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<div id="content" class="content">
<h1 class="title">Structure and Interpretation of Computer Programs</h1>
<div id="table-of-contents" role="doc-toc">
<h2>Table of Contents</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#org1ab68a2">Foreword and Preface</a></li>
<li><a href="#org6693cbf">1. Grajenje abstrakcij s procedurami</a>
<ul>
<li><a href="#org6b0ed2e">1.1. Elementi programiranja</a></li>
<li><a href="#orgebcf1d6">1.2. Izvajanje kombinacij(e)</a></li>
<li><a href="#org8937279">1.3. 1.1.4 Sestavljene procedure</a></li>
<li><a href="#orgcb5c684">1.4. 1.1.5 Substitucijski model za izvajanje procedur</a></li>
<li><a href="#org0a42e4c">1.5. meta</a>
<ul>
<li><a href="#orgb0f9514">1.5.1. video lekcije</a></li>
</ul>
</li>
<li><a href="#orgd2a78f0">1.6. vaje</a>
<ul>
<li><a href="#org7790bc5">1.6.1. 1.3</a></li>
<li><a href="#org3ccc9ff">1.6.2. 1.5</a></li>
<li><a href="#orge03b4b9">1.6.3. 1.6</a></li>
<li><a href="#org62edd3c">1.6.4. 1.7</a></li>
<li><a href="#org42d25fe">1.6.5. 1.8</a></li>
</ul>
</li>
<li><a href="#org670694e">1.7. 1.1.8 Procedure kot crne skatle abstrakcij</a></li>
<li><a href="#org058363a">1.8. 1.2.2 Drevesna rekurzija</a></li>
<li><a href="#orga2d0d00">1.9. 1.2.3 Redi rasti</a></li>
<li><a href="#orgdb2bb3d">1.10. 1.2.4 Eksponentna funkcija</a></li>
<li><a href="#org867a680">1.11. 1.2.5 Najvecji skupni deljitel</a></li>
<li><a href="#org29472e2">1.12. 1.2.6 Primer: Iskanje prastevil</a></li>
<li><a href="#org84f4b2d">1.13. 1.3 Sestavljanje abstrakcij s procedurami visjega reda</a></li>
<li><a href="#org43a7808">1.14. 1.3.1 Procedure kot argumenti</a></li>
<li><a href="#orga384969">1.15. 1.3.2 Sestavljanje procedur z <code>Lambda</code></a></li>
<li><a href="#org590844a">1.16. 1.3.3 Procedure kot splosne metode</a></li>
<li><a href="#org8a3aa7d">1.17. 1.3.4 Procedure kot vrnjene vrednosti</a></li>
</ul>
</li>
<li><a href="#org66fd37e">2. Grajenje absrakcij s podatki</a>
<ul>
<li><a href="#org501bf16">2.1. Uvod v podatkovne abstrakcije</a>
<ul>
<li><a href="#orga2f86a5">2.1.1. Aritmeticne operacije z racionalnimi stevili</a></li>
<li><a href="#org9d926fd">2.1.2. Pregrade abstrakcij</a></li>
<li><a href="#org518e1e2">2.1.3. Kaj so podatki?</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org1ab68a2" class="outline-2">
<h2 id="org1ab68a2">Foreword and Preface</h2>
<div class="outline-text-2" id="text-org1ab68a2">
<blockquote>
<p>
Lisp je preživeli, v uporabi je že "polovico stoletja".
</p>
</blockquote>
<blockquote>
<p>
The discretionary exportable functionality entrusted to the individual Lisp programmer
is more than an order of magniture greater than that to be found within Pascal enterprises.
</p>
</blockquote>
<blockquote>
<p>
Želimo vzpostaviti idejo, da programski jezik ni samo način, da računalnik izvaja operacije,
ampak da je predvsem nov formalni medij za izražanje idej o metodologiji. Zato morajo biti
programi napisani predvsem zato, da jih ljudje berejo, in slučajno, da jih izvajajo računalniki.
</p>
<p>
Bistvena tema ni sintaksa določenih struktur v programskem jeziku, niti &#x2026;, temveč tehnike
nadzora intelektualne kompleksnosti veliki programskih sistemov.
</p>
</blockquote>
<blockquote>
<p>
Naš pristop k temi izvira iz prepričanja, da "computer science" ni znanost in da ima njen
pomen bolj malo opraviti z računalniki. Računalniška revolucija je revolucija v načinu
mišljenja in izražanju idej. Bistvo teh sprememb najbolše opiše pojem
<span class="underline">proceduralne epistemologije</span>, ki se ukvarja s strukturo vednosti z imperativnega stališča
za razliko od klasične matematike, ki je bolj deklerativna. Matematika postavi okvir za
natančno spoprijemanje s pojmovanjem "kaj je". Računanje pa ponudi okvir za natančno
ukvarjanje s pojmovanjem "kako".
</p>
</blockquote>
</div>
</div>
<div id="outline-container-org6693cbf" class="outline-2">
<h2 id="org6693cbf"><span class="section-number-2">1.</span> Grajenje abstrakcij s procedurami</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org6b0ed2e" class="outline-3">
<h3 id="org6b0ed2e"><span class="section-number-3">1.1.</span> Elementi programiranja</h3>
<div class="outline-text-3" id="text-1-1">
<dl class="org-dl">
<dt>Primitivni izrazi</dt><dd>predstavtljajo najpreprostejše gradnike (entitete)
programskega jezika</dd>
<dt>Načini kombinacije,</dt><dd>s katerimi so sestavljeni elementi zgrajeni iz
preprostejših</dd>
<dt>Načini abstrakcije,</dt><dd>s katerimi so lahko sestavljeni elementi poimenovani in
omogočajo upravljanje z njimii kot enotami</dd>
</dl>
</div>
</div>
<div id="outline-container-orgebcf1d6" class="outline-3">
<h3 id="orgebcf1d6"><span class="section-number-3">1.2.</span> Izvajanje kombinacij(e)</h3>
<div class="outline-text-3" id="text-1-2">
<p>
Postopek za izvajanje kombinacij:
</p>
<ol class="org-ol">
<li>Izvedi podizraz kombinacije.</li>
<li>Uporabi/uveljavi proceduro, ki je najbolje levi podizraz (operator) z
argumenti, ki so vrednosti drugih podizrazov (operandi).</li>
</ol>
<p>
Postopek evalvacije je rekurziven, saj drugi korak v sebi vključuje prvega,
oziroma vključuje svojo definicijo.
