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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Introduction to Haskell - Lecture 3</title>
<meta name="description" content="A course on the world's fastest growing functional programming language">
<meta name="author" content="Nishant Shukla">
<meta name="apple-mobile-web-app-capable" content="yes" />
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<style>
body {
padding-top: 30px;
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</style>
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</script>
<div class="reveal">
<!-- Slides begin here! -->
<div class="slides">
<section>
<section>
<h1>Introduction To Haskell</h1>
<p>Lecture 3</p>
<p>
<br>
</p>
<p>types :: type1 → type2</p>
</section>
<section>
<h3>Using These Slides</h3>
<h4>Every slide has a secret note.</h4>
<small>
<ul>
<li>On <b>Chrome</b>: press <code>F12</code>, then click <b>Console</b></li>
<li>On <b>IE</b>: press <code>F12</code>, then click <b>Console</b></li>
<li>On <b>Firefox</b>: <code>Ctrl+Shift+k</code></li>
</ul>
</small>
<br>
<br>
<p><h3>Shortcut Keys:</h3></p>
<center>
<table width="80%">
<tr>
<td><code>↓</code>, <code>PgDn</code>, <code>n</code>, <code>j</code></td>
<td>next slide</td>
</tr>
<tr>
<td><code>↑</code>, <code>PgUp</code>, <code>p</code>, <code>k</code></td>
<td>prev slide</td>
</tr>
<tr>
<td><code>Esc</code></td>
<td>enables <code>ctrl+f</code> globally</td>
</tr>
</table>
</center>
<aside class="notes">Hi there! This is a secret lecture note. Every slide has a little blurb of text like this!</aside>
</section>
<script>
function clearAll() {
document.getElementById('facA').style.display = 'none';
document.getElementById('facB').style.display = 'none';
document.getElementById('facC').style.display = 'none';
document.getElementById('facD').style.display = 'none';
document.getElementById('facE').style.display = 'none';
document.getElementById('facF').style.display = 'none';
document.getElementById('facG').style.display = 'none';
document.getElementById('facH').style.display = 'none';
document.getElementById('facI').style.display = 'none';
document.getElementById('facJ').style.display = 'none';
}
function showOne(fac) {
clearAll();
document.getElementById(fac).style.display = 'block';
}
</script>
<section>
<h3>Haskell Programming</h3>
<ul>
<li>Code lives in a file with a .hs extension</li>
<br>
<li>Open the file with GHCi
<table>
<tr>
<td>
<small>Run it from the terminal</small>
<pre><code class="haskell">
$ ghci myfile.hs
</code></pre>
</td>
<td>
<small>Or run ghci, then load the file</small>
<pre><code class="haskell">
$ ghci
Prelude> :load myfile
</code></pre>
</td>
</tr>
</table>
</li>
<li>Call your function through ghci</li>
</ul>
<aside class="notes">This is just a review.</aside>
</section>
<section>
<h2>Previous Homework</h2>
<small><q><a href="./lec02.html#/0/22" target="_blank">Implement factorial</a></q></small>
<table style="width:100%">
<tr>
<td><a onclick="showOne('facA');">A</a></td>
<td><a onclick="showOne('facB');">B</a></td>
<td><a onclick="showOne('facC');">C</a></td>
<td><a onclick="showOne('facD');">D</a></td>
<td><a onclick="showOne('facE');">E</a></td>
<td><a onclick="showOne('facF');">F</a></td>
<td><a onclick="showOne('facG');">G</a></td>
<td><a onclick="showOne('facH');">H</a></td>
<td><a onclick="showOne('facI');">I</a></td>
<td><a onclick="showOne('facJ');">J</a></td>
<td><a target="_blank" href="http://willamette.edu/~fruehr/haskell/evolution.html">...</a></td>
</tr>
</table>
<pre id='facA'><code>
-- Most popular solution
facA n = if n > 1
then n * facA(n-1)
else n
</code></pre>
<pre id='facB' style="display:none;"><code>
-- Right tools for the right job
facB n = product [1..n]
</code></pre>
<pre id='facC' style="display:none;"><code>
-- Oh, you.
