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<title>Exercises and notes for book "Haskell Programming from first principles" - Unofficial</title>
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<div id="header">
<h1>Exercises and notes for book "Haskell Programming from first principles" - Unofficial</h1>
<div id="toc" class="toc">
<div id="toctitle">Table of Contents</div>
<ul class="sectlevel1">
<li><a href="#_1_all_you_need_is_lambda">1 All you need is lambda</a>
<ul class="sectlevel2">
<li><a href="#_1_6_multiple_arguments">1.6 Multiple arguments</a></li>
<li><a href="#_1_11_exercises">1.11 Exercises</a></li>
</ul>
</li>
<li><a href="#_2_hello_haskell">2 Hello, Haskell!</a>
<ul class="sectlevel2">
<li><a href="#_2_4_functions">2.4 Functions</a></li>
<li><a href="#_2_5_infix">2.5 Infix</a></li>
<li><a href="#_2_6_declaring_values">2.6 Declaring values</a></li>
<li><a href="#_2_12_let_and_where">2.12 Let and where</a></li>
<li><a href="#_2_13_chapter_exercises">2.13 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_3_string">3 String</a>
<ul class="sectlevel2">
<li><a href="#_3_3_printing_simple_things">3.3 Printing simple things</a></li>
<li><a href="#_3_4_type_sigmatures_of_concatenation_functions">3.4 Type sigmatures of concatenation functions</a></li>
<li><a href="#_3_5_concatenation_and_scoping">3.5 Concatenation and scoping</a></li>
<li><a href="#_3_7_chapter_exercises">3.7 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_4_basic_datatypes">4 Basic datatypes</a>
<ul class="sectlevel2">
<li><a href="#_4_2_anatomy_of_a_data_declaration">4.2 Anatomy of a data declaration</a></li>
<li><a href="#_4_4_comparing_values">4.4 Comparing values</a></li>
<li><a href="#_4_7_chapter_exercises">4.7 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_5_types">5 Types</a>
<ul class="sectlevel2">
<li><a href="#_5_4_typeclass_constrained_type_variables">5.4 Typeclass-constrained type variables</a></li>
<li><a href="#_5_5_currying">5.5 Currying</a></li>
<li><a href="#_5_6_polymorphism">5.6 Polymorphism</a></li>
<li><a href="#_5_7_type_inference">5.7 Type inference</a></li>
<li><a href="#_5_9_chapter_exercises">5.9 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_6_typeclasses">6 Typeclasses</a>
<ul class="sectlevel2">
<li><a href="#_6_7_ord">6.7 Ord</a></li>
<li><a href="#_6_12_writing_instances_for_your_typeclasses">6.12 Writing instances for your typeclasses</a></li>
<li><a href="#_6_14_chapter_exercises">6.14 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_7_more_functional_patterns">7 More functional patterns</a>
<ul class="sectlevel2">
<li><a href="#_7_4_anonymous_functions">7.4 Anonymous functions</a></li>
<li><a href="#_7_5_pattern_matching">7.5 Pattern matching</a></li>
<li><a href="#_7_6_case_expressions">7.6 Case expressions</a></li>
<li><a href="#_7_7_higher_order_functions">7.7 Higher-order functions</a></li>
<li><a href="#_7_8_guards">7.8 Guards</a></li>
<li><a href="#_7_10_pointfree_style">7.10 Pointfree style</a></li>
<li><a href="#_7_12_chapter_exercises">7.12 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_8_recursion">8 Recursion</a>
<ul class="sectlevel2">
<li><a href="#_8_2_factorial">8.2 Factorial</a></li>
<li><a href="#_8_6_chapter_exercises">8.6 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_9_lists">9 Lists</a>
<ul class="sectlevel2">
<li><a href="#_9_5_using_ranges_to_construct_lists">9.5 Using ranges to construct lists</a></li>
<li><a href="#_9_6_extracting_portions_of_lists">9.6 Extracting portions of lists</a></li>
<li><a href="#_9_7_list_comprehensions">9.7 List comprehensions</a></li>
<li><a href="#_9_8_spines_and_non_strict_evaluation">9.8 Spines and non-strict evaluation</a></li>
<li><a href="#_9_9_transforming_lists_of_values">9.9 Transforming lists of values</a></li>
<li><a href="#_9_10_filtering_lists_of_values">9.10 Filtering lists of values</a></li>
<li><a href="#_9_11_zipping_lists">9.11 Zipping lists</a></li>