</p>
<p>
Tako se zgradi akumulacijsko drevo. Na koncu vedno prideš do točke, ko izvajaš
primitivne izraze, ki so:
</p>
<ul class="org-ul">
<li>vrednosti numeričnih števk, ki jo označujejo.</li>
<li>vrednosti vgrajenih operatorjev so strojni ukazi sekvenc, ki izvedejo te
operacije.</li>
<li>vrednosti drugih imen so objekti asociirani s temi imeni v okolju.</li>
</ul>
<p>
Drugo pravilo je poseben primer tretjega pravila. Simboli + in * so tudi
vključeni v globalno okolje in so asociirani s strojnimi ukazi, ki so njihove
vrednosti. <b>Pomembno je prepoznati vlogo okolja pri določanju pomena simbolov v
izrazih.</b>
</p>
<p>
To pravilo se ne nanaša na <span class="underline">posebne oblike (special forms)</span>. <code>define</code> je posebna
oblika.
</p>
</div>
</div>
<div id="outline-container-org8937279" class="outline-3">
<h3 id="org8937279"><span class="section-number-3">1.3.</span> 1.1.4 Sestavljene procedure</h3>
<div class="outline-text-3" id="text-1-3">
<ul class="org-ul">
<li>Številke in aritmetične operacije so primitivni podatki in procedure.</li>
<li>Gnezdenje kombinacij omogoča način za združevanje operacij.</li>
<li>Definicije, ki asociirajo imena z vrednostmi omogočajo omejene načine
abstrakcije.</li>
</ul>
<p>
<code>(define (square x) (* x x))</code>
</p>
<p>
<code>(define square (lambda (x) (* x x)))</code>
</p>
</div>
</div>
<div id="outline-container-orgcb5c684" class="outline-3">
<h3 id="orgcb5c684"><span class="section-number-3">1.4.</span> 1.1.5 Substitucijski model za izvajanje procedur</h3>
<div class="outline-text-3" id="text-1-4">
<p>
Za izvajanje sestavljenih procedur z argumenti, izvedeš telo procedure z vsakim
formalnim parametrom, ki ga nadomestiš s pripadajočim argumentom.
</p>
<p>
<span class="underline">ergh, tukaj se zapletam s slovenskimi prevodi</span>
</p>
<p>
<span class="underline">kaj je application in kaj evaluation?</span>
</p>
<p>
Načini, na katere deluje interpreter (prevajalnik):
</p>
<dl class="org-dl">
<dt>Aplikativni vrstni red</dt><dd>Najprej evalviraj operator in operande, potem pa
izvedi proizvedeno proceduro s pridobljenimi argumenti.</dd>
<dt>Normalni vrstni red</dt><dd>Ne izvajaj operandov dokler njihove vrednost niso
potrebne. Najprej zamenjaj izraze operandov s parametri, dokler ne pride do
izraza, ki vsebuje zgolj primitivne izraze in potem izvedi (vso) evalvacijo.</dd>
</dl>
</div>
</div>
<div id="outline-container-org0a42e4c" class="outline-3">
<h3 id="org0a42e4c"><span class="section-number-3">1.5.</span> meta</h3>
<div class="outline-text-3" id="text-1-5">
<p>
Linki:
<a href="https://develop.spacemacs.org/layers/+lang/scheme/README.html">https://develop.spacemacs.org/layers/+lang/scheme/README.html</a>
<a href="https://www.nongnu.org/geiser/">https://www.nongnu.org/geiser/</a>
<a href="https://www.gnu.org/software/guile/learn/">https://www.gnu.org/software/guile/learn/</a>
<a href="https://spritely.institute/static/papers/scheme-primer.html#introduction">https://spritely.institute/static/papers/scheme-primer.html#introduction</a>
</p>
<p>
Kako nastavit spacemacs, in malo o guile-u.
</p>
</div>
<div id="outline-container-orgb0f9514" class="outline-4">
<h4 id="orgb0f9514"><span class="section-number-4">1.5.1.</span> video lekcije</h4>
<div class="outline-text-4" id="text-1-5-1">
<p>
<a href="https://yewtu.be/channel/UCEBb1b_L6zDS3xTUrIALZOw">https://yewtu.be/channel/UCEBb1b_L6zDS3xTUrIALZOw</a> (6.001 SICP: Structure and Interpretation of Computer Programs (2004))
<a href="https://yewtu.be/playlist?list=PL7BcsI5ueSNFPCEisbaoQ0kXIDX9rR5FF">https://yewtu.be/playlist?list=PL7BcsI5ueSNFPCEisbaoQ0kXIDX9rR5FF</a> (MIT 6.001 Structure and Interpretation, 1986)
</p>
</div>
</div>
</div>
<div id="outline-container-orgd2a78f0" class="outline-3">
<h3 id="orgd2a78f0"><span class="section-number-3">1.6.</span> vaje</h3>
<div class="outline-text-3" id="text-1-6">
</div>
<div id="outline-container-org7790bc5" class="outline-4">
<h4 id="org7790bc5"><span class="section-number-4">1.6.1.</span> 1.3</h4>
<div class="outline-text-4" id="text-1-6-1">
</div>
<ol class="org-ol">
<li><a id="orga11bbd9"></a>najprej narobe<br />
<div class="outline-text-5" id="text-1-6-1-1">
<p>
Define a procedure that takes three numbers as arguments and returns the sum of
the squares of the two larger numbers.
