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task2.html
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN"
"http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<meta http-equiv="Content-Type" content="application/xhtml+xml; charset=UTF-8" />
<meta name="generator" content="AsciiDoc 8.6.9" />
<title>Hints for Task 2</title>
<style type="text/css">
/* Shared CSS for AsciiDoc xhtml11 and html5 backends */
/* Default font. */
body {
font-family: Georgia,serif;
}
/* Title font. */
h1, h2, h3, h4, h5, h6,
div.title, caption.title,
thead, p.table.header,
#toctitle,
#author, #revnumber, #revdate, #revremark,
#footer {
font-family: Arial,Helvetica,sans-serif;
}
body {
margin: 1em 5% 1em 5%;
}
a {
color: blue;
text-decoration: underline;
}
a:visited {
color: fuchsia;
}
em {
font-style: italic;
color: navy;
}
strong {
font-weight: bold;
color: #083194;
}
h1, h2, h3, h4, h5, h6 {
color: #527bbd;
margin-top: 1.2em;
margin-bottom: 0.5em;
line-height: 1.3;
}
h1, h2, h3 {
border-bottom: 2px solid silver;
}
h2 {
padding-top: 0.5em;
}
h3 {
float: left;
}
h3 + * {
clear: left;
}
h5 {
font-size: 1.0em;
}
div.sectionbody {
margin-left: 0;
}
hr {
border: 1px solid silver;
}
p {
margin-top: 0.5em;
margin-bottom: 0.5em;
}
ul, ol, li > p {
margin-top: 0;
}
ul > li { color: #aaa; }
ul > li > * { color: black; }
.monospaced, code, pre {
font-family: "Courier New", Courier, monospace;
font-size: inherit;
color: navy;
padding: 0;
margin: 0;
}
pre {
white-space: pre-wrap;
}
#author {
color: #527bbd;
font-weight: bold;
font-size: 1.1em;
}
#email {
}
#revnumber, #revdate, #revremark {
}
#footer {
font-size: small;
border-top: 2px solid silver;
padding-top: 0.5em;
margin-top: 4.0em;
}
#footer-text {
float: left;
padding-bottom: 0.5em;
}
#footer-badges {
float: right;
padding-bottom: 0.5em;
}
#preamble {
margin-top: 1.5em;
margin-bottom: 1.5em;
}
div.imageblock, div.exampleblock, div.verseblock,
div.quoteblock, div.literalblock, div.listingblock, div.sidebarblock,
div.admonitionblock {
margin-top: 1.0em;
margin-bottom: 1.5em;
}
div.admonitionblock {
margin-top: 2.0em;
margin-bottom: 2.0em;
margin-right: 10%;
color: #606060;
}
div.content { /* Block element content. */
padding: 0;
}
/* Block element titles. */
div.title, caption.title {
color: #527bbd;
font-weight: bold;
text-align: left;
margin-top: 1.0em;
margin-bottom: 0.5em;
}
div.title + * {
margin-top: 0;
}
td div.title:first-child {
margin-top: 0.0em;
}
div.content div.title:first-child {
margin-top: 0.0em;
}
div.content + div.title {
margin-top: 0.0em;
}
div.sidebarblock > div.content {
background: #ffffee;
border: 1px solid #dddddd;
border-left: 4px solid #f0f0f0;
padding: 0.5em;
}
div.listingblock > div.content {
border: 1px solid #dddddd;
border-left: 5px solid #f0f0f0;
background: #f8f8f8;
padding: 0.5em;
}
div.quoteblock, div.verseblock {
padding-left: 1.0em;
margin-left: 1.0em;
margin-right: 10%;
border-left: 5px solid #f0f0f0;
color: #888;
}
div.quoteblock > div.attribution {
padding-top: 0.5em;
text-align: right;
}
div.verseblock > pre.content {
font-family: inherit;
font-size: inherit;
}
div.verseblock > div.attribution {
padding-top: 0.75em;
text-align: left;
}
/* DEPRECATED: Pre version 8.2.7 verse style literal block. */
div.verseblock + div.attribution {
text-align: left;
}
div.admonitionblock .icon {
vertical-align: top;
font-size: 1.1em;
font-weight: bold;
text-decoration: underline;
color: #527bbd;
padding-right: 0.5em;
}
div.admonitionblock td.content {
padding-left: 0.5em;
border-left: 3px solid #dddddd;
}
div.exampleblock > div.content {
border-left: 3px solid #dddddd;
padding-left: 0.5em;
}
div.imageblock div.content { padding-left: 0; }
span.image img { border-style: none; vertical-align: text-bottom; }