facC n = foldr (*) 1 [1..n]
</code></pre>
<pre id='facD' style="display:none;"><code>
-- Sophomore Haskell programmer
-- (studied Scheme as a freshman)
-- http://willamette.edu/~fruehr/haskell/evolution.html
facD = (\(n) ->
(if ((==) n 0)
then 1
else ((*) n (facD ((-) n 1)))))
</code></pre>
<pre id='facE' style="display:none;"><code>
-- Memoizing Haskell programmer
-- http://willamette.edu/~fruehr/haskell/evolution.html
facs = scanl (*) 1 [1..]
facE n = facs !! n
</code></pre>
<pre id='facF' style="display:none;"><code>
-- Iterative Haskell programmer
-- (former Pascal programmer)
-- http://willamette.edu/~fruehr/haskell/evolution.html
facF n = result (for init next done)
where init = (0,1)
next (i,m) = (i+1, m * (i+1))
done (i,_) = i==n
result (_,m) = m
for i n d = until d n i
</code></pre>
<pre id='facG' style="display:none;"><code>
-- Continuation-passing Haskell programmer
-- http://willamette.edu/~fruehr/haskell/evolution.html
facCps k 0 = k 1
facCps k n = facCps (k . (n *)) (n-1)
facG = facCps id
</code></pre>
<pre id='facH' style="display:none;"><code>
-- Boy Scout Haskell programmer
-- http://willamette.edu/~fruehr/haskell/evolution.html
y f = f (y f)
facH = y (\f n -> if (n==0) then 1 else n * f (n-1))
</code></pre>
<pre id='facI' style="display:none;"><code>
-- Combinatory Haskell programmer
-- http://willamette.edu/~fruehr/haskell/evolution.html
s f g x = f x (g x)
k x y = x
b f g x = f (g x)
c f g x = f x g
y f = f (y f)
cond p f g x = if p x then f x else g x
facI = y (b (cond ((==) 0) (k 1)) (b (s (*)) (c b pred)))
</code></pre>
<pre id='facJ' style="display:none;"><code>
-- List-encoding Haskell programmer
-- (prefers to count in unary)
-- http://willamette.edu/~fruehr/haskell/evolution.html
arb = ()
listenc n = replicate n arb
listprj f = length . f . listenc
listprod xs ys = [ i (x,y) | x<-xs, y<-ys ]
where i _ = arb
facl [] = listenc 1
facl n@(_:pred) = listprod n (facl pred)
facJ = listprj facl
</code></pre>
<aside class="notes">There's always multiple ways to implement any function.</aside>
</section>
<section>
<h3>Types</h3>
<ul>
<li class="fragment"><p><code class="haskell">Bool</code> = False | True</p></li>
<li class="fragment"><p><code class="haskell">Char</code> = 'a' | 'b' | ... | 'A' | 'B' | ...</p></li>
<li class="fragment"><p><code class="haskell">Int</code> = -2<sup>31</sup> | ... | -1 | 0 | 1 | ... | 2<sup>31</sup>-1</p></li>
<li class="fragment"><p><code class="haskell">Integer</code></p></li>
<li class="fragment"><p><code class="haskell">Double</code></p></li>
</ul>
<br>
<br>
<p>Types always start with a capital letter</p>
<aside class="notes">Think of these almost as Java types (int, String, etc).</aside>
</section>
<section>
<h2>Everything has a Type</h2>
<p>Haskell secretly infers that <code class="haskell">True</code> is a <code class="haskell">Bool</code>.</p>
<pre><code class="haskell">
Prelude> :type True
True :: Bool
</code></pre>
<br>
<div class="fragment roll-in">
<p>You can also explicitly use a type.</p>
<pre><code class="haskell">
Prelude> 3 :: Int
3
Prelude> 3 :: Double
3.0
</code></pre>
</div>
<aside class="notes">'::' is pronounced 'has the type of'</aside>
</section>
<section>
<h3>Yes, Functions have a Type</h3>
<div class="fragment roll-in">
<pre><code class="haskell">
Prelude> head [1,2,3,4]
1
Prelude> :type head
head :: [a] -> a
</code></pre>
<small><code>head</code> has the type <i>List of <code class="haskell">a</code>'s</i> to just <i><code class="haskell">a</code></i></small>
</div>
<div class="fragment roll-in">
<pre><code class="haskell">
Prelude> fst ("left", "right")
"left"
Prelude> :type fst
fst :: (a, b) -> a
</code></pre>
<small>fst has the type <i>tuple of <code class="haskell">a</code> and <code class="haskell">b</code></i> to just <i><code class="haskell">a</code></i></small>
</div>
<aside class="notes">'a' and 'b' here are called Type variables.</aside>
</section>
<!--
Strong; bugs are usually caught when compiling. Strings can't accidentally be treated as Ints.
