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<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="#org92eb632">Foreword and Preface</a></li>
<li><a href="#orga3d4d8f">1. Grajenje abstrakcij s procedurami</a>
<ul>
<li><a href="#orgd76336d">1.1. Elementi programiranja</a></li>
<li><a href="#orgbe756c4">1.2. Izvajanje kombinacij(e)</a></li>
<li><a href="#org0d500db">1.3. Sestavljene procedure</a></li>
<li><a href="#orga5db6cc">1.4. Substitucijski model za izvajanje procedur</a></li>
<li><a href="#orgb86605e">1.5. meta</a>
<ul>
<li><a href="#org11a4e3a">1.5.1. video lekcije</a></li>
</ul>
</li>
<li><a href="#org4306995">1.6. vaje</a>
<ul>
<li><a href="#org4dd2665">1.6.1. 1.3</a></li>
<li><a href="#org1867345">1.6.2. 1.5</a></li>
<li><a href="#orgcd62f1e">1.6.3. 1.6</a></li>
<li><a href="#org919fcc4">1.6.4. 1.7</a></li>
<li><a href="#orge0d0642">1.6.5. 1.8</a></li>
</ul>
</li>
<li><a href="#org92f6e90">1.7. 1.1.8 Procedure kot crne skatle abstrakcij</a></li>
<li><a href="#org4576647">1.8. 1.2.2 Drevesna rekurzija</a></li>
<li><a href="#orgded8727">1.9. 1.2.3 Redi rasti</a></li>
<li><a href="#orgffe59eb">1.10. 1.2.4 Eksponentna funkcija</a></li>
<li><a href="#org31cb68b">1.11. Najvecji skupni deljitel</a></li>
<li><a href="#org9de0305">1.12. Primer: Iskanje prastevil</a></li>
<li><a href="#org6f2098e">1.13. 1.3 Sestavljanje abstrakcij s procedurami visjega reda</a></li>
<li><a href="#org0231c23">1.14. 1.3.1 Procedure kot argumenti</a></li>
<li><a href="#org2509c48">1.15. 1.3.2 Sestavljanje procedur z <code>Lambda</code></a></li>
<li><a href="#orga7b7a47">1.16. 1.3.3 Procedure kot splosne metode</a></li>
<li><a href="#org234a112">1.17. 1.3.4 Procedure kot vrnjene vrednosti</a></li>
</ul>
</li>
<li><a href="#org167bb3c">2. Grajenje absrakcij s podatki</a>
<ul>
<li><a href="#orgf1c9c2f">2.1. Uvod v podatkovne abstrakcije</a>
<ul>
<li><a href="#org1795f67">2.1.1. Aritmeticne operacije z racionalnimi stevili</a></li>
<li><a href="#orgc0ea90c">2.1.2. Pregrade abstrakcij</a></li>
<li><a href="#org76e7cee">2.1.3. Kaj so podatki?</a></li>
<li><a href="#org9507a61">2.1.4. razsirjena vaja: aritmetika z intervali</a></li>
</ul>
</li>
<li><a href="#orgf662eab">2.2. Hierarhični podatki in lastnosti zaprtosti</a>
<ul>
<li><a href="#org32e5993">2.2.1. Reprezentacija sekvenc</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org92eb632" class="outline-2">
<h2 id="org92eb632">Foreword and Preface</h2>
<div class="outline-text-2" id="text-org92eb632">
<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-orga3d4d8f" class="outline-2">
<h2 id="orga3d4d8f"><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-orgd76336d" class="outline-3">
<h3 id="orgd76336d"><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-orgbe756c4" class="outline-3">
<h3 id="orgbe756c4"><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-org0d500db" class="outline-3">
<h3 id="org0d500db"><span class="section-number-3">1.3.</span> 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-orga5db6cc" class="outline-3">
<h3 id="orga5db6cc"><span class="section-number-3">1.4.</span> 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-orgb86605e" class="outline-3">
<h3 id="orgb86605e"><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-org11a4e3a" class="outline-4">
<h4 id="org11a4e3a"><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-org4306995" class="outline-3">
<h3 id="org4306995"><span class="section-number-3">1.6.</span> vaje</h3>