a.image:visited { color: white; }
dl {
margin-top: 0.8em;
margin-bottom: 0.8em;
}
dt {
margin-top: 0.5em;
margin-bottom: 0;
font-style: normal;
color: navy;
}
dd > *:first-child {
margin-top: 0.1em;
}
ul, ol {
list-style-position: outside;
}
ol.arabic {
list-style-type: decimal;
}
ol.loweralpha {
list-style-type: lower-alpha;
}
ol.upperalpha {
list-style-type: upper-alpha;
}
ol.lowerroman {
list-style-type: lower-roman;
}
ol.upperroman {
list-style-type: upper-roman;
}
div.compact ul, div.compact ol,
div.compact p, div.compact p,
div.compact div, div.compact div {
margin-top: 0.1em;
margin-bottom: 0.1em;
}
tfoot {
font-weight: bold;
}
td > div.verse {
white-space: pre;
}
div.hdlist {
margin-top: 0.8em;
margin-bottom: 0.8em;
}
div.hdlist tr {
padding-bottom: 15px;
}
dt.hdlist1.strong, td.hdlist1.strong {
font-weight: bold;
}
td.hdlist1 {
vertical-align: top;
font-style: normal;
padding-right: 0.8em;
color: navy;
}
td.hdlist2 {
vertical-align: top;
}
div.hdlist.compact tr {
margin: 0;
padding-bottom: 0;
}
.comment {
background: yellow;
}
.footnote, .footnoteref {
font-size: 0.8em;
}
span.footnote, span.footnoteref {
vertical-align: super;
}
#footnotes {
margin: 20px 0 20px 0;
padding: 7px 0 0 0;
}
#footnotes div.footnote {
margin: 0 0 5px 0;
}
#footnotes hr {
border: none;
border-top: 1px solid silver;
height: 1px;
text-align: left;
margin-left: 0;
width: 20%;
min-width: 100px;
}
div.colist td {
padding-right: 0.5em;
padding-bottom: 0.3em;
vertical-align: top;
}
div.colist td img {
margin-top: 0.3em;
}
@media print {
#footer-badges { display: none; }
}
#toc {
margin-bottom: 2.5em;
}
#toctitle {
color: #527bbd;
font-size: 1.1em;
font-weight: bold;
margin-top: 1.0em;
margin-bottom: 0.1em;
}
div.toclevel0, div.toclevel1, div.toclevel2, div.toclevel3, div.toclevel4 {
margin-top: 0;
margin-bottom: 0;
}
div.toclevel2 {
margin-left: 2em;
font-size: 0.9em;
}
div.toclevel3 {
margin-left: 4em;
font-size: 0.9em;
}
div.toclevel4 {
margin-left: 6em;
font-size: 0.9em;
}
span.aqua { color: aqua; }
span.black { color: black; }
span.blue { color: blue; }
span.fuchsia { color: fuchsia; }
span.gray { color: gray; }
span.green { color: green; }
span.lime { color: lime; }
span.maroon { color: maroon; }
span.navy { color: navy; }
span.olive { color: olive; }
span.purple { color: purple; }
span.red { color: red; }
span.silver { color: silver; }
span.teal { color: teal; }
span.white { color: white; }
span.yellow { color: yellow; }
span.aqua-background { background: aqua; }
span.black-background { background: black; }
span.blue-background { background: blue; }
span.fuchsia-background { background: fuchsia; }
span.gray-background { background: gray; }
span.green-background { background: green; }
span.lime-background { background: lime; }
span.maroon-background { background: maroon; }
span.navy-background { background: navy; }
span.olive-background { background: olive; }
span.purple-background { background: purple; }
span.red-background { background: red; }
span.silver-background { background: silver; }
span.teal-background { background: teal; }
span.white-background { background: white; }
span.yellow-background { background: yellow; }
span.big { font-size: 2em; }
span.small { font-size: 0.6em; }
span.underline { text-decoration: underline; }
span.overline { text-decoration: overline; }
span.line-through { text-decoration: line-through; }
div.unbreakable { page-break-inside: avoid; }
/*
* xhtml11 specific
*
* */
div.tableblock {
margin-top: 1.0em;
margin-bottom: 1.5em;
}
div.tableblock > table {
border: 3px solid #527bbd;
}
thead, p.table.header {
font-weight: bold;
color: #527bbd;
}
p.table {
margin-top: 0;
}
