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<div class="reveal">
<div class="slides">
<section id="title-slide">
<h1 class="title">Correct-by-construction programming in Agda</h1>
<p class="subtitle">Lecture 3: Side effects, type classes, and monads</p>
<p class="author">Jesper Cockx</p>
<p class="date">2 September 2019</p>
</section>
<section><section id="type-classes" class="title-slide slide level1"><h1>Type classes</h1></section><section id="what-is-a-type-class" class="slide level2">
<h2>What is a type class?</h2>
<p>A type class offers one or more functions for a <strong>generic</strong> type. <strong>Examples</strong>:</p>
<ul>
<li><code>Print A</code>:
<ul>
<li><code>print : A → String</code></li>
</ul></li>
<li><code>Monoid M</code> type class:
<ul>
<li><code>∅ : M</code></li>
<li><code>_+_ : M → M → M</code></li>
</ul></li>
<li><code>Eq A</code>:
<ul>
<li><code>_==_ : A → A → Bool</code> and/or <code>_≟_ : (x y : A) -> Dec (x ≡ y)</code></li>
</ul></li>
<li><code>Functor F</code>:
<ul>
<li><code>fmap : {A B : Set} → F A → F B</code></li>
</ul></li>
</ul>
</section><section id="parametric-vs-ad-hoc-overloading" class="slide level2">
<h2>Parametric vs ad-hoc overloading</h2>
<p>Why not have <code>print : {A : Set} -> A -> String</code>?</p>
<div class="fragment">
<p>Because of <em>parametricity</em>, <code>print</code> would have to be a constant function.</p>
<p>Type classes allow a <em>different</em> implementation at each type!</p>
</div>
</section><section id="type-classes-in-agda" class="slide level2">
<h2>Type classes in Agda</h2>
<p>A type class is implemented by using a <strong>record type</strong> + <strong>instance arguments</strong></p>
<ul>
<li>Record type: a <strong>dictionary</strong> holding implementation of each function for a specific type</li>
<li>Instance arguments: <em>automatically</em> pick the ‘right’ dictionary for the given type</li>
</ul>
</section><section id="instance-arguments" class="slide level2">
<h2>Instance arguments</h2>
<p><em>Instance arguments</em> are Agda’s builtin mechanism for ad-hoc overloading (~ type classes in Haskell).</p>
<p>Syntax:</p>
<ul>
<li>Using an instance: <code>{{x : A}} → ...</code></li>
<li>Defining new instances: <code>instance ...</code></li>
</ul>
<p>When using a function of type <code>{{x : A}} → B</code>, Agda will automatically resolve the argument if there is a <strong>unique</strong> instance of the right type in scope.</p>
</section><section id="defining-a-typeclass-with-instance-arguments" class="slide level2">
<h2>Defining a typeclass with instance arguments</h2>
<!--
<pre class="Agda"><a id="1555" class="Keyword">module</a> <a id="1562" href="slides3.html" class="Module">_</a> <a id="1564" class="Keyword">where</a>
<a id="1570" class="Keyword">open</a> <a id="1575" class="Keyword">import</a> <a id="1582" href="Data.Bool.Base.html" class="Module">Data.Bool.Base</a>
<a id="1597" class="Keyword">open</a> <a id="1602" class="Keyword">import</a> <a id="1609" href="Data.String.Base.html" class="Module">Data.String.Base</a>
</pre>-->
<pre class="Agda"><a id="1643" class="Keyword">record</a> <a id="Print"></a><a id="1650" href="slides3.html#1650" class="Record">Print</a> <a id="1656" class="Symbol">{</a><a id="1657" href="slides3.html#1657" class="Bound">ℓ</a><a id="1658" class="Symbol">}</a> <a id="1660" class="Symbol">(</a><a id="1661" href="slides3.html#1661" class="Bound">A</a> <a id="1663" class="Symbol">:</a> <a id="1665" class="PrimitiveType">Set</a> <a id="1669" href="slides3.html#1657" class="Bound">ℓ</a><a id="1670" class="Symbol">)</a> <a id="1672" class="Symbol">:</a> <a id="1674" class="PrimitiveType">Set</a> <a id="1678" href="slides3.html#1657" class="Bound">ℓ</a> <a id="1680" class="Keyword">where</a>
<a id="1688" class="Keyword">field</a>
