;">(</span>sqrt-iter <span style="color: #d65d0e;">(</span>improve guess x<span style="color: #d65d0e;">)</span>
|
||
|
|
x<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Navaden <code>if</code> je v bistvu makro in deluje po normalnem zaporedju. Ker je <code>new-if</code> definiran kot procedura, mora zaradi aplikativnega zaporedja najprej evalvirati argumente. Zato se zacikla oz. zamrzne.
|
||
|
|
</p>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org0bb7889" class="outline-3">
|
||
|
|
<h3 id="org0bb7889">1.7 good-enough? ni dovolj dober?</h3>
|
||
|
|
<div class="outline-text-3" id="text-org0bb7889">
|
||
|
|
<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;">average</span> x y<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>/ <span style="color: #8ec07c;">(</span>+ x y<span style="color: #8ec07c;">)</span> 2<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;">improve</span> guess x<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>average guess <span style="color: #8ec07c;">(</span>/ x guess<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;">good-enough?</span> guess x<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>< <span style="color: #8ec07c;">(</span>abs <span style="color: #d65d0e;">(</span>- <span style="color: #458588;">(</span>square guess<span style="color: #458588;">)</span> x<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span> 0.001<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;">sqrt-iter</span> guess x<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #9d0006;">if</span> <span style="color: #8ec07c;">(</span>good-enough? guess x<span style="color: #8ec07c;">)</span>
|
||
|
|
guess
|
||
|
|
<span style="color: #8ec07c;">(</span>sqrt-iter <span style="color: #d65d0e;">(</span>improve guess x<span style="color: #d65d0e;">)</span>
|
||
|
|
x<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;">sqrt</span> x<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>sqrt-iter 1.0 x<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Pri premajhnih številih <code>good-enough?</code> prehitro "odneha" in dobimo slab približek, pri prevelikih številih pa "predolgo vztraja", saj ne potrebujemo tako natančnega približka. Boljša rešitev s precej elegance je, recimo, primerjava s promilom <code>x</code> namesto 0.001.
|
||
|
|
</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;">good-enough?</span> guess x<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>< <span style="color: #8ec07c;">(</span>abs <span style="color: #d65d0e;">(</span>- <span style="color: #458588;">(</span>square guess<span style="color: #458588;">)</span> x<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>* 0.001 x<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org019423b" class="outline-3">
|
||
|
|
<h3 id="org019423b">1.8 kubični koren</h3>
|
||
|
|
<div class="outline-text-3" id="text-org019423b">
|
||
|
|
<p>
|
||
|
|
Formula za izboljšanje približka <code>y</code> kubičnemu korenu <code>x</code> je
|
||
|
|
</p>
|
||
|
|
\begin{equation}
|
||
|
|
\frac{x/y^{2}+2y}{3}
|
||
|
|
\end{equation}
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Postopek: TODO
|
||
|
|
</p>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org9849c85" class="outline-3">
|
||
|
|
<h3 id="org9849c85">1.10 Ackermannov postopek</h3>
|
||
|
|
<div class="outline-text-3" id="text-org9849c85">
|
||
|
|
<p>
|
||
|
|
Sledeči postopek je Ackermannov:
|
||
|
|
</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;">A</span> x y<span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span><span style="color: #9d0006;">cond</span> <span style="color: #8ec07c;">(</span><span style="color: #d65d0e;">(</span>= y 0<span style="color: #d65d0e;">)</span> 0<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #d65d0e;">(</span>= x 0<span style="color: #d65d0e;">)</span>
|
||
|
|
<span style="color: #d65d0e;">(</span>* 2 y<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #d65d0e;">(</span>= y 1<span style="color: #d65d0e;">)</span> 2<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span><span style="color: #9d0006;">else</span> <span style="color: #d65d0e;">(</span>A <span style="color: #458588;">(</span>- x 1<span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A x <span style="color: #b16286;">(</span>- y 1<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: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Kakšni so rezultati sledečih izrazov?