<li><a href="#_9_12_chapter_exercises">9.12 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_10_folding_lists">10 Folding lists</a>
<ul class="sectlevel2">
<li><a href="#_10_5_fold_left">10.5 Fold left</a></li>
<li><a href="#_10_6_how_to_write_fold_functions">10.6 How to write fold functions</a></li>
<li><a href="#_10_9_scans">10.9 Scans</a></li>
<li><a href="#_10_10_chapter_exercises">10.10 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_11_algebraic_datatypes">11 Algebraic datatypes</a>
<ul class="sectlevel2">
<li><a href="#_11_4_data_constructors_and_values">11.4 Data constructors and values</a></li>
<li><a href="#_11_5_what_s_a_type_and_what_s_data">11.5 What’s a type and what’s data?</a></li>
<li><a href="#_11_7_what_makes_these_datatypes_algebraic">11.7 What makes these datatypes algebraic?</a></li>
<li><a href="#_11_8_sum_types">11.8 Sum types</a></li>
<li><a href="#_11_9_product_types">11.9 Product types</a></li>
<li><a href="#_11_10_normal_form">11.10 Normal form</a></li>
<li><a href="#_11_11_constructing_and_deconstructing_values">11.11 Constructing and deconstructing values</a></li>
<li><a href="#_11_12_function_type_is_exponential">11.12 Function type is exponential</a></li>
<li><a href="#_11_15_binary_tree">11.15 Binary Tree</a></li>
<li><a href="#_11_16_chapter_exercises">11.16 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_12_signaling_adversity">12 Signaling adversity</a>
<ul class="sectlevel2">
<li><a href="#_12_5_chapter_exercises">12.5 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_13_building_projects_in_haskell">13 Building projects in Haskell</a>
<ul class="sectlevel3">
<li><a href="#_differences_between_cabal_and_stack">Differences between cabal and stack</a></li>
<li><a href="#_13_3_working_with_a_basic_project">13.3 Working with a basic project</a></li>
<li><a href="#_13_7_more_on_importing_modules">13.7 More on importing modules</a></li>
<li><a href="#_13_9_do_syntax_and_io">13.9 do syntax and IO</a></li>
<li><a href="#_13_15_chapter_exercises">13.15 Chapter exercises</a></li>
</ul>
</li>
<li><a href="#_14_testing">14 Testing</a>
<ul class="sectlevel2">
<li><a href="#_14_3_conventional_testing">14.3 Conventional testing</a></li>
<li><a href="#_14_5_morse_code">14.5 Morse code</a></li>
<li><a href="#_14_7_chapter_exercises">14.7 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_15_monoid_semigroup">15 Monoid, Semigroup</a>
<ul class="sectlevel2">
<li><a href="#_15_10_reusing_algebras_by_asking_for_algebras">15.10 Reusing algebras by asking for algebras</a></li>
<li><a href="#_15_11_madness">15.11 Madness</a></li>
<li><a href="#_15_12_better_living_through_quickcheck">15.12 Better living through QuickCheck</a></li>
<li><a href="#_15_14_chapter_exercises">15.14 Chapter exercises</a></li>
</ul>
</li>
<li><a href="#_16_functor">16 Functor</a>
<ul class="sectlevel2">
<li><a href="#_16_4_let_s_talk_about_f_baby">16.4 Let’s talk about f , baby</a></li>
<li><a href="#_16_7_commonly_used_functors">16.7 Commonly used functors</a></li>
<li><a href="#_16_10_intermission_exercises">16.10 Intermission: Exercises</a></li>
<li><a href="#_16_11_ignoring_possibilities">16.11 Ignoring possibilities</a></li>
<li><a href="#_16_17_chapter_exercises">16.17 Chapter exercises</a></li>
</ul>
</li>
<li><a href="#_17_applicative">17 Applicative</a>
<ul class="sectlevel2">
<li><a href="#_17_5_applicative_in_use">17.5 Applicative in use</a></li>
<li><a href="#_17_8_ziplist_monoid">17.8 ZipList Monoid</a></li>
<li><a href="#_17_9_chapter_exercises">17.9 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_18_monad">18 Monad</a>
<ul class="sectlevel2">
<li><a href="#_18_2_sorry_monad_is_not_a_burrito">18.2 Sorry — Monad is not a burrito</a></li>
<li><a href="#_18_4_examples_of_monad_use">18.4 Examples of Monad use</a></li>
<li><a href="#_18_5_monad_laws">18.5 Monad laws</a></li>
<li><a href="#_18_7_chapter_exercises">18.7 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_19_applying_structure">19 Applying structure</a></li>