</p>
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sum-of-large</span> x y z<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>+
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>&gt; x y<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>* x x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>* y y<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>&gt; y z<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>* y y<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>* z z<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span>sum-of-large <span style="color: #a45bad;">3</span> <span style="color: #a45bad;">8</span> <span style="color: #a45bad;">5</span><span style="color: #4f97d7;">)</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sum-of-larger</span> x y z<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">let*</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>s <span style="color: #b1951d;">(</span><span style="color: #4f97d7; font-weight: bold;">lambda</span> <span style="color: #4f97d7;">(</span>a<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>* a a<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>sl <span style="color: #b1951d;">(</span><span style="color: #4f97d7; font-weight: bold;">lambda</span> <span style="color: #4f97d7;">(</span>b c<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #bc6ec5;">(</span>&gt; b c<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>s b<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>s c<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>+ <span style="color: #67b11d;">(</span>sl x y<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>sl y z<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span>sum-of-larger <span style="color: #a45bad;">3</span> <span style="color: #a45bad;">8</span> <span style="color: #a45bad;">5</span><span style="color: #4f97d7;">)</span>
</pre>
</div>
</div>
</li>
<li><a id="orga97ce26"></a>pravilno<br />
<div class="outline-text-5" id="text-1-6-1-2">
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sum-squares-of-larger</span> x y z<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>&gt; x y<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>&gt; y z<span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>+ <span style="color: #b1951d;">(</span>* x x<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* y y<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>+ <span style="color: #b1951d;">(</span>* x x<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* z z<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>&gt; x z<span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>+ <span style="color: #b1951d;">(</span>* y y<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* x x<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>+ <span style="color: #b1951d;">(</span>* y y<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* z z<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span>sum-squares-of-larger <span style="color: #a45bad;">9</span> <span style="color: #a45bad;">10</span> <span style="color: #a45bad;">8</span><span style="color: #4f97d7;">)</span>
</pre>
</div>
</div>
</li>
</ol>
</div>
<div id="outline-container-org3ccc9ff" class="outline-4">
<h4 id="org3ccc9ff"><span class="section-number-4">1.6.2.</span> 1.5</h4>
<div class="outline-text-4" id="text-1-6-2">
<p>
Aplikativni vrstni red: pade takoj v neskoncno zanko.
Normalni vrstni red: izvrsi test in pride v if, ki ne izvrsi drugega dela.
</p>
</div>
</div>
<div id="outline-container-orge03b4b9" class="outline-4">
<h4 id="orge03b4b9"><span class="section-number-4">1.6.3.</span> 1.6</h4>
<div class="outline-text-4" id="text-1-6-3">
<p>
<a href="sqrt-newton.scm">sqrt-newton.scm</a>
</p>
</div>
</div>
<div id="outline-container-org62edd3c" class="outline-4">
<h4 id="org62edd3c"><span class="section-number-4">1.6.4.</span> 1.7</h4>
<div class="outline-text-4" id="text-1-6-4">
<ul class="org-ul">
<li><code>good-enough?</code> ni vredu za iskanje korenov majhnih stevil.</li>
<li>pravtako za zelo velika stevila</li>
<li>napisi alternativno <code>good-enough?</code> proceduro, ki bo gledala, kdaj so spremembe
dovolj majhne in takrat prekini funkcijo.</li>
</ul>
<p>
// Poglej v sqrt-newton.scm
</p>
</div>
</div>
<div id="outline-container-org42d25fe" class="outline-4">
<h4 id="org42d25fe"><span class="section-number-4">1.6.5.</span> 1.8</h4>
<div class="outline-text-4" id="text-1-6-5">
<p>
// Glej v sqrt-newton.sqm
</p>
</div>
</div>
</div>
<div id="outline-container-org670694e" class="outline-3">
<h3 id="org670694e"><span class="section-number-3">1.7.</span> 1.1.8 Procedure kot crne skatle abstrakcij</h3>
<div class="outline-text-3" id="text-1-7">
<ul class="org-ul">
<li>block structure</li>
<li>lexical scoping</li>
</ul>
</div>
</div>
<div id="outline-container-org058363a" class="outline-3">
<h3 id="org058363a"><span class="section-number-3">1.8.</span> 1.2.2 Drevesna rekurzija</h3>
</div>
<div id="outline-container-orga2d0d00" class="outline-3">
<h3 id="orga2d0d00"><span class="section-number-3">1.9.</span> 1.2.3 Redi rasti</h3>
</div>
<div id="outline-container-orgdb2bb3d" class="outline-3">
<h3 id="orgdb2bb3d"><span class="section-number-3">1.10.</span> 1.2.4 Eksponentna funkcija</h3>
<div class="outline-text-3" id="text-1-10">
<p>
Tukaj se naucimu successive squaring, ki potem se veckrat prav pride.