Static; the compiler knows the type of every value
It Haskell code compiles, you can bet there won't be any type errors
If you've ever been surprised that your long piece of code worked on the first run,
then Haskell will spoil you.
Type inference; The compiler deduces what you mean, without surprises
talk about variables "Just what is a variable, anyway?"
-->
<section>
<h3>Like a Jigsaw Puzzle</h3>
<small>Analogy from <a target="_blank" href="http://book.realworldhaskell.org/read/types-and-functions.html"><i>Real World Haskell</i></a></small>
<p><small>"if a piece has the wrong shape, it simply won't fit"</small></p>
<table border="1">
<tr>
<td>Haskell</td>
<td>Python<a target="_blank" href="http://en.wikipedia.org/wiki/Duck_typing">*</a></td>
</tr>
<tr>
<td><img src="L03_files/zoidberg1.png"></td>
<td><img src="L03_files/zoidberg2.png"></td>
</tr>
</table>
<aside class="notes">Bugs are usually caught at compile-time. The compiler knows the type of every value, so there is never ambiguity.</aside>
</section>
<section data-state="soothe">
<p><small>What should be the <b>type declaration</b> for <code class="haskell">fac</code>?</small>
<small>
<a onclick="toggleElements('b', 'a');">(clear answer)</a>
<a onclick="toggleElements('a', 'b');">(show answer)</a>
</small>
</p>
<pre id="a"><code class="haskell" contenteditable>
fac n = product [1..n]
</code></pre>
<pre id="b" style="display:none;"><code class="haskell">
fac :: Integer -> Integer
fac n = product [1..n]
</code></pre>
<br>
<div class="fragment roll-in">
<p><small>What's the <b>type declaration</b> for <code class="haskell">&&</code> ?</small>
<small>
<a onclick="toggleElements('d', 'c');">(clear answer)</a>
<a onclick="toggleElements('c', 'd');">(show answer)</a>
</small>
</p>
<pre id="c"><code class="haskell" contenteditable>
(&&) ::
</code></pre>
<pre id="d" style="display:none;"><code class="haskell">
(&&) :: Bool -> Bool -> Bool
</code></pre>
</div>
<br>
<div class="fragment roll-in">
<p><small>How about <code class="haskell">:</code> ?</small>
<small>
<a onclick="toggleElements('f', 'e');">(clear answer)</a>
<a onclick="toggleElements('e', 'f');">(show answer)</a>
</small>
</p>
<pre id="e"><code class="haskell" contenteditable>
Prelude> 0:[1,2,3]
[0,1,2,3]
Prelude> :type (:)
</code></pre>
<pre id="f" style="display:none;"><code class="haskell">
Prelude> 0:[1,2,3]
[0,1,2,3]
Prelude> :type (:)
(:) :: a -> [a] -> [a]
</code></pre>
</div>
<aside class="notes">In GHCi, you can do ':type f' to find the type of function 'f'</aside>
</section>
<section>
<h2>Google Tech Talk</h2>
<p><small>(8:00 to 9:22)</small></p>
<iframe width="672" height="504" src="http://www.youtube.com/embed/b9FagOVqxmI?start=480&end=562" frameborder="0" allowfullscreen></iframe>
<aside class="notes">The Haskell compiler tries to infer the type for you. If ambiguous, the programmer must specify the Type explicitly.</aside>
</section>
<section>
<h2>Typeclass</h2>
<p>A Typeclass lets you generalize a function.</p>
<small><p>For example, the less-than sign can be used multiple ways.</p></small>
<ul>
<li><code class="haskell">10 < 20</code></li>
<li><code class="haskell">'a' < 'b'</code></li>
<li><code class="haskell">"aardvark" < "zzz"</code></li>
<li><code class="haskell">[6,2,4] < [6,3,8]</code></li>
</ul>
<aside class="notes">This is a type of polymorphism.</aside>
</section>
<section>
<h2>The <code class="haskell">Ord</code> Typeclass</h2>
<p>is used for things with total order</p>
<pre id="g"><code class="haskell" contenteditable>
Prelude> :type (<)
</code></pre>
<pre id="h" style="display:none;"><code class="haskell" contenteditable>
Prelude> :type (<)
(<) :: a -> a -> Bool
</code></pre>
<pre id="i" style="display:none;"><code class="haskell">
Prelude> :type (<)
(<) :: Ord a => a -> a -> Bool
</code></pre>
<span style="font-size:12px;">
<a onclick="toggleElements('h', 'g');toggleElements('i', 'g');">(clear answer)</a>
<a onclick="toggleElements('g', 'h');toggleElements('i', 'h');">(show incorrect answer)</a>
<a onclick="toggleElements('g', 'i');toggleElements('h', 'i');">(show answer)</a>
</span>
<aside class="notes">Less-than is a function that that takes two comparable things, and outputs a Bool.</aside>
</section>
<section>
<h3>Similar to Interfaces</h3>
<p><small>Remember them from Java?</small></p>
<pre><code class="haskell">
public class NumberUsedByLessThanSign implements Comparable {
...