<li><a href="#_20_foldable">20 Foldable</a>
<ul class="sectlevel2">
<li><a href="#_20_5_some_basic_derived_operations">20.5 Some basic derived operations</a></li>
<li><a href="#_20_6_chapter_exercises">20.6 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_21_traversable">21 Traversable</a>
<ul class="sectlevel2">
<li><a href="#_21_12_chapter_exercises">21.12 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_22_reader">22 Reader</a>
<ul class="sectlevel2">
<li><a href="#_22_2_a_new_beginning">22.2 A new beginning</a></li>
<li><a href="#_22_5_but_uh_reader">22.5 But uh, Reader?</a></li>
<li><a href="#_22_6_functions_have_an_applicative_too">22.6 Functions have an Applicative too</a></li>
<li><a href="#_22_7_the_monad_of_functions">22.7 The Monad of functions</a></li>
<li><a href="#_22_11_chapter_exercises">22.11 Chapter Exercises</a></li>
</ul>
</li>
<li><a href="#_23_state">23 State</a>
<ul class="sectlevel2">
<li><a href="#_23_5_throw_down">23.5 Throw down</a></li>
<li><a href="#_23_6_write_state_for_yourself">23.6 Write State for yourself</a></li>
<li><a href="#_23_7_get_a_coding_job_with_one_weird_trick">23.7 Get a coding job with one weird trick</a></li>
<li><a href="#_23_8_chapter_exercises">23.8 Chapter exercises</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="content">
<div id="preamble">
<div class="sectionbody">
<div class="paragraph">
<p>This is <strong>UNOFFICIAL</strong>. In this document you will find finished exercises (hopefully without bugs) and notes for the book <strong>Haskell Programming from first principles</strong> from <strong>Chris Allen</strong> and <strong>Julie Monoruki</strong>. More details about the book and a place where to purchase it - <a href="http://haskellbook.com/" class="bare">http://haskellbook.com/</a></p>
</div>
<div class="paragraph">
<p>Sources for this documents are at <a href="https://github.com/lukleh/haskell-book-exercises" class="bare">https://github.com/lukleh/haskell-book-exercises</a></p>
</div>
<div class="admonitionblock important">
<table>
<tr>
<td class="icon">
<i class="fa icon-important" title="Important"></i>
</td>
<td class="content">
These are my personal notes and solved exercises for the book. I did this for myself and thought it may as well help others. I claim nothing. As I progress in book, I try to update this document.
</td>
</tr>
</table>
</div>
<div class="admonitionblock note">
<table>
<tr>
<td class="icon">
<i class="fa icon-note" title="Note"></i>
</td>
<td class="content">
This document is written in asciidoc, use Asciidoctor to build <code>asciidoctor index.adoc</code>
</td>
</tr>
</table>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_1_all_you_need_is_lambda">1 All you need is lambda</h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_1_6_multiple_arguments">1.6 Multiple arguments</h3>
<div class="sect3">
<h4 id="_intermission_exercises">Intermission: Exercises</h4>
<div class="olist arabic">
<ol class="arabic">
<li>
<p>b) <code>λxy.xz</code> equals <code>λmn.mz</code></p>
</li>
<li>
<p>c) <code>λxy.xxy</code> equals <code>λa(λb).aab</code> although it should be <code>λa(λb.aab)</code> I think</p>
</li>
<li>
<p>b) <code>λxyz.zx</code> equals <code>λtos.st</code></p>
</li>
</ol>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_1_11_exercises">1.11 Exercises</h3>
<div class="sect3">
<h4 id="_combinators">Combinators</h4>
<div class="paragraph">
<p>Combinator is lambda term with no free variable</p>
</div>
<div class="paragraph">
<p><code>λxyz.xz(yz) → λyz.yz(z) → λz.zz</code></p>
</div>
<div class="olist arabic">
<ol class="arabic">
<li>
<p><code>λx.xxx</code> - yes</p>
</li>
<li>
<p><code>λxy.zx</code> - no, <code>z</code> not in head</p>
</li>
<li>
<p><code>λxyz.xy(zx)</code> - yes</p>
</li>
<li>
<p><code>λxyz.xy(zxy)</code> - yes</p>
</li>
<li>
<p><code>λxy.xy(zxy)</code> - no, <code>z</code> not in head</p>
</li>
</ol>
</div>
</div>
<div class="sect3">