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<ul class="org-ul">
|
||
|
|
<li><code>(A 1 10)</code></li>
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>A 1 10<span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 1 9<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 1 8<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 1 7<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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 1 6<span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 1 5<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: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 1 4<span style="color: #8ec07c;">)</span><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: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 1 3<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><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: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 1 2<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><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: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 1 1<span style="color: #458588;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><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: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 2<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><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: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 4<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><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: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 8<span style="color: #8ec07c;">)</span><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: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 16<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: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 32<span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 64<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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 128<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 256<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 512<span style="color: #458588;">)</span>
|
||
|
|
|
||
|
|
1024
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<ul class="org-ul">
|
||
|
|
<li><code>(A 2 4)</code></li>
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>A 2 4<span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 2 3<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 2 2<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 2 1<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 1 2<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 1 2<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
||
|
|
<span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 1 1<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 1 <span style="color: #458588;">(</span>A 0 2<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 1 <span style="color: #458588;">(</span>A 0 2<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 1 4<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 1 3<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 1 2<span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 1 1<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 2<span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 4<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 0 8<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 1 16<span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 1 15<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
|
||
|
|
<span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 1 14<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
|
||
|
|
...
|
||
|
|
<span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 1 14<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 1<span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><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: #458588;">)</span><span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 2<span style="color: #458588;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><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: #458588;">)</span><span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 4<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><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: #458588;">)</span><span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 8<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><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: #458588;">)</span><span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 16<span style="color: #8ec07c;">)</span><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: #458588;">)</span><span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 32<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: #458588;">)</span><span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 64<span style="color: #458588;">)</span><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: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 128<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: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 256<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 512<span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 <span style="color: #458588;">(</span>A 0 1024<span style="color: #458588;">)</span><span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 0 2048<span style="color: #458588;">)</span><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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 4096<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>A 0 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 8192<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 <span style="color: #b16286;">(</span>A 0 16384<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 0 32768<span style="color: #458588;">)</span>
|
||
|
|
|
||
|
|
65536
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<ul class="org-ul">
|
||
|
|
<li><code>(A 3 3)</code></li>
|
||
|
|
</ul>
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span>A 3 3<span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 2 <span style="color: #b16286;">(</span>A 3 2<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 2 <span style="color: #b16286;">(</span>A 2 <span style="color: #8ec07c;">(</span>A 3 1<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 2 <span style="color: #b16286;">(</span>A 2 2<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 2 <span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 2 1<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 2 <span style="color: #b16286;">(</span>A 1 2<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 2 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 1 1<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 2 <span style="color: #b16286;">(</span>A 0 2<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 2 4<span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 2 3<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 2 2<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 1 <span style="color: #d65d0e;">(</span>A 2 1<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>A 1 <span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 1 2<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 1 1<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>A 1 <span style="color: #b16286;">(</span>A 1 <span style="color: #8ec07c;">(</span>A 0 2<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 1 4<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 1 3<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 1 2<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>A 1 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 <span style="color: #458588;">(</span>A 1 1<span style="color: #458588;">)</span><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>A 1 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 <span style="color: #d65d0e;">(</span>A 0 2<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>A 1 <span style="color: #b16286;">(</span>A 0 <span style="color: #8ec07c;">(</span>A 0 4<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 <span style="color: #b16286;">(</span>A 0 8<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
<span style="color: #458588;">(</span>A 1 16<span style="color: #458588;">)</span>
|
||
|
|
|
||
|
|
65536
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Če imamo še sledeče postopke:
|
||
|
|
</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;">f</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>A 0 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;">g</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>A 1 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;">h</span> n <span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>A 2 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;">k</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* 5 n n<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>
|
||
|
|
Jedrnato opredeli matematične funkcije izračuna postopkov <code>f</code>, <code>g</code> in <code>h</code>. <code>k</code>, recimo izračuna <code>5n^2</code>.
|
||
|
|
</p>
|
||
|
|
|
||
|
|
<blockquote>
|
||
|
|
<p>
|
||
|
|
<code>f</code>: 2n
|
||
|
|
</p>
|
||
|
|
</blockquote>
|
||
|
|
|
||
|
|
<blockquote>
|
||
|
|
<p>
|
||
|
|
<code>g</code>: 2<sup>n</sup>
|
||
|
|
</p>
|
||
|
|
</blockquote>
|
||
|
|
|
||
|
|
<blockquote>
|
||
|
|
<p>
|
||
|
|
<code>h</code>: 2<sup>2<sup>n</sup></sup>
|
||
|
|
</p>
|
||
|
|
</blockquote>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</body>
|
||
|
|
</html>
|