</p>
<p>
#name: exponent
</p>
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">O(n) korakov in O(n) prostora</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">expt</span> b n<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>= n <span style="color: #a45bad;">0</span><span style="color: #2d9574;">)</span>
<span style="color: #a45bad;">1</span>
<span style="color: #2d9574;">(</span>* b <span style="color: #67b11d;">(</span>expt b <span style="color: #b1951d;">(</span>- n <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">expt-i</span> b n<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>expt-iter b n <span style="color: #a45bad;">1</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">O(n) korakov O(1) prostor</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">expt-iter</span> b cnt prod<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>= cnt <span style="color: #a45bad;">0</span><span style="color: #2d9574;">)</span>
prod
<span style="color: #2d9574;">(</span>expt-iter b <span style="color: #67b11d;">(</span>- cnt <span style="color: #a45bad;">1</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>* b prod<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fast-expt</span> b n<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">cond</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>= n <span style="color: #a45bad;">0</span><span style="color: #67b11d;">)</span> <span style="color: #a45bad;">1</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>even? n<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>square <span style="color: #b1951d;">(</span>fast-expt b <span style="color: #4f97d7;">(</span>/ n <span style="color: #a45bad;">2</span><span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">else</span> <span style="color: #67b11d;">(</span>* b <span style="color: #b1951d;">(</span>fast-expt b <span style="color: #4f97d7;">(</span>- n <span style="color: #a45bad;">1</span><span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">even?</span> n<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>= <span style="color: #2d9574;">(</span>remainder n <span style="color: #a45bad;">2</span><span style="color: #2d9574;">)</span> <span style="color: #a45bad;">0</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">square</span> x<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>* x x<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">1.16</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">successive squaring (fast-expt) but with iteration.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">transformation (* a (expt b n)) constant</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fast-expt-i</span> b n<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>fast-expt-iter b n <span style="color: #a45bad;">1</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fast-expt-iter</span> b n a<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">cond</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>= n <span style="color: #a45bad;">0</span><span style="color: #67b11d;">)</span> a<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>even? n<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>fast-expt-iter <span style="color: #b1951d;">(</span>square b<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>/ n <span style="color: #a45bad;">2</span><span style="color: #b1951d;">)</span> a<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">else</span> <span style="color: #67b11d;">(</span>fast-expt-iter b <span style="color: #b1951d;">(</span>- n <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* a b<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">I'm not sure why this works. I was just guessing.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">excersize 1.17</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">slow-multi</span> a b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>= b <span style="color: #a45bad;">0</span><span style="color: #2d9574;">)</span> <span style="color: #a45bad;">0</span>
<span style="color: #2d9574;">(</span>+ a <span style="color: #67b11d;">(</span>* a <span style="color: #b1951d;">(</span>- b <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">halve</span> x<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>/ x <span style="color: #a45bad;">2</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">double</span> x<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>* x <span style="color: #a45bad;">2</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fast-multi</span> a b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">cond</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>= b <span style="color: #a45bad;">0</span><span style="color: #67b11d;">)</span> <span style="color: #a45bad;">0</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>even? b<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>double <span style="color: #b1951d;">(</span>fast-multi a <span style="color: #4f97d7;">(</span>halve b<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">else</span> <span style="color: #67b11d;">(</span>+ a <span style="color: #b1951d;">(</span>fast-multi a <span style="color: #4f97d7;">(</span>- b <span style="color: #a45bad;">1</span><span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">excersize 1.18</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fast-multi-i</span> a b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>fast-multi-iter a b <span style="color: #a45bad;">0</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fast-multi-iter</span> a b s<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">cond</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>= b <span style="color: #a45bad;">0</span><span style="color: #67b11d;">)</span> s<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>even? b<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>fast-multi-iter <span style="color: #b1951d;">(</span>double a<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>halve b<span style="color: #b1951d;">)</span> s<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">else</span> <span style="color: #67b11d;">(</span>fast-multi-iter a <span style="color: #b1951d;">(</span>- b <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>+ s a<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">excercise 1.19 - fast fibnonachi</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fast-fibo</span> n<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>fast-fibo-iter <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">0</span> <span style="color: #a45bad;">0</span> <span style="color: #a45bad;">1</span> n<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fast-fibo-iter</span> a b p q count<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">cond</span> <span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>= count <span style="color: #a45bad;">0</span><span style="color: #67b11d;">)</span> b<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>even? count<span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>fast-fibo-iter
a
b
<span style="color: #b1951d;">(</span>+ <span style="color: #4f97d7;">(</span>* p p<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>* q q<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span>
<span style="color: #b1951d;">(</span>+ <span style="color: #4f97d7;">(</span>* q q<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>* <span style="color: #a45bad;">2</span> p q<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span>
<span style="color: #b1951d;">(</span>/ count <span style="color: #a45bad;">2</span><span style="color: #b1951d;">)</span>
<span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">else</span> <span style="color: #67b11d;">(</span>fast-fibo-iter
<span style="color: #b1951d;">(</span>+ <span style="color: #4f97d7;">(</span>* b q<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>* a q<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>* a p<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span>
<span style="color: #b1951d;">(</span>+ <span style="color: #4f97d7;">(</span>* b p<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>* a q<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span>
p
q
<span style="color: #b1951d;">(</span>- count <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span>
<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">p' = q^2 + 2pq</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">p' = p^2 + q^2</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">slow-fibo</span> n<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">cond</span> <span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>= n <span style="color: #a45bad;">0</span><span style="color: #67b11d;">)</span> <span style="color: #a45bad;">0</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span>= n <span style="color: #a45bad;">1</span><span style="color: #67b11d;">)</span> <span style="color: #a45bad;">1</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">else</span> <span style="color: #67b11d;">(</span>+
<span style="color: #b1951d;">(</span>slow-fibo <span style="color: #4f97d7;">(</span>- n <span style="color: #a45bad;">1</span><span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span>
<span style="color: #b1951d;">(</span>slow-fibo <span style="color: #4f97d7;">(</span>- n <span style="color: #a45bad;">2</span><span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span>
<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">melje melje in melje . fast-fibo iypljune takoj</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org867a680" class="outline-3">
<h3 id="org867a680"><span class="section-number-3">1.11.</span> 1.2.5 Najvecji skupni deljitel</h3>
</div>
<div id="outline-container-org29472e2" class="outline-3">
<h3 id="org29472e2"><span class="section-number-3">1.12.</span> 1.2.6 Primer: Iskanje prastevil</h3>
</div>
<div id="outline-container-org84f4b2d" class="outline-3">
<h3 id="org84f4b2d"><span class="section-number-3">1.13.</span> 1.3 Sestavljanje abstrakcij s procedurami visjega reda</h3>
<div class="outline-text-3" id="text-1-13">
<p>
Procedure, ki spreminjajo druge procedure se imenujejo <b>procedure višjega reda</b>.
</p>
</div>
</div>
<div id="outline-container-org43a7808" class="outline-3">
<h3 id="org43a7808"><span class="section-number-3">1.14.</span> 1.3.1 Procedure kot argumenti</h3>
<div class="outline-text-3" id="text-1-14">
<p>
Primer vsote.