<div class="outline-text-3" id="text-1-6">
</div>
<div id="outline-container-org4dd2665" class="outline-4">
<h4 id="org4dd2665"><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="org76f9a89"></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="orga438f24"></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-org1867345" class="outline-4">
<h4 id="org1867345"><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-orgcd62f1e" class="outline-4">
<h4 id="orgcd62f1e"><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-org919fcc4" class="outline-4">
<h4 id="org919fcc4"><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-orge0d0642" class="outline-4">
<h4 id="orge0d0642"><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-org92f6e90" class="outline-3">
<h3 id="org92f6e90"><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-org4576647" class="outline-3">
<h3 id="org4576647"><span class="section-number-3">1.8.</span> 1.2.2 Drevesna rekurzija</h3>
</div>
<div id="outline-container-orgded8727" class="outline-3">
<h3 id="orgded8727"><span class="section-number-3">1.9.</span> 1.2.3 Redi rasti</h3>
</div>
<div id="outline-container-orgffe59eb" class="outline-3">
<h3 id="orgffe59eb"><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>slow-multi 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: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">Russian paesant method - zelo star algoritem.</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-org31cb68b" class="outline-3">
<h3 id="org31cb68b"><span class="section-number-3">1.11.</span> Najvecji skupni deljitel</h3>
<div class="outline-text-3" id="text-1-11">
<p>
Evklidov algoritem je zelo star algoritem.
</p>
<p>
Ce je <code>r</code> ostanek pri deljenju <code>a</code> z <code>b</code>, potem so skupni deljitelji <code>a</code> in <code>b</code>
enaki kot skupni deljitelji kot <code>b</code> in <code>r</code>.
</p>
<p>
<b>Lamejev teorem</b> :: Ce evklidov algoritem potrebuje <code>k</code> korakov, da izracuna NSD
nekega para, potem mora biti manjsa stevilka v paru vecja ali enaka <code>k</code>-ti
Fibonaccijevi stevilki.
</p>
<p>
<b>footnote</b> Gabriel Lame - francoski matematik rojen 1845, ki je postavil veliko
tez, ampak nobene ni dokazal.
</p>
<p>
Lamejev teorem lahko uporabis za ocen velikosti rasti evklidovega algoritma:
<code>n &gt;= Fib(k) =. fi^k/sqrt(5)</code>. Torej stevilo korako rase logaritemsko.
</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;">gcd</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>
a
<span style="color: #2d9574;">(</span>gcd b <span style="color: #67b11d;">(</span>remainder a 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;">naloga 1.20</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org9de0305" class="outline-3">
<h3 id="org9de0305"><span class="section-number-3">1.12.</span> Primer: Iskanje prastevil</h3>
</div>
<div id="outline-container-org6f2098e" class="outline-3">
<h3 id="org6f2098e"><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-org0231c23" class="outline-3">
<h3 id="org0231c23"><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;">0.0001</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-org2509c48" class="outline-3">
<h3 id="org2509c48"><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="org8bfd4f0">
(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="orgba2a10b">
((lambda (&lt;var1&gt; ... &lt;varn&gt;)
&lt;body&gt;)
&lt;exp1&gt;
...