/* Because the table frame attribute is overriden by CSS in most browsers. */
div.tableblock > table[frame="void"] {
border-style: none;
}
div.tableblock > table[frame="hsides"] {
border-left-style: none;
border-right-style: none;
}
div.tableblock > table[frame="vsides"] {
border-top-style: none;
border-bottom-style: none;
}
/*
* html5 specific
*
* */
table.tableblock {
margin-top: 1.0em;
margin-bottom: 1.5em;
}
thead, p.tableblock.header {
font-weight: bold;
color: #527bbd;
}
p.tableblock {
margin-top: 0;
}
table.tableblock {
border-width: 3px;
border-spacing: 0px;
border-style: solid;
border-color: #527bbd;
border-collapse: collapse;
}
th.tableblock, td.tableblock {
border-width: 1px;
padding: 4px;
border-style: solid;
border-color: #527bbd;
}
table.tableblock.frame-topbot {
border-left-style: hidden;
border-right-style: hidden;
}
table.tableblock.frame-sides {
border-top-style: hidden;
border-bottom-style: hidden;
}
table.tableblock.frame-none {
border-style: hidden;
}
th.tableblock.halign-left, td.tableblock.halign-left {
text-align: left;
}
th.tableblock.halign-center, td.tableblock.halign-center {
text-align: center;
}
th.tableblock.halign-right, td.tableblock.halign-right {
text-align: right;
}
th.tableblock.valign-top, td.tableblock.valign-top {
vertical-align: top;
}
th.tableblock.valign-middle, td.tableblock.valign-middle {
vertical-align: middle;
}
th.tableblock.valign-bottom, td.tableblock.valign-bottom {
vertical-align: bottom;
}
/*
* manpage specific
*
* */
body.manpage h1 {
padding-top: 0.5em;
padding-bottom: 0.5em;
border-top: 2px solid silver;
border-bottom: 2px solid silver;
}
body.manpage h2 {
border-style: none;
}
body.manpage div.sectionbody {
margin-left: 3em;
}
@media print {
body.manpage div#toc { display: none; }
}
</style>
<script type="text/javascript">
/*<+'])');
// Function that scans the DOM tree for header elements (the DOM2
// nodeIterator API would be a better technique but not supported by all
// browsers).
var iterate = function (el) {
for (var i = el.firstChild; i != null; i = i.nextSibling) {
if (i.nodeType == 1 /* Node.ELEMENT_NODE */) {
var mo = re.exec(i.tagName);
if (mo && (i.getAttribute("class") || i.getAttribute("className")) != "float") {
result[result.length] = new TocEntry(i, getText(i), mo[1]-1);
}
iterate(i);
}
}
}
iterate(el);
return result;
}
var toc = document.getElementById("toc");
if (!toc) {
return;
}
// Delete existing TOC entries in case we're reloading the TOC.
var tocEntriesToRemove = [];
var i;
for (i = 0; i < toc.childNodes.length; i++) {
var entry = toc.childNodes[i];
if (entry.nodeName.toLowerCase() == 'div'
&& entry.getAttribute("class")
&& entry.getAttribute("class").match(/^toclevel/))
tocEntriesToRemove.push(entry);
}
for (i = 0; i < tocEntriesToRemove.length; i++) {
toc.removeChild(tocEntriesToRemove[i]);
}
// Rebuild TOC entries.
var entries = tocEntries(document.getElementById("content"), toclevels);
for (var i = 0; i < entries.length; ++i) {
var entry = entries[i];
if (entry.element.id == "")
entry.element.id = "_toc_" + i;
var a = document.createElement("a");
a.href = "#" + entry.element.id;
a.appendChild(document.createTextNode(entry.text));
var div = document.createElement("div");
div.appendChild(a);
div.className = "toclevel" + entry.toclevel;
toc.appendChild(div);
}
if (entries.length == 0)
toc.parentNode.removeChild(toc);
},
/////////////////////////////////////////////////////////////////////
// Footnotes generator
/////////////////////////////////////////////////////////////////////
/* Based on footnote generation code from:
* http://www.brandspankingnew.net/archive/2005/07/format_footnote.html
*/
footnotes: function () {
// Delete existing footnote entries in case we're reloading the footnodes.