</p>
<div class="org-src-container">
<pre class="src src-guile">
</pre>
</div>
<p>
//exercise 1.29
#name: simpson
</p>
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sum</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>&gt; a b<span style="color: #2d9574;">)</span>
<span style="color: #a45bad;">0</span>
<span style="color: #2d9574;">(</span>+ <span style="color: #67b11d;">(</span>term a<span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>sum term <span style="color: #b1951d;">(</span>next a<span style="color: #b1951d;">)</span> next b<span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">integral</span> f a b dx<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #2d9574;">(</span><span style="color: #bc6ec5; font-weight: bold;">add-dx</span> x<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>+ x dx<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>* <span style="color: #2d9574;">(</span>sum f <span style="color: #67b11d;">(</span>+ a <span style="color: #b1951d;">(</span>/ dx <span style="color: #a45bad;">2.0</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> add-dx b<span style="color: #2d9574;">)</span> dx<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sum-s</span> term a next b fact<span style="color: #bc6ec5;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">fact is altering between 4 and 2</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #2d9574;">(</span><span style="color: #bc6ec5; font-weight: bold;">check-fact</span> fact<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>= fact <span style="color: #a45bad;">4</span><span style="color: #67b11d;">)</span> <span style="color: #a45bad;">2</span> <span style="color: #a45bad;">4</span><span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>&gt; a b<span style="color: #2d9574;">)</span>
<span style="color: #a45bad;">0</span>
<span style="color: #2d9574;">(</span>+ <span style="color: #67b11d;">(</span>* fact <span style="color: #b1951d;">(</span>term a<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>sum-s term <span style="color: #b1951d;">(</span>next a<span style="color: #b1951d;">)</span> next b <span style="color: #b1951d;">(</span>check-fact fact<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">simpson</span> f a b dx<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #2d9574;">(</span><span style="color: #bc6ec5; font-weight: bold;">add-dx</span> x<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>+ x dx<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>* <span style="color: #2d9574;">(</span>+ <span style="color: #67b11d;">(</span>f a<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>f b<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>sum-s f <span style="color: #b1951d;">(</span>add-dx a<span style="color: #b1951d;">)</span> add-dx <span style="color: #b1951d;">(</span>- b dx<span style="color: #b1951d;">)</span> <span style="color: #a45bad;">4</span><span style="color: #67b11d;">)</span> <span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>/ dx <span style="color: #a45bad;">3.0</span><span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">simpson-gizmo</span> f a b dx<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #2d9574;">(</span><span style="color: #bc6ec5; font-weight: bold;">add-dxdx</span> x<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>+ x dx dx<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>* <span style="color: #2d9574;">(</span>+
<span style="color: #67b11d;">(</span>* <span style="color: #a45bad;">4</span> <span style="color: #b1951d;">(</span>sum f <span style="color: #4f97d7;">(</span>+ a dx<span style="color: #4f97d7;">)</span> add-dxdx b<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>* <span style="color: #a45bad;">2</span> <span style="color: #b1951d;">(</span>sum f a add-dxdx b<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>- <span style="color: #b1951d;">(</span>f a<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>- <span style="color: #b1951d;">(</span>f b<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>/ dx <span style="color: #a45bad;">3.0</span><span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">cube</span> x<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>* x x x<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span>list
<span style="color: #bc6ec5;">(</span>integral cube <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">2</span> <span style="color: #a45bad;">0.01</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>integral cube <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">2</span> <span style="color: #a45bad;">0.001</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>simpson cube <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">2</span> <span style="color: #a45bad;">0.01</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>simpson cube <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">2</span> <span style="color: #a45bad;">0.001</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>simpson cube <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">2</span> <span style="color: #2d9574;">(</span>/ <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">1000</span><span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>simpson-gizmo cube <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">2</span> <span style="color: #a45bad;">0.01</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>simpson-gizmo cube <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">2</span> <span style="color: #2d9574;">(</span>/ <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">10000</span><span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>simpson-gizmo cube <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">2</span> <span style="color: #a45bad;">0.00001</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
</pre>
</div>
<p>
// exercise 1.30
</p>
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sum-i</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #2d9574;">(</span><span style="color: #bc6ec5; font-weight: bold;">iter</span> a result<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>&gt; a b<span style="color: #67b11d;">)</span>
result
<span style="color: #67b11d;">(</span>iter <span style="color: #b1951d;">(</span>next a<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>+ result <span style="color: #4f97d7;">(</span>term a<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>iter a <span style="color: #a45bad;">0</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
</pre>
</div>
<p>
// excercise 1.30, 1.31. 1.32
</p>
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">Analogno napisi produkt kot vsoto.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">Pokazi kako izgleda fakulteta.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">Aproksimacija pi/4 = 2/3*4/3*4/5*6/5*6/7*8/7...</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">produkt-r</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">a, b sta spodnja in zgornja meja</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>&gt; a b<span style="color: #2d9574;">)</span>
<span style="color: #a45bad;">1</span>
<span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>term a<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>produkt-r term <span style="color: #b1951d;">(</span>next a<span style="color: #b1951d;">)</span> next b<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fakulteta-p</span> n<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>produkt-r <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">lambda</span> <span style="color: #67b11d;">(</span>x<span style="color: #67b11d;">)</span> x<span style="color: #2d9574;">)</span> <span style="color: #a45bad;">1</span> <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">lambda</span> <span style="color: #67b11d;">(</span>x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>+ x <span style="color: #a45bad;">1</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> n<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">pribl-pi</span> n<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>produkt-r <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">lambda</span> <span style="color: #67b11d;">(</span>a<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>/ <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>- a <span style="color: #a45bad;">1.0</span><span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>+ a <span style="color: #a45bad;">1.0</span><span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* a a<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #a45bad;">3.0</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">lambda</span> <span style="color: #67b11d;">(</span>x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>+ x <span style="color: #a45bad;">2.0</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
n
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">gizmo se je spomnil resitve - dva produkta (zgornji in spodnji)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">iterativni produkt-i</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">produkt-i</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #2d9574;">(</span><span style="color: #bc6ec5; font-weight: bold;">iter-p</span> a result<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>&gt; a b<span style="color: #67b11d;">)</span>
result