}
</code></pre>
<aside class="notes">A Typeclass gives a Type some property. For example, both Int and String are comparable, so they both has the type class of Ord.</aside>
</section>
<section>
<h3>Other Typeclasses</h3>
<ul>
<li><code class="haskell">Show</code> - representable as a string
<pre><code class="haskell">
Prelude> show 42
"42"
</code></pre>
</li>
<li><code class="haskell">Enum</code> - enumerable in a list
<pre><code class="haskell">
Prelude> ['R'..'t']
"RSTUVWXYZ[\\]^_`abcdefghijklmnopqrst"
</code></pre>
</li>
<li><code class="haskell">Num</code> - usable as a number
<pre><code class="haskell">
Prelude> 5.2 * 2.5
13.0
</code></pre>
</li>
</ul>
<aside class="notes">42 has the Show Typeclass because we can print it out as a String. Characters have the Enum Typeclass because we can put them in order of ASCII code. Numbers have the Num Typeclass because they can do number-like operations.</aside>
</section>
<section>
<h3>Have you noticed?</h3>
<p>Functions with multiple arguments look funny.</p>
<div class="fragment">
<p>The <code class="haskell">take</code> function has <b>two arguments</b>:</p>
<ul>
<li>an integer, <code class="haskell">n</code></li>
<li>a list, <code class="haskell">ls</code></li>
</ul>
<p>and it produces the first <code class="haskell">n</code> elements of <code class="haskell">ls</code></p>
<pre><code class="haskell">
Prelude> take 5 [1..]
[1,2,3,4,5]
</code></pre>
<div class="fragment roll-in">
<p>The type declaration is</p>
<pre><code class="haskell">
Prelude> :type take
take :: Int -> [a] -> [a]
</code></pre>
<p class="fragment roll-in">Weird...</p>
</div>
</div>
<aside class="notes">It appears like this function has one argument 'Int', and one output '[a]' with something in-between.</aside>
</section>
<section>
<h2>The Concept of <a href="http://www.haskell.org/haskellwiki/Currying" target="_blank">Currying</a></h2>
<p>All Haskell functions take only one argument</p>
<aside class="notes">Take a moment to think about that statement.</aside>
</section>
<section>
<img src="L03_files/grumpycat.png">
<aside class="notes">You mind is about to be blown.</aside>
</section>
<section>
<h3>A Closer Look</h3>
<p>at the <code class="haskell">take</code> function:</p>
<pre><code class="haskell">
take :: Int -> [a] -> [a]
</code></pre>
<br>
<div class="fragment roll-in">
<p>The <code class="haskell">-></code> operator is <i>right-associative</i></p>
<pre><code class="haskell">
take :: Int -> ([a] -> [a])
</code></pre>
<p><code class="haskell">take</code> actually has type of <i>Int to a function</i></p>
</div>
<aside class="notes">So technically, 'take' has just one argument (something of type Int)</aside>
</section>
<section>
<h3>Partial Applications</h3>
<p>Every function technically has one argument.</p>
<p>Actually, this is really cool!</p>
<pre><code class="haskell">
Prelude> :type take
take :: Int -> [a] -> [a]
Prelude> let takeFive = take 5
Prelude> :type takeFive
takeFive :: [a] -> [a]
Prelude> takeFive [1..]