var i;
var noteholder = document.getElementById("footnotes");
if (!noteholder) {
return;
}
var entriesToRemove = [];
for (i = 0; i < noteholder.childNodes.length; i++) {
var entry = noteholder.childNodes[i];
if (entry.nodeName.toLowerCase() == 'div' && entry.getAttribute("class") == "footnote")
entriesToRemove.push(entry);
}
for (i = 0; i < entriesToRemove.length; i++) {
noteholder.removeChild(entriesToRemove[i]);
}
// Rebuild footnote entries.
var cont = document.getElementById("content");
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<body class="article">
<div id="header">
<h1>Hints for Task 2</h1>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph"><p>This document contains hints and guidelines for solving task 2 of the
project task for the 2015 iteration of the course Introduction to
Compilers at DIKU.</p></div>
<div class="paragraph"><p>You are not required to follow these hints, but you are strongly
encouraged to do so. (If you choose not to, you will be on the
threshold where strong bravery turns into unjustified fearlessness.)</p></div>
<div class="paragraph"><p>This task involves implementing three array combinators (special
array-oriented functions): <code>iota</code>, <code>map</code>, and <code>reduce</code>.</p></div>
<div class="paragraph"><p>This is the big one. Compare it to task 1 and task 3:</p></div>
<div class="ulist"><ul>
<li>
<p>
While you are indeed asked to make a lot of modifications in task 1,
none of the individual modifications require large code insertions.
Task 1 has many, small tasks.
</p>
</li>
<li>
<p>
Task 3 requires you to complete an optimization, which may not
require extremely much code, but does involve thinking a lot about
recursion.
</p>
</li>
</ul></div>
<div class="paragraph"><p>Task 2 asks you to make fundamental additions to your Fasto compiler,
and write a lot of code. To get you properly started on this large
task, we essentially provide you with a solution for <code>iota</code>. However,
we don’t hand it out directly. Instead we ask you to follow this
guide, which will tell you which code to insert where, how to test
that the new code works, and why it works.</p></div>
<div class="paragraph"><p>Once you have implemented <code>iota</code> by following our very detailed guide,
you’re much more on your own with <code>map</code> and <code>reduce</code> — however, those
two combinators share many features with <code>iota</code>, so we hope that
you’ll have an idea of how to progress.</p></div>
<div class="paragraph"><p><strong>If you find any errors in this text, please tell us!</strong></p></div>
</div>
</div>
<div class="sect1">
<h2 id="_overview_of_code_iota_code_code_map_code_and_code_reduce_code">Overview of <code>iota</code>, <code>map</code> and <code>reduce</code></h2>
<div class="sectionbody">
<div class="paragraph"><p>Before you hack away on <code>iota</code>, here is a quick overview of the three
array combinators. Remember to also read the group project PDF file,
which provides more theoretical detail.</p></div>
<div class="sect2">
<h3 id="_code_iota_code"><code>iota</code></h3>
<div class="paragraph"><p>Type: <code>int -> [int]</code></p></div>
<div class="paragraph"><p>Result for <code>iota(n)</code>: <code>[0, 1, ..., n - 2, n - 1]</code></p></div>
<div class="paragraph"><p>Example: <code>iota(5)</code> should return <code>[0, 1, 2, 3, 4]</code>.</p></div>
</div>
<div class="sect2">
<h3 id="_code_map_code"><code>map</code></h3>
<div class="paragraph"><p>Type: <code>(a -> b) -> [a] -> [b]</code></p></div>
<div class="paragraph"><p>This has the same semantics as the <code>map</code> function in SML.</p></div>
</div>
<div class="sect2">
<h3 id="_code_reduce_code"><code>reduce</code></h3>
<div class="paragraph"><p>Type: <code>(a * a -> a) -> a * [a] -> a</code></p></div>
<div class="paragraph"><p>Result for <code>reduce(f, x, [])</code>: <code>x</code></p></div>
<div class="paragraph"><p>Result for <code>reduce(f, x, [y0])</code>: <code>f(x, y0)</code></p></div>
<div class="paragraph"><p>Result for <code>reduce(f, x, [y0, y1])</code>: <code>f(f(x, y0), y1)</code></p></div>
<div class="paragraph"><p>And so on.</p></div>
<div class="paragraph"><p>You may have noticed that this seems very similar to the SML function
<code>foldl</code>. <code>foldl</code> is actually a more general function, meaning it can
do more than <code>reduce</code>. It is perfectly fine to use <code>foldl</code> to
implement <code>reduce</code> in your interpreter, or to just get inspired.</p></div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_testing_your_solution">Testing your solution</h2>
<div class="sectionbody">
<div class="paragraph"><p>We provide several tests for <code>iota</code>, <code>map</code> and <code>reduce</code>. Once your
solution passes all the relevant tests, great! But please write your
own test programs as well. One can always write more tests.</p></div>
</div>
</div>
<div class="sect1">
<h2 id="_the_grand_guide_to_implementing_code_iota_code">The grand guide to implementing <code>iota</code></h2>
<div class="sectionbody">
<div class="paragraph"><p>First, let’s consider which parts of the compiler will need to be modified.