<span style="color: #67b11d;">(</span>iter-p <span style="color: #b1951d;">(</span>next a<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* result <span style="color: #4f97d7;">(</span>term a<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>iter-p a <span style="color: #a45bad;">1</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">pribl-pi-term</span> a<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>/ <span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>- a <span style="color: #a45bad;">1.0</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>+ a <span style="color: #a45bad;">1</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>* a a<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">pribl-pi-next</span> a<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>+ a <span style="color: #a45bad;">2.0</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">pribl-pii</span> n<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>produkt-i
pribl-pi-term
<span style="color: #a45bad;">3.0</span>
pribl-pi-next
n
<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">excercise 1.32</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">recursive accumulate</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">accumulate-r</span> combiner null-val term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">combiner is a procedure of two arguments.</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>&gt; a b<span style="color: #2d9574;">)</span>
null-val
<span style="color: #2d9574;">(</span>combiner <span style="color: #67b11d;">(</span>term a<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>accumulate-r combiner null-val term <span style="color: #b1951d;">(</span>next a<span style="color: #b1951d;">)</span> next b<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sum-combiner</span> t acc<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>+ t acc<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sum-a</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>accumulate-r <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">lambda</span> <span style="color: #67b11d;">(</span>t acc<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>+ t acc<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #a45bad;">0</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">prod-a</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>accumulate-r <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">lambda</span> <span style="color: #67b11d;">(</span>t acc<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>* t acc<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #a45bad;">1</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">accumulate-i</span> combiner null-val term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">Iterative accumulator.</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #2d9574;">(</span><span style="color: #bc6ec5; font-weight: bold;">iter-a</span> a result<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>&gt; a b<span style="color: #67b11d;">)</span>
result
<span style="color: #67b11d;">(</span>iter-a <span style="color: #b1951d;">(</span>next a<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>combiner <span style="color: #4f97d7;">(</span>term a<span style="color: #4f97d7;">)</span> result<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>iter-a a null-val<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">identity</span> x<span style="color: #bc6ec5;">)</span> x<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">add1</span> x<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>+ x <span style="color: #a45bad;">1</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sum-ai</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>accumulate-i sum-combiner <span style="color: #a45bad;">0</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">prod-ai</span> term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>accumulate-i <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">lambda</span> <span style="color: #67b11d;">(</span>t acc<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>* t acc<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #a45bad;">1</span> term a next b<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">fakulteta-ai</span> n<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>prod-ai identity <span style="color: #a45bad;">2</span> add1 n<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">excercise 1.33 filtered accumulate - combine only those term derived from</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">values in the range that satisfy a specified condition (predicate).</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">a) sum of squares of prime numbers - assuming prime? exists already</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">filtered-accumulate-r</span> combiner null-val predicate term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">combiner 2 args - element and accumulation</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">predicate 1 arg - a condition when to apply combiner</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">term 1 arg - a function to compute the term</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">next 1 arg - compute a next step</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>&gt; a b<span style="color: #2d9574;">)</span>
null-val
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>predicate a<span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>combiner <span style="color: #b1951d;">(</span>term a<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>filtered-accumulate-r combiner null-val predicate term <span style="color: #4f97d7;">(</span>next a<span style="color: #4f97d7;">)</span> next b<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">should I call combiner with null-val instead of (term a) or can I</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">directly call filtered-accumulate-r?</span>
<span style="color: #67b11d;">(</span>filtered-accumulate-r combiner null-val predicate term <span style="color: #b1951d;">(</span>next a<span style="color: #b1951d;">)</span> next b<span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">(filtered-accumulate-r sum-combiner 0 even? identity 1 add1 11)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">filtered-accumulate-i</span> combiner null-val predicate term a next b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #2d9574;">(</span><span style="color: #bc6ec5; font-weight: bold;">iter-fa</span> a result<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #67b11d;">(</span>&gt; a b<span style="color: #67b11d;">)</span>
result
<span style="color: #67b11d;">(</span>iter-fa <span style="color: #b1951d;">(</span>next a<span style="color: #b1951d;">)</span>
<span style="color: #b1951d;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #4f97d7;">(</span>predicate a<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span>combiner <span style="color: #bc6ec5;">(</span>term a<span style="color: #bc6ec5;">)</span> result<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span>combiner null-val result<span style="color: #4f97d7;">)</span>
<span style="color: #b1951d;">)</span>
<span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>iter-fa a null-val<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orga384969" class="outline-3">
<h3 id="orga384969"><span class="section-number-3">1.15.</span> 1.3.2 Sestavljanje procedur z <code>Lambda</code></h3>
<div class="outline-text-3" id="text-1-15">
<p>
Splosna forma <code>let</code> izraza
</p>
<pre class="example" id="org861d813">
(let ((&lt;var1&gt; &lt;exp1&gt;)
(&lt;var2&gt; &lt;exp2&gt;)
...
(&lt;varn&gt; &lt;expn&gt;))
&lt;body&gt;)
</pre>
<p>
To je okrajsava za
</p>
<pre class="example" id="orge922f38">
((lambda (&lt;var1&gt; ... &lt;varn&gt;)
&lt;body&gt;)
&lt;exp1&gt;
...
&lt;exp2&gt;
)
</pre>
</div>
</div>
<div id="outline-container-org590844a" class="outline-3">
<h3 id="org590844a"><span class="section-number-3">1.16.</span> 1.3.3 Procedure kot splosne metode</h3>
<div class="outline-text-3" id="text-1-16">
<p>
Ce pogledamo proceduro za integral, vidimo mocnejse abstrakcije: procedure, ki
izrazajo splosne racunske metode, neodvisne od posameznih vkljucenih funkcij.
</p>
</div>
</div>
<div id="outline-container-org8a3aa7d" class="outline-3">
<h3 id="org8a3aa7d"><span class="section-number-3">1.17.</span> 1.3.4 Procedure kot vrnjene vrednosti</h3>
<div class="outline-text-3" id="text-1-17">
<p>
V splošnem programski jeziki omejujo, kateri komputacijski elemente lahko (koda)
spreminja. Elementi z najmanj omejitvami imajo <i>prvorazredni</i> status. Pravice in
privilegiji prvorazrednih elementov so:
</p>
<ul class="org-ul">
<li>lahko so poimenovani s spremenljivkami</li>
<li>lahko so podani kot argumenti procedur</li>
<li>lahko so vrnjeni kot rezultati procedur</li>
<li>lahko so vključeni v podatkovne strukture</li>
</ul>
<p>
V Lispu imajo, za razliko od drugih programskih jezikov, procedure prvorazredni
status. To predstavlja težave za implementacijo, ampak nudi višjo ekspresivno
moč programskega jezika. Najvišja cena pri implementaciji procedur s
prvorazrednim statusom je, da je potrebno rezervirati prostor za procedurine
proste spremenljivke tudi, ko se procedura ne izvaja. V scheme-u so te
spremenljivke shranjene v procedurino okolje (poglavje 4.1).