<h4 id="_normal_form_or_diverge">Normal form or diverge</h4>
<div class="paragraph">
<p>Diverge - reduction does not end</p>
</div>
<div class="olist arabic">
<ol class="arabic">
<li>
<p><code>λx.xxx</code> - converge, no reduction</p>
</li>
<li>
<p><code>(λz.zzz)(λy.yy)</code> - diverge, <code>(λz.zzz)(λy.yy) → (λy.yy)(λy.yy)(λy.yy) → λy.yy)(λy.yy(λy.yy)</code> into more nested expressions</p>
</li>
<li>
<p><code>(λx.xxx)z</code> - converge, <code>(λx.xxx)z → zzz</code></p>
</li>
</ol>
</div>
</div>
<div class="sect3">
<h4 id="_beta_reduce">Beta reduce</h4>
<div class="paragraph">
<p>Reduce in normal order, that is leftmost outermost first. Otherwise you get different results.</p>
</div>
<div class="olist arabic">
<ol class="arabic">
<li>
<p><code>(λabc.cba)zz(λwv.w) → (λc.czz)(λwv.w) → (λwv.w)zz → z</code></p>
</li>
<li>
<p><code>(λx.λy.xyy)(λa.a)b → (λy.(λa.a)yy)b → (λa.a)bb → bb</code></p>
</li>
<li>
<p><code>(λy.y)(λx.xx)(λz.zq) → (λx.xx)(λz.zq) → (λz.zq)(λz.zq) → (λz.zq)q → qq</code></p>
</li>
<li>
<p><code>(λz.z)(λz.zz)(λz.zy) → (λz.zz)(λz.zy) → (λz.zy)(λz.zy) → (λz.zy)y → yy</code></p>
</li>
<li>
<p><code>(λx.λy.xyy)(λy.y)y → (λy.(λy.y)yy)y → (λy.y)yy → yy</code></p>
</li>
<li>
<p><code>(λa.aa)(λb.ba)c → (λb.ba)(λb.ba)c → ((λb.ba)a)c → aac</code></p>
</li>
<li>
<p><code>(λxyz.xz(yz))(λx.z)(λx.a) → (λyz1.(λx.z)z1(yz1))(λx.a) → (λz1.(λx.z)z1λx.a)z1 → (λz1.zλx.a)z1 → λz1.za</code></p>
</li>
</ol>
</div>
</div>
</div>
</div>
</div>
<div class="sect1">
<h2 id="_2_hello_haskell">2 Hello, Haskell!</h2>
<div class="sectionbody">
<div class="sect2">
<h3 id="_2_4_functions">2.4 Functions</h3>
<div class="sect3">
<h4 id="_intermission_exercises_2">Intermission: Exercises</h4>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">let half x = x / 2
let square x = x * x</code></pre>
</div>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">dpi x = 3.14 * (x * x)</code></pre>
</div>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_2_5_infix">2.5 Infix</h3>
<div class="sect3">
<h4 id="_associativity_and_precedence">Associativity and precedence</h4>
<div class="paragraph">
<p>Higher precedence is applied first. Scale is 0-9.</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">Prelude> :info (^)
(^) :: (Num a, Integral b) => a -> b -> a -- Defined in ‘GHC.Real’
infixr 8 ^</code></pre>
</div>
</div>
<div class="paragraph">
<p>Left associative</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">2 * 3 * 4
-- is evaluated as if it was
(2 * 3) * 4</code></pre>
</div>
</div>
<div class="paragraph">
<p>Right associative</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">Prelude> 2 ^ 3 ^ 4
2417851639229258349412352
Prelude> 2 ^ (3 ^ 4)
2417851639229258349412352
Prelude> (2 ^ 3) ^ 4
4096</code></pre>
</div>
</div>
</div>
<div class="sect3">
<h4 id="_intermission_exercises_3">Intermission: Exercises</h4>
<div class="paragraph">
<p>they differ</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">8 + 7 * 9 = 71
(8 + 7) * 9 = 135</code></pre>
</div>
</div>
<div class="paragraph">
<p>they are the same</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">perimeter x y = (x * 2) + (y * 2)
perimeter x y = x * 2 + y * 2</code></pre>
</div>
</div>
<div class="paragraph">
<p>they differ</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">f x = x / 2 + 9
f x = x / (2 + 9)</code></pre>
</div>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_2_6_declaring_values">2.6 Declaring values</h3>
<div class="paragraph">
<p>fix mistakes</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">let area x = 3. 14 * (x * x)
let area x = 3.14 * (x * x)</code></pre>
</div>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">let double x = b * 2
let double x = x * 2</code></pre>
</div>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">-- file ch02_2.6_1.hs
x = 7
y = 10
f = x + y
Prelude> :l ch02_2.6_1.hs
[1 of 1] Compiling Main ( ch02_2.6_1.hs, interpreted )
ch02_2.6_1.hs:2:4: parse error on input ‘=’
Failed, modules loaded: none.