&lt;exp2&gt;
)
</pre>
</div>
</div>
<div id="outline-container-orga7b7a47" class="outline-3">
<h3 id="orga7b7a47"><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-org234a112" class="outline-3">
<h3 id="org234a112"><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-org167bb3c" class="outline-2">
<h2 id="org167bb3c"><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-orgf1c9c2f" class="outline-3">
<h3 id="orgf1c9c2f"><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-org1795f67" class="outline-4">
<h4 id="org1795f67"><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>
<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-gcd</span> n d<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>g <span style="color: #b1951d;">(</span>gcd n d<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>make-rat-norm <span style="color: #67b11d;">(</span>/ n g<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>/ d g<span style="color: #67b11d;">)</span><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="orga6cc3e8"></a>Predstavljanje racionalnih stevil<br />
<div class="outline-text-5" id="text-orga6cc3e8">
<p>
<i>Glej zgornji codeblock.</i>
</p>
</div>
</li>
</ul>
</div>
<div id="outline-container-orgc0ea90c" class="outline-4">
<h4 id="orgc0ea90c"><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>numer</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: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5;">(</span><span style="color: #bc6ec5; font-weight: bold;">make-rectangle</span> point-a point-c<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-segment point-a point-c<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) ali</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">lahko obseg in ploscina se vedno delujeta? odvisna sta od side-a in side-b.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">Ce to zemanjam, bosta obseg in ploscina se vedno delovali.</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;">mk-rect</span> point-a sirina visina<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;">get-point-c</span> point-a sirina visina<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>cons <span style="color: #67b11d;">(</span>+ <span style="color: #b1951d;">(</span>x-point point-a<span style="color: #b1951d;">)</span> sirina<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>+ <span style="color: #b1951d;">(</span>y-point point-a<span style="color: #b1951d;">)</span> visina<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-rectangle point-a <span style="color: #2d9574;">(</span>get-point-c point-a sirina visina<span style="color: #2d9574;">)</span><span style="color: #bc6ec5;">)</span>
<span style="color: #4f97d7;">)</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org76e7cee" class="outline-4">
<h4 id="org76e7cee"><span class="section-number-4">2.1.3.</span> Kaj so podatki?</h4>
<div class="outline-text-4" id="text-2-1-3">
<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:
</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;">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>
</pre>
</div>
<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).
</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;">naloga 2.5</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;">cons-2a3b</span> a b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>* <span style="color: #2d9574;">(</span>expt <span style="color: #a45bad;">2</span> a<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>expt <span style="color: #a45bad;">3</span> b<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;">car-2a3b</span> x<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>= <span style="color: #a45bad;">0</span> <span style="color: #67b11d;">(</span>modulo x <span style="color: #a45bad;">2</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>+ <span style="color: #a45bad;">1</span> <span style="color: #67b11d;">(</span>car-2a3b <span style="color: #b1951d;">(</span>/ x <span style="color: #a45bad;">2</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</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;">cdr-2a3b</span> x<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span>= <span style="color: #a45bad;">0</span> <span style="color: #67b11d;">(</span>modulo x <span style="color: #a45bad;">3</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>+ <span style="color: #a45bad;">1</span> <span style="color: #67b11d;">(</span>cdr-2a3b <span style="color: #b1951d;">(</span>/ x <span style="color: #a45bad;">3</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</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>cons-2a3b <span style="color: #a45bad;">3</span> <span style="color: #a45bad;">5</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span>car-2a3b <span style="color: #bc6ec5;">(</span>cons-2a3b <span style="color: #a45bad;">3</span> <span style="color: #a45bad;">5</span><span style="color: #bc6ec5;">)</span><span style="color: #4f97d7;">)</span>
<span style="color: #4f97d7;">(</span>cdr-2a3b <span style="color: #bc6ec5;">(</span>cons-2a3b <span style="color: #a45bad;">3</span> <span style="color: #a45bad;">5</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;">naloga 2.6 church numerals</span>
<span style="color: #4f97d7;">(</span><span style="color: #4f97d7; font-weight: bold;">define</span> <span style="color: #bc6ec5; font-weight: bold;">zero</span> <span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">&#955;</span> <span style="color: #2d9574;">(</span>x<span style="color: #2d9574;">)</span> 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;">add-1</span> n<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">&#955;</span> <span style="color: #2d9574;">(</span>f<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">&#955;</span> <span style="color: #67b11d;">(</span>x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>f <span style="color: #b1951d;">(</span><span style="color: #4f97d7;">(</span>n f<span style="color: #4f97d7;">)</span> x<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; font-weight: bold;">one</span> <span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">&#955;</span> <span style="color: #2d9574;">(</span>f<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">&#955;</span> <span style="color: #67b11d;">(</span>x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>f <span style="color: #b1951d;">(</span>f x<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; font-weight: bold;">two</span> <span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">&#955;</span> <span style="color: #2d9574;">(</span>f<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">&#955;</span> <span style="color: #67b11d;">(</span>x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>f <span style="color: #b1951d;">(</span>f <span style="color: #4f97d7;">(</span>f x<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;">pomoje je to narobe, en f prevec je. ampak, ko sva z gizmotom na papir</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">napisala je bilo kul.</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org9507a61" class="outline-4">
<h4 id="org9507a61"><span class="section-number-4">2.1.4.</span> razsirjena vaja: aritmetika z intervali</h4>
<div class="outline-text-4" id="text-2-1-4">