<code>iota</code> isn’t just a new operator, a group of new literals or an improved
optimization; it is an entirely new language construct. There is no way to
implement something similar to <code>iota</code> in a Fasto program with existing
constructs only. Think about that.</p></div>
<div class="paragraph"><p>These are the files that you will need to modify:</p></div>
<div class="ulist"><ul>
<li>
<p>
<code>Lexer.lex</code>
</p>
</li>
<li>
<p>
<code>Parser.grm</code>
</p>
</li>
<li>
<p>
<code>TypeChecker.sml</code>
</p>
</li>
<li>
<p>
<code>Interpreter.sml</code>
</p>
</li>
<li>
<p>
<code>CodeGen.sml</code>
</p>
</li>
</ul></div>
<div class="paragraph"><p>It’s the same files as in task 1. The difference is that you’ll write much more
code.</p></div>
<div class="paragraph"><p>Here’s is a file that you specifically should <strong>not</strong> modify:</p></div>
<div class="ulist"><ul>
<li>
<p>
<code>Fasto.sml</code>
</p>
</li>
</ul></div>
<div class="paragraph"><p>This is because we have been kind enough to define the relevant constructors
for you. From <code>Fasto.sml</code>:</p></div>
<div class="listingblock">
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt> <span style="font-weight: bold"><span style="color: #0000FF">datatype</span></span> Exp <span style="color: #990000">=</span>
<span style="font-style: italic"><span style="color: #9A1900">(* ... *)</span></span>
<span style="font-style: italic"><span style="color: #9A1900">(* The following are project tasks. *)</span></span>
<span style="color: #990000">|</span> Iota <span style="font-weight: bold"><span style="color: #0000FF">of</span></span> Exp <span style="color: #990000">*</span> pos <span style="font-style: italic"><span style="color: #9A1900">(* iota(n) *)</span></span>
<span style="color: #990000">|</span> Map <span style="font-weight: bold"><span style="color: #0000FF">of</span></span> FunArg <span style="color: #990000">*</span> Exp <span style="color: #990000">*</span> <span style="font-weight: bold"><span style="color: #000080">T</span></span><span style="color: #990000">.</span>TypeAnnot <span style="color: #990000">*</span> <span style="font-weight: bold"><span style="color: #000080">T</span></span><span style="color: #990000">.</span>TypeAnnot <span style="color: #990000">*</span> pos <span style="font-style: italic"><span style="color: #9A1900">(* map(f, arr) *)</span></span>
<span style="color: #990000">|</span> Reduce <span style="font-weight: bold"><span style="color: #0000FF">of</span></span> FunArg <span style="color: #990000">*</span> Exp <span style="color: #990000">*</span> Exp <span style="color: #990000">*</span> <span style="font-weight: bold"><span style="color: #000080">T</span></span><span style="color: #990000">.</span>TypeAnnot <span style="color: #990000">*</span> pos <span style="font-style: italic"><span style="color: #9A1900">(* reduce(f, 0, arr) *)</span></span>
<span style="font-style: italic"><span style="color: #9A1900">(* ... *)</span></span>
<span style="font-weight: bold"><span style="color: #0000FF">and</span></span> FunArg <span style="color: #990000">=</span> Lambda <span style="font-weight: bold"><span style="color: #0000FF">of</span></span> Type <span style="color: #990000">*</span> Param list <span style="color: #990000">*</span> Exp <span style="color: #990000">*</span> pos
<span style="color: #990000">|</span> FunName <span style="font-weight: bold"><span style="color: #0000FF">of</span></span> string</tt></pre></div></div>