-- fixed
x = 7
y = 10
f = x + y</code></pre>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_2_12_let_and_where">2.12 Let and where</h3>
<div class="sect3">
<h4 id="_intermission_exercises_4">Intermission: Exercises</h4>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">let x = 5 in x
-- 5
let x = 5 in x * x
-- 25
let x = 5; y = 6 in x * y
-- 30
let x = 3; y = 1000 in x + 3
-- 6</code></pre>
</div>
</div>
<div class="paragraph">
<p><code><strong>let</strong></code> rewritten to <code><strong>where</strong></code></p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">f1 = x
where x = 5
f2 = x * x
where x = 5
f3 = x * y
where x = 5
y = 6
f4 = x + 3
where x = 3
y = 1000</code></pre>
</div>
</div>
</div>
<div class="sect3">
<h4 id="_more_exercises">More exercises!</h4>
<div class="paragraph">
<p><code><strong>let</strong></code> rewritten to <code><strong>where</strong></code></p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">--let x = 3; y = 1000 in x * 3 + y
f1 = x * 3 + y
where x = 3
y = 1000
--let y = 10; x = 10 * 5 + y in x * 5
f2 = x * 5
where y = 10
x = 10 * 5 + y
--let x = 7; y = negate x; z = y * 10 in z / x + y
f3 = z / x + y
where x = 7
y = negate x
z = y * 10</code></pre>
</div>
</div>
</div>
</div>
<div class="sect2">
<h3 id="_2_13_chapter_exercises">2.13 Chapter Exercises</h3>
<div class="sect3">
<h4 id="_parenthesization">Parenthesization</h4>
<div class="olist arabic">
<ol class="arabic">
<li>
<p><code>2 + 2 * 3 - 1</code> == <code>2 + (2 * 3) - 1</code></p>
</li>
<li>
<p><code>(^) 10 $ 1 + 1</code> == <code>(^) 10 (1 + 1)</code></p>
</li>
<li>
<p><code>2 ^ 2 * 4 ^ 5 + 1</code> == <code>( (2 ^ 2) * (4 ^ 5) ) + 1</code></p>
</li>
</ol>
</div>
</div>
<div class="sect3">
<h4 id="_equivalent_expressions">Equivalent expressions</h4>
<div class="olist arabic">
<ol class="arabic">
<li>
<p><code>1 + 1 == 2</code></p>
</li>
<li>
<p><code>10 ^ 2 == 10 + 9 * 10</code></p>
</li>
<li>
<p><code>400 - 37 /= (-) 37 400</code></p>
</li>
<li>
<p><code>100 `div` 3 /= 100 / 3</code></p>
</li>
<li>
<p><code>2 * 5 + 18 /= 2 * (5 + 18)</code></p>
</li>
</ol>
</div>
</div>
<div class="sect3">
<h4 id="_more_fun_with_functions">More fun with functions</h4>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">z = 7
x = y ^ 2
waxOn = x * 5
y = z + 8</code></pre>
</div>
</div>
<div class="paragraph">
<p>to REPL</p>
</div>
<div class="listingblock">
<div class="content">
<pre class="prettyprint highlight"><code class="language-haskell" data-lang="haskell">let z = 7
let y = z + 8
let x = y ^ 2
let waxOn = x * 5</code></pre>
</div>
</div>
<div class="paragraph">