</p>
</div>
</div>
</div>
<div id="outline-container-org66fd37e" class="outline-2">
<h2 id="org66fd37e"><span class="section-number-2">2.</span> Grajenje absrakcij s podatki</h2>
<div class="outline-text-2" id="text-2">
<p>
Poglavje bo govorilo o kompleksnih podatkih. Poglavje 1 govori o grajenju
abstrakcij z zdruzevanjem procedur, ki tvorijo sestavljene procedure (compound).
V poglavju 2 pa bo fokus na grajenju abstrakcij z zdruzevanjem podatkovnih
objektov v sestavljene podatke (compound).
</p>
<p>
Z zdruzenimi podatkovnimi objekti lahko procedure delajo nad njimi ne da bi bile
odvisne od njihove natancne strukture.
</p>
<p>
Podobno kot pri sestavljenih procedurah gre tudi pri sestavljenih podatkovnih
objektih za nacin spoprijemanja s kompleksnostjo - podatkovne abstrakcije
omogocijo postavitev primernih abstrakcijskih pregrad med razlicnimi deli
programa.
</p>
<p>
Napoved, kaj se bo pregledalo v 2. poglavju (bi bilo smiselno povzet).
</p>
</div>
<div id="outline-container-org501bf16" class="outline-3">
<h3 id="org501bf16"><span class="section-number-3">2.1.</span> Uvod v podatkovne abstrakcije</h3>
<div class="outline-text-3" id="text-2-1">
<p>
Podatkovna abstrakcija je metodologija, ki nam omogoci, da locimo kako so
sestavljeni podatki uporabljeni od detajlov o tem, kako so izgrejeni iz
primitivnih podatkovnih objektov. (To je analogno grajenju produceur, ki imajo
vgrajene druge procedue iz poglavja 1.1.8)
</p>
<p>
Skratka programe hocemo graditi tako, da uporabljajo podatke na nacin, da nimajo
nobenih predpostavk o tem, kaksni naj so ti podatki (oziroma cim manj), ravno
dovolj za izvajanje potrebnih operacij. Hkrati so konkretne reprezentacije
podatkov definirane neodvisno od programov, ki podatke uporabljajo.
</p>
<p>
Selektorji in konstruktorji.
</p>
</div>
<div id="outline-container-orga2f86a5" class="outline-4">
<h4 id="orga2f86a5"><span class="section-number-4">2.1.1.</span> Aritmeticne operacije z racionalnimi stevili</h4>
<div class="outline-text-4" id="text-2-1-1">
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">add-rat</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-rat <span style="color: #2d9574;">(</span>+ <span style="color: #67b11d;">(</span>* <span style="color: #b1951d;">(</span>numer x<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>denom y<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>* <span style="color: #b1951d;">(</span>numer y<span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>denom x<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>denom x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>denom y<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">sub-rat</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-rat <span style="color: #2d9574;">(</span>- <span style="color: #67b11d;">(</span>numer x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>denom y<span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>numer y<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>denom x<span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>denom x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>denom y<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">mul-rat</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-rat <span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>numer x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>numer y<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>denom x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>denom y<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">div-rat</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-rat <span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>numer x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>denom y<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>denom x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>numer y<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">equal-rat?</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>= <span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>numer x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>denom y<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>numer y<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>denom x<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">make-rat</span> n d<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>cons n d<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">numer</span> x<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>car x<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">denom</span> x<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>cdr x<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">print-rat</span> x<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>display <span style="color: #2d9574;">(</span>numer x<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>display <span style="color: #2d9574;">"/"</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>display <span style="color: #2d9574;">(</span>denom x<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>newline<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5; font-weight: bold;">one-half</span> <span style="color: #bc6ec5;">(</span>make-rat <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">2</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5; font-weight: bold;">one-third</span> <span style="color: #bc6ec5;">(</span>make-rat <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">3</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">excercise 2.1</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">make-rat-norm</span> n d<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>&lt; d <span style="color: #a45bad;">0</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>make-rat <span style="color: #67b11d;">(</span>* n <span style="color: #a45bad;">-1</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>* d <span style="color: #a45bad;">-1</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>make-rat n d<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
</pre>
</div>
<p>
Sestavljena strkutura <code>par</code>, ki je konstruirana s primitivno proceduro <code>cons</code>. S
primitivnimi procedurami <code>car</code> in <code>cdr</code> lahko dobimo prvi in ostale elemente
para.
</p>
</div>
<ul class="org-ul">
<li><a id="org06ac49c"></a>Predstavljanje racionalnih stevil<br />
<div class="outline-text-5" id="text-org06ac49c">
<p>
<i>Glej zgornji codeblock.</i>
</p>
</div>
</li>
</ul>
</div>
<div id="outline-container-org9d926fd" class="outline-4">
<h4 id="org9d926fd"><span class="section-number-4">2.1.2.</span> Pregrade abstrakcij</h4>
<div class="outline-text-4" id="text-2-1-2">
<p>
Splosna ideja podatkovnih abstrakcij je, da se identificira za vsak tip podatka
osnovni set opraracij, s katerimi bodo vse procedure, ki bodo manipulirale
podatke operirale, oziroma bodo iz njih sestavljene. Nato se uporabljamo samo te
operacije pri delu s podatki.