<div class="paragraph"><p>This is already done. It might seem like <code>map</code> and <code>reduce</code> are much more
complex to implement than <code>iota</code>, since they have all these extra arguments, but
it’s mostly in the parser stage that this is very true, but we’ll get to that.</p></div>
<div class="sect2">
<h3 id="_step_0_running_the_compiler">Step 0: Running the compiler</h3>
<div class="paragraph"><p>Let’s compile the test program <code>tests/iota.fo</code>:</p></div>
<div class="listingblock">
<div class="content">
<pre><code>$ ./bin/fasto -c tests/iota.fo</code></pre>
</div></div>
<div class="paragraph"><p>That should print out this:</p></div>
<div class="listingblock">
<div class="content">
<pre><code>Type error: Unknown function iota at line 4, column 11</code></pre>
</div></div>
<div class="paragraph"><p>This is because the handed out Fasto compiler has no notion of <code>iota</code>
and assumes that it’s just an ordinary function that you’ve forgotten
to define. But it’s not! It’s special!</p></div>
</div>
<div class="sect2">
<h3 id="_step_1_extending_the_lexer">Step 1: Extending the lexer</h3>
<div class="paragraph"><p>We must tell the compiler to handle <code>iota</code> in our very own way. In
<code>Lexer.lex</code>, add</p></div>
<div class="listingblock">
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt> <span style="color: #990000">|</span> <span style="color: #FF0000">"iota"</span> <span style="color: #990000">=></span> <span style="font-weight: bold"><span style="color: #000080">Parser</span></span><span style="color: #990000">.</span>IOTA pos</tt></pre></div></div>
<div class="paragraph"><p>to the <code>fun keyword (s, pos)</code> function. Then, in <code>Parser.grm</code>, add</p></div>
<div class="listingblock">
<div class="content">
<pre><code>%token <(int*int)> IOTA</code></pre>
</div></div>
<div class="paragraph"><p>to the top section. This last part is necessary because lexeme names
are stored in the parser.</p></div>
<div class="paragraph"><p>Once you have changed these things and recompiled your compiler (using
<code>make</code>), your lexer now makes sure that <code>iota</code> is handled on its own.
But it doesn’t do anything useful yet, and you’ll get a parse error if
you try to compile <code>tests/iota.fo</code>.</p></div>
</div>
<div class="sect2">
<h3 id="_step_2_extending_the_parser">Step 2: Extending the parser</h3>
<div class="paragraph"><p>The compiler now reads <code>iota</code> and turns it into <code>Parser.IOTA</code>, but no
rule in the parser uses that, so the parser will give up on any
program containing <code>iota</code>.</p></div>
<div class="paragraph"><p><code>iota(n)</code> is an expression, so we find the <code>Exp :</code> group of rules in
<code>Parser.grm</code> and add this:</p></div>
<div class="listingblock">
<div class="content">
<pre><code> | IOTA LPAR Exp RPAR
{ Iota ($3, $1) }</code></pre>
</div></div>
<div class="paragraph"><p>When you have done this and run the rebuilt compiler, try running
<code>./bin/fasto -c tests/iota.fo</code> once more. You should get this back:</p></div>
<div class="listingblock">
<div class="content">
<pre><code>Uncaught exception:
Fail: Unimplemented feature iota</code></pre>
</div></div>
<div class="paragraph"><p>This means that <code>iota</code> is successfully parsed and put into a syntax
tree, but there’s no code capable of generating MIPS code for <code>iota</code>.