[1,2,3,4,5]
</pre></code>
<aside class="notes">Try it out yourself.</aside>
</section>
<section>
<h2>Functional and Pure</h2>
<p class="fragment roll-in">A function only depends on its aguments.</p>
<p class="fragment roll-in">A type declaration is a strong promise.</p>
<p class="fragment roll-in">Focus on <i>what</i> is done, not <i>how</i>.</p>
<p class="fragment roll-in">Inherently modular</p>
<p class="fragment roll-in">Elegant</p>
<aside class="notes">I hope you're beginning to see why Haskell is a little different.</aside>
</section>
<section data-state="soothe">
<h3>Get Our Hands Dirty</h3>
<p>Create <code class="haskell">mycode.hs</code> and write a function called <code class="haskell">zipTogether</code></p>
<pre id="j"><code class="haskell" contenteditable>
-- mycode.hs
-- |The 'zipTogether' function binds together two lists.
zipTogether :: [a] -> [b] -> [(a,b)]
</code></pre>
<pre id="k" style="display:none;"><code class="haskell" contenteditable>
-- mycode.hs
-- |The 'zipTogether' function binds together two lists.
zipTogether :: [a] -> [b] -> [(a,b)]
zipTogether [] [] = []
zipTogether [] ys = []
zipTogether xs [] = []
zipTogether xs ys = (head xs, head ys):
(zipTogether (tail xs) (tail ys))
</code></pre>
<pre id="l" style="display:none;"><code class="haskell" contenteditable>
-- mycode.hs
-- |The 'zipTogether' function binds together two lists.
zipTogether :: [a] -> [b] -> [(a,b)]
zipTogether [] [] = []
zipTogether [] ys = []
zipTogether xs [] = []
zipTogether (x:xs) (y:ys) = (x,y) : zipTogether xs ys
</code></pre>
<span style="font-size:12px;">
<a onclick="toggleElements('k', 'j');toggleElements('l', 'j');">(clear answer)</a>
<a onclick="toggleElements('j', 'k');toggleElements('l', 'k');">(show answer 1)</a>
<a onclick="toggleElements('j', 'l');toggleElements('k', 'l');">(show answer 2)</a>
</span>
<br>
<p>Expected output:</p>
<pre><code class="haskell" contenteditable>
Prelude> zipTogether [1,2,3] "abc"
[(1,'a'),(2,'b'),(3,'c')]
</code></pre>
<small class="fragment roll-in">by the way, Haskell comes with <code class="haskell">zip</code></small>
<aside class="notes">Zipping is actually used a lot in functional programming. Think of it as zipping together the x-y axes of a graph to plot points.</aside>
</section>
<section>
<h1>Homework</h1>
<h2></h2>
<ol>
<li>
Write a Caesar Cipher function called <code class="haskell">cipher</code>
<div id="p">
<pre><code class="haskell" contenteditable>
cipher :: [Char] -> Int -> [Char]
</code></pre>
<pre><code class="haskell" contenteditable>
Prelude> cipher "hello" 13
"uryyb"
</code></pre>
</div>
<div id="m" style="display:none;">
<small>Are you sure?</small>
<span style="font-size:12px;">
<p><a onclick="toggleElements('m', 'n');toggleElements('o', 'n');toggleElements('p','n');">(please show hint!)</a></p>
</span>
</div>
<div id="n" style="display:none;">
<pre><code class="haskell">
cipher :: [Char] -> Int -> [Char]
cipher [] _ = []
cipher (s:ss) n = (rotate s n) : (cipher ss n)
rotate :: Char -> Int -> Char
</pre></code>
<span style="font-size:12px;">
<p> Now define this 'rotate' function</p>
</span>
</div>
<span id="o" style="font-size:12px;">
<a onclick="toggleElements('n', 'm');toggleElements('o', 'm');">(show hint)</a>
</span>
</li>
<li>
<p>Bonus points for a cool solution!</p>
</li>
<li>
<p>Submit this week's <a href="https://docs.google.com/spreadsheet/viewform?formkey=dC1VWVo4OXFXcWZqTjEzUnoySDRLV1E6MQ">homework form!</a></p>
</li>
</ol>
</section>
</section>
</div>
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