<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;">aritmetika z intervali</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;">add-interval</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-interval <span style="color: #2d9574;">(</span>+ <span style="color: #67b11d;">(</span>lower-bound x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>lower-bound y<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>+ <span style="color: #67b11d;">(</span>upper-bound x<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>upper-bound 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-interval</span> x y<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>p1 <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>p2 <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>p3 <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>p4 <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<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>make-interval <span style="color: #67b11d;">(</span>min p1 p2 p3 p4<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>max p1 p2 p3 p4<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;">@todo tukaj ne razumem, kako to, da ni p1 vedno najmanjsi in p4 vedno najvecji.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">https://en.wikipedia.org/wiki/Interval_arithmetic</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-interval</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>mul-interval x
<span style="color: #2d9574;">(</span>make-interval <span style="color: #67b11d;">(</span>/ <span style="color: #a45bad;">1.0</span> <span style="color: #b1951d;">(</span>upper-bound y<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>/ <span style="color: #a45bad;">1.0</span> <span style="color: #b1951d;">(</span>lower-bound y<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;">naloga 2.7</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;">make-interval</span> a b<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>cons a 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;">upper-bound</span> i<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>cdr i<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;">lower-bound</span> i<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>car i<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;">naloga 2.8</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-interval</span> a b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-interval <span style="color: #2d9574;">(</span>- <span style="color: #67b11d;">(</span>lower-bound a<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>upper-bound b<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>- <span style="color: #67b11d;">(</span>upper-bound a<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>lower-bound 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;">od spodnje meje odstejes zgornjo mejo drugega intervala</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">naloga 2.9</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">Pokazi, da je sirina intervala (polovica razdalje med zgornjo in spodnjo</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">mejo),oziroma, da je sirina vsote in razlike intervalov funkcija sirin</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">argumentov ter da sirina proudkta in deljenja ni funkcija sirine.</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;">width</span> a<span style="color: #bc6ec5;">)</span> <span style="color: #bc6ec5;">(</span>/ <span style="color: #2d9574;">(</span>- <span style="color: #67b11d;">(</span>upper-bound a<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>lower-bound a<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #a45bad;">2.0</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;">sirina vsote je enaka vsoti sirin, ce razpises je hitro jasno.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">sirina razlike je enaka vsoti sirin.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">pri mnozenju imamo funkcijo min in max in ubistvu se nikjer notri ne pojavi</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">sirina.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">naloga 2.10</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;">safe-div-interval</span> x y<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span> <span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">or</span> <span style="color: #67b11d;">(</span>= <span style="color: #a45bad;">0</span> <span style="color: #b1951d;">(</span>lower-bound y<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>= <span style="color: #a45bad;">0</span> <span style="color: #b1951d;">(</span>upper-bound y<span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>error <span style="color: #2d9574;">"Division by zero?"</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>div-interval x y<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;">naloga 2.11</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">S preverjanjem predznakov v mejah intervalov lahko locis mnozenje intervalov</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">na 9 primermov, od katerih samo eden potrebuje vec kot 2 mnozenji. Razpisi</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">s to metodo.</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">verjetno bi rabil se neko preverjanje, da je nizja meja intervala res nizja.</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-interval-signs</span> x y<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><span style="color: #4f97d7; font-weight: bold;">and</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval x<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval y<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>make-interval <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<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><span style="color: #4f97d7; font-weight: bold;">and</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval x<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">-1</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval y<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">-1</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>make-interval <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">en cel pozit, drug cel negat</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span><span style="color: #4f97d7; font-weight: bold;">and</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval x<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">-1</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval y<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>make-interval <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<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><span style="color: #4f97d7; font-weight: bold;">and</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval x<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval y<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">-1</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>make-interval <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">en cez nic, drug cel pozit</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span><span style="color: #4f97d7; font-weight: bold;">and</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval x<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">0</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval y<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>make-interval <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<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><span style="color: #4f97d7; font-weight: bold;">and</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval x<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval y<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">0</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>make-interval <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">en cez nic, drug cel negat</span>