You can also try interpreting (<code>./bin/fasto -i tests/iota.fo</code>), which
will give you the same error message, since there’s no interpreter
code either.</p></div>
</div>
<div class="sect2">
<h3 id="_step_3_checking_the_types">Step 3: Checking the types</h3>
<div class="paragraph"><p>Actually, we lied a little in the previous section. While it might
make sense that it throws an <code>Unimplemented feature iota</code> error
because it has no code generation support yet, the error actually
happens at an earlier state: the type checking.</p></div>
<div class="paragraph"><p>Before Fasto generates code, it does type checking to make sure that
the input program makes sense. In <code>TypeChecker.sml</code>, find this code:</p></div>
<div class="listingblock">
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt> <span style="color: #990000">|</span> <span style="font-weight: bold"><span style="color: #000080">In</span></span><span style="color: #990000">.</span>Iota <span style="color: #990000">(</span>n_exp<span style="color: #990000">,</span> pos<span style="color: #990000">)</span>
<span style="color: #990000">=></span> <span style="font-weight: bold"><span style="color: #0000FF">raise</span></span> Fail <span style="color: #FF0000">"Unimplemented feature iota"</span></tt></pre></div></div>
<div class="paragraph"><p>and replace it with this code:</p></div>
<div class="listingblock">
<div class="content"><!-- Generator: GNU source-highlight 3.1.8
by Lorenzo Bettini
http://www.lorenzobettini.it
http://www.gnu.org/software/src-highlite -->
<pre><tt> <span style="color: #990000">|</span> <span style="font-weight: bold"><span style="color: #000080">In</span></span><span style="color: #990000">.</span>Iota <span style="color: #990000">(</span>n_exp<span style="color: #990000">,</span> pos<span style="color: #990000">)</span>
<span style="color: #990000">=></span> <span style="font-weight: bold"><span style="color: #0000FF">let</span></span> <span style="font-weight: bold"><span style="color: #0000FF">val</span></span> <span style="color: #990000">(</span>e_type<span style="color: #990000">,</span> n_exp_dec<span style="color: #990000">)</span> <span style="color: #990000">=</span> checkExp ftab vtab n_exp
<span style="font-weight: bold"><span style="color: #0000FF">in</span></span> <span style="font-weight: bold"><span style="color: #0000FF">if</span></span> e_type <span style="color: #990000">=</span> Int
<span style="font-weight: bold"><span style="color: #0000FF">then</span></span> <span style="color: #990000">(</span>Array Int<span style="color: #990000">,</span> <span style="font-weight: bold"><span style="color: #000080">Out</span></span><span style="color: #990000">.</span>Iota <span style="color: #990000">(</span>n_exp_dec<span style="color: #990000">,</span> pos<span style="color: #990000">))</span>
<span style="font-weight: bold"><span style="color: #0000FF">else</span></span> <span style="font-weight: bold"><span style="color: #0000FF">raise</span></span> Error <span style="color: #990000">(</span><span style="color: #FF0000">"Iota: wrong argument type "</span> <span style="color: #990000">^</span>
ppType e_type<span style="color: #990000">,</span> pos<span style="color: #990000">)</span>
<span style="font-weight: bold"><span style="color: #0000FF">end</span></span></tt></pre></div></div>
<div class="paragraph"><p>This piece of code checks that the argument <code>n</code> in <code>iota(n)</code> is an
integer. First it needs to find the type of <code>n</code> and also check that
<strong>that</strong> type checks out — it is important that you understand that <code>n</code>
can be any expression of type <code>int</code>, and not just a plain integer.
For example, <code>n</code> could be <code>2 + 5</code>, which is fine, or it could be <code>2 +
true</code>, which isn’t okay, and which the <code>checkExp</code> call in the above
code would throw an error for.</p></div>
<div class="paragraph"><p>If everything checks out, <code>(Array Int, Out.Iota (n_exp_dec, pos))</code> is
returned. Here, <code>Array Int</code> is our internal representation of the
type <code>[int]</code>, and <code>Out.Iota (n_exp_dec, pos)</code> is an expression that
has the same inner expression as the original <code>In.Iota (n_exp, pos)</code>,
but type checked and decorated with a type.</p></div>
<div class="paragraph"><p>Once you have inserted this, you can try compiling <code>iota.fo</code> again,
but you’ll still get an <code>Unimplemented feature iota</code> error. <em>This time</em>
it’s because you’re missing code generation.</p></div>
</div>
<div class="sect2">
<h3 id="_step_4_interpreting">Step 4: Interpreting</h3>
<div class="paragraph"><p>Before we get started on the code generator, we’ll take a detour in
interpreter land. Typically (and certainly in this case), filling in
the interpreter code is much easier than filling in the code generator
code. This is because you don’t have to think about low-level MIPS
details, and because you have the entire SML language and library at