</p>
<p>
Pregrade:
</p>
<ul class="org-ul">
<li>programi, ki uporabljajo racionalna stevila</li>
<li>racionalna stevila v problemskem polju
<ul class="org-ul">
<li><code>add-rat</code>, <code>sub-rat</code> &#x2026;</li>
</ul></li>
<li>racionalna stevila kot stevci in imenovalci
<ul class="org-ul">
<li><code>make-rat</code>, <code>number</code>, <code>denom</code></li>
</ul></li>
<li>racionalna stevila kot pari
<ul class="org-ul">
<li><code>cons</code>, <code>car</code>, <code>cdr</code></li>
</ul></li>
<li>kakor so pac pari implementirani</li>
</ul>
<p>
Procedure na vsakem nivoju so vmesniki, ki definirajo abstrakcijski nivo in med
sabo povezujejo razlicne nivoje.
</p>
<p>
Ena od prednosti razdelitve na nivoje je, da je programe lazje vzdrzevati in
spreminjati, ker lahko delas spremembe na posameznem nivoju, ki ne vplivajo
izven svojega nivoja.
</p>
<p>
<i>vaja 2.2</i>
</p>
<div class="org-src-container">
<pre class="src src-scheme"><span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">crte v prostoru</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">make-segment</span> startp endp<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>cons startp endp<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">make-line</span> x1 y1 x2 y2<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-segment <span style="color: #2d9574;">(</span>make-point x1 y1<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>make-point x2 y2<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">start-segment</span> segment<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>car segment<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">end-segment</span> segment<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>cdr segment<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">make-point</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>cons x y<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">x-point</span> p<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>car p<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">y-point</span> p<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>cdr p<span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">mid-point</span> segment<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-point
<span style="color: #2d9574;">(</span>/ <span style="color: #67b11d;">(</span>+ <span style="color: #b1951d;">(</span>x-point <span style="color: #4f97d7;">(</span>start-segment segment<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>x-point <span style="color: #4f97d7;">(</span>end-segment segment<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #a45bad;">2</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>/ <span style="color: #67b11d;">(</span>+ <span style="color: #b1951d;">(</span>y-point <span style="color: #4f97d7;">(</span>start-segment segment<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>y-point <span style="color: #4f97d7;">(</span>end-segment segment<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #a45bad;">2</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">print-point</span> p<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>display <span style="color: #2d9574;">"("</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>display <span style="color: #2d9574;">(</span>x-point p<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>display <span style="color: #2d9574;">","</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>display <span style="color: #2d9574;">(</span>y-point p<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>display <span style="color: #2d9574;">")"</span><span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>newline<span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">vaja 2.3 :: segment je lahko tudi pravokotnik, ce nimamo rotacije in je crta</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">vedno diagonala. Delal bom brez rotacije, zato ker potem ni dovolj imeti</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">konstruktorja, ki je samo kons, ampak rabim 3 parametre, segment in rotacija</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">in potem nvm kako delat selektorje in pa se vse se mi zakomplicira in se mi</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">ne da, ker je nedelja zvecer.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">brez rotacije - 2a + 2b</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">perimeter</span> rectangle<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>+ <span style="color: #2d9574;">(</span>* <span style="color: #a45bad;">2</span> <span style="color: #67b11d;">(</span>side-a rectangle<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>* <span style="color: #a45bad;">2</span> <span style="color: #67b11d;">(</span>side-b rectangle<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">area</span> rectangle<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>* <span style="color: #2d9574;">(</span>side-a rectangle<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>side-b rectangle<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">selektor (brez rotacije)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">side-a</span> rectangle<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>abs <span style="color: #2d9574;">(</span>- <span style="color: #67b11d;">(</span>x-point <span style="color: #b1951d;">(</span>start-segment rectangle<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>x-point <span style="color: #b1951d;">(</span>end-segment rectangle<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">side-b</span> rectangle<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>abs <span style="color: #2d9574;">(</span>- <span style="color: #67b11d;">(</span>y-point <span style="color: #b1951d;">(</span>start-segment rectangle<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>y-point <span style="color: #b1951d;">(</span>end-segment rectangle<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">sedaj vpeljemo drugo reprezentacijo pravokotnikov (nic vec s segmentom)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">ali lahko obseg in ploscina se vedno delujeta?</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">odvisna sta od side-a in side-b. Ce to zemanjam, bosta obseg in ploscina se</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">vedno delovali.</span>
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<h4 id="org518e1e2"><span class="section-number-4">2.1.3.</span> Kaj so podatki?</h4>
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<p>
Pri racionalnih stevilih imamo se en pogoj:
</p>
<p>
<code>(/ (numer x) (denom x)) = n/d</code>
</p>
<p>
Selektorji konstruktorji in pogoji tvorijo veljavno reprezentacijo.
</p>
<p>
Vsaka trojica procedur, ki ustreza pogoju, da ce zdruzis dva objekta, in potem z
eno proceduro dobis iz zdruzenih prvi objekt in z drugo drugi objekt, je potem
trojica procedu za delanje s pari.
</p>
<p>
Trojico procedur (cons, car, cdr) se da implementirati brez podatkov:
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<pre class="src src-scheme"><span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">cons-p</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #2d9574;">(</span><span style="color: #bc6ec5; font-weight: bold;">dispatch</span> m<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">cond</span>
<span style="color: #67b11d;">(</span><span style="color: #b1951d;">(</span>= m <span style="color: #a45bad;">0</span><span style="color: #b1951d;">)</span> x<span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span><span style="color: #b1951d;">(</span>= m <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span> y<span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span><span style="color: #4f97d7; font-weight: bold;">else</span> <span style="color: #b1951d;">(</span>error <span style="color: #2d9574;">"Argument not 0 or 1 -- CONS"</span> m<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
dispatch<span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">car-p</span> z<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>z <span style="color: #a45bad;">0</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">cdr-p</span> z<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>z <span style="color: #a45bad;">1</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
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<p>
Zdaj imamo procedure za delanje s pari, ki so definirane brez podatkov.
Obskurno, ampak v okviru definije delanja s pari. Na tem primeru vidimo, da
zmoznost manipuliranja procedur kot objektov avtomaticno omogoci moznost za
reprezentacijo sestavljenih podatkov. (Proceduralna reprezentacija podatkov bo
igrala osrednjo vlogo v nadaljevanju - temu se rece <i>message passing</i> in bo
osnovno orodje v tretjem poglavju o problemih modeliranja in simulacije).
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