<span style="color: #2d9574;">(</span><span style="color: #67b11d;">(</span><span style="color: #4f97d7; font-weight: bold;">and</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval x<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">0</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval y<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">-1</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>make-interval <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>upper-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<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><span style="color: #4f97d7; font-weight: bold;">and</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval x<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">-1</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>= <span style="color: #4f97d7;">(</span>test-sign-interval y<span style="color: #4f97d7;">)</span> <span style="color: #a45bad;">0</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>make-interval <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>upper-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #b1951d;">(</span>* <span style="color: #4f97d7;">(</span>lower-bound x<span style="color: #4f97d7;">)</span> <span style="color: #4f97d7;">(</span>lower-bound y<span style="color: #4f97d7;">)</span><span style="color: #b1951d;">)</span> <span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">oba cez nic, je treba sprobat</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">else</span> <span style="color: #67b11d;">(</span>mul-interval x y<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;">returns -1 if lower and upper bound are below 0</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">return 0 if lower bound is below 0 and upper bound is above</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">return 1 if both bounds are above 0</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;">test-sign-interval</span> x<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>&gt;= <span style="color: #b1951d;">(</span>lower-bound x<span style="color: #b1951d;">)</span> <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>&lt; <span style="color: #b1951d;">(</span>upper-bound x<span style="color: #b1951d;">)</span> <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: #4f97d7; font-weight: bold;">else</span> <span style="color: #a45bad;">0</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;">test mul intervals - definiram 3 intervale in jih mnozim same s sabo in</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">drugega z drugim.</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;">test-mul-int</span><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>i1 <span style="color: #b1951d;">(</span>make-interval <span style="color: #a45bad;">2</span> <span style="color: #a45bad;">3</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>i2 <span style="color: #b1951d;">(</span>make-interval <span style="color: #a45bad;">-5</span> <span style="color: #a45bad;">7</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #67b11d;">(</span>i3 <span style="color: #b1951d;">(</span>make-interval <span style="color: #a45bad;">-13</span> <span style="color: #a45bad;">-11</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span>
<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>display i1<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" * "</span><span style="color: #2d9574;">)(</span>display i1<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" mul: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval i1 i1<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" sig: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval-signs i1 i1<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>newline<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>display i2<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" * "</span><span style="color: #2d9574;">)(</span>display i2<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" mul: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval i2 i2<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" sig: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval-signs i2 i2<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>newline<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>display i3<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" * "</span><span style="color: #2d9574;">)(</span>display i3<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" mul: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval i3 i3<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" sig: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval-signs i3 i3<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>newline<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>display i1<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" * "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display i2<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" mul: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval i1 i2<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" sig: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval-signs i1 i2<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>newline<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>display i1<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" * "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display i3<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" mul: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval i1 i3<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" sig: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval-signs i1 i3<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>newline<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>display i2<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" * "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display i3<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" mul: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval i2 i3<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" sig: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval-signs i2 i3<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>newline<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>display i3<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" * "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display i2<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" mul: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval i3 i2<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" sig: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval-signs i3 i2<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>newline<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>display i3<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" * "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display i1<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" mul: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval i3 i1<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" sig: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval-signs i3 i1<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>newline<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>display i2<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" * "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display i1<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" mul: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval i2 i1<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #2d9574;">" sig: "</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>display <span style="color: #67b11d;">(</span>mul-interval-signs i2 i1<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>newline<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-center-width</span> c w<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-interval <span style="color: #2d9574;">(</span>- c w<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>+ c w<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;">center</span> i<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>/ <span style="color: #2d9574;">(</span>+ <span style="color: #67b11d;">(</span>lower-bound i<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>upper-bound i<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <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;">width</span> i<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>/ <span style="color: #2d9574;">(</span>- <span style="color: #67b11d;">(</span>upper-bound i<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>lower-bound i<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #a45bad;">2.0</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;">nalog 2.12</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-center-percent</span> c p<span style="color: #bc6ec5;">)</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">percentage is between 0 and 1</span>
<span style="color: #bc6ec5;">(</span><span style="color: #4f97d7; font-weight: bold;">if</span>
<span style="color: #2d9574;">(</span><span style="color: #4f97d7; font-weight: bold;">or</span> <span style="color: #67b11d;">(</span>&lt; p <span style="color: #a45bad;">0.0</span><span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>&gt; p <span style="color: #a45bad;">1.0</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>error <span style="color: #2d9574;">"Percentage should be a decimal number between 0 and 1"</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>make-center-width c <span style="color: #67b11d;">(</span>* c p<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;">percent</span> i<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>/ <span style="color: #2d9574;">(</span>width i<span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>center i<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;">naloga 2.13</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">za majhne odstotke je preprosta forumalu za priblizek produkta.</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;">interval-mul-pribl</span> a b<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>make-center-percent <span style="color: #2d9574;">(</span>* <span style="color: #67b11d;">(</span>center a<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>center b<span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span> <span style="color: #2d9574;">(</span>+ <span style="color: #67b11d;">(</span>percent a<span style="color: #67b11d;">)</span> <span style="color: #67b11d;">(</span>percent 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;">nvm ce je to to, ampak za mnozejnje (make-center-percent 1000 0.01) in (mcp</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">2000 0.01) dobim za produkt po direktni formuli percent produkta 0.019998, po</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">moji formuli za priblizek pa 0.02, kar je dost podobno.</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;">par1</span> r1 r2<span style="color: #bc6ec5;">)</span>
<span style="color: #bc6ec5;">(</span>div-interval <span style="color: #2d9574;">(</span>mul-interval r1 r2<span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>add-interval r1 r2<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;">par2</span> r1 r2<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>one <span style="color: #b1951d;">(</span>make-interval <span style="color: #a45bad;">1</span> <span style="color: #a45bad;">1</span><span style="color: #b1951d;">)</span><span style="color: #67b11d;">)</span><span style="color: #2d9574;">)</span>
<span style="color: #2d9574;">(</span>div-interval one
<span style="color: #67b11d;">(</span>add-interval <span style="color: #b1951d;">(</span>div-interval one r1<span style="color: #b1951d;">)</span>
<span style="color: #b1951d;">(</span>div-interval one r2<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;">naloga 2.14</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">hja dobimo drugacne rezultate, nvm zakaj...</span>
<span style="color: #2aa1ae; background-color: #292e34;">;; </span><span style="color: #2aa1ae; background-color: #292e34;">naloga 2.15</span>
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-orgf662eab" class="outline-3">
<h3 id="orgf662eab"><span class="section-number-3">2.2.</span> Hierarhični podatki in lastnosti zaprtosti</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-center">
<p>
Closure Property =&gt;
<a href="https://dis-slovarcek.ijs.si/list_searched">https://dis-slovarcek.ijs.si/list_searched</a>
</p>
</div>
<p>
Pare sestavljamo s <code>cons</code>.
</p>
<p>
Sposobnost ustvarjanja/sestavljanja parov, katerih elementi so pari je bistvo
strukture podatkovnih seznamov kot orodja za reprezentacijo. Temu recemo
lastnosti zaprtosti. Na splosno, operacija za zdruzevanje podatkov zadosca
<b>lastnosti zaprtosti</b>, ce so lahko rezultati zdruzevanja podatkov tudi sami
zdruzeni z istimi operacijami.
</p>
<p>
<i>Treba je pazit, ker closure tukaj pride iz abstraktne algebre. Lisp skupnost pa</i>
<i>s closure opisuje tudi nepovezan koncept - implementacijsko tehniko za procedure</i>
<i>s prostimi spremenljivkami. V sicp closure nima tega pomena.</i>
</p>
<p>
Zaprtost je kljuc do sredstev kombinacij, ker omogoca ustvarjanje hierarhicnih
struktur - struktur, ki so sestavljene iz struktur.
</p>
</div>
<div id="outline-container-org32e5993" class="outline-4">
<h4 id="org32e5993"><span class="section-number-4">2.2.1.</span> Reprezentacija sekvenc</h4>
<div class="outline-text-4" id="text-2-2-1">
<p>
<code>list</code> funkcija je ekvivalentna konsanju argumentov na <code>cons</code>.
</p>
</div>
<ol class="org-ol">
<li><a id="orgcee6513"></a>operacije s seznami<br /></li>
</ol>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Lio Novelli</p>
<p class="date">Created: 2024-09-04 Wed 19:20</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
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