<a id="Print.print"></a><a id="1698" href="slides3.html#1698" class="Field">print</a> <a id="1704" class="Symbol">:</a> <a id="1706" href="slides3.html#1661" class="Bound">A</a> <a id="1708" class="Symbol">→</a> <a id="1710" href="Agda.Builtin.String.html#247" class="Postulate">String</a>
<a id="1717" class="Keyword">open</a> <a id="1722" href="slides3.html#1650" class="Module">Print</a> <a id="1728" class="Symbol">{{...}}</a> <a id="1737" class="Comment">-- print : {{r : Print A}} → A → String</a>
<a id="1778" class="Keyword">instance</a>
<a id="PrintBool"></a><a id="1789" href="slides3.html#1789" class="Function">PrintBool</a> <a id="1799" class="Symbol">:</a> <a id="1801" href="slides3.html#1650" class="Record">Print</a> <a id="1807" href="Agda.Builtin.Bool.html#135" class="Datatype">Bool</a>
<a id="1814" href="slides3.html#1698" class="Field">print</a> <a id="1820" class="Symbol">{{</a><a id="1822" href="slides3.html#1789" class="Function">PrintBool</a><a id="1831" class="Symbol">}}</a> <a id="1834" href="Agda.Builtin.Bool.html#160" class="InductiveConstructor">true</a> <a id="1840" class="Symbol">=</a> <a id="1842" class="String">"true"</a>
<a id="1851" href="slides3.html#1698" class="Field">print</a> <a id="1857" class="Symbol">{{</a><a id="1859" href="slides3.html#1789" class="Function">PrintBool</a><a id="1868" class="Symbol">}}</a> <a id="1871" href="Agda.Builtin.Bool.html#154" class="InductiveConstructor">false</a> <a id="1877" class="Symbol">=</a> <a id="1879" class="String">"false"</a>
<a id="PrintString"></a><a id="1890" href="slides3.html#1890" class="Function">PrintString</a> <a id="1902" class="Symbol">:</a> <a id="1904" href="slides3.html#1650" class="Record">Print</a> <a id="1910" href="Agda.Builtin.String.html#247" class="Postulate">String</a>
<a id="1919" href="slides3.html#1698" class="Field">print</a> <a id="1925" class="Symbol">{{</a><a id="1927" href="slides3.html#1890" class="Function">PrintString</a><a id="1938" class="Symbol">}}</a> <a id="1941" href="slides3.html#1941" class="Bound">x</a> <a id="1943" class="Symbol">=</a> <a id="1945" href="slides3.html#1941" class="Bound">x</a>
<a id="testPrint"></a><a id="1948" href="slides3.html#1948" class="Function">testPrint</a> <a id="1958" class="Symbol">:</a> <a id="1960" href="Agda.Builtin.String.html#247" class="Postulate">String</a>
<a id="1967" href="slides3.html#1948" class="Function">testPrint</a> <a id="1977" class="Symbol">=</a> <a id="1979" class="Symbol">(</a><a id="1980" href="slides3.html#1698" class="Field">print</a> <a id="1986" href="Agda.Builtin.Bool.html#160" class="InductiveConstructor">true</a><a id="1990" class="Symbol">)</a> <a id="1992" href="Data.String.Base.html#1744" class="Function Operator">++</a> <a id="1995" class="Symbol">(</a><a id="1996" href="slides3.html#1698" class="Field">print</a> <a id="2002" class="String">"a string"</a><a id="2012" class="Symbol">)</a>
</pre>
</section></section>
<section><section id="monads" class="title-slide slide level1"><h1>Monads</h1></section><section id="section" class="slide level2">
<h2></h2>
<p>“To be is to do” –Socrates</p>
<p>“To do is to be” –Sartre</p>
<p>“Do be do be do” –Sinatra.</p>
</section><section id="side-effects-in-a-pure-language" class="slide level2">
<h2>Side effects in a pure language</h2>
<p>Agda is a <strong>pure</strong> language: functions have no side effects</p>
<p>But a typechecker has many side effects:</p>
<ul>
<li>raise error messages</li>
<li>read or write files</li>
<li>maintain a state for declared variables</li>
</ul>
</section><section id="monads-1" class="slide level2">
<h2>Monads</h2>
<p><code>Monad</code> is a typeclass with two fields <code>return</code> and <code>_>>=_</code>.</p>
<p><code>M A</code> ~ “computations that may have some side-effects (depending on M) and return an A”</p>
<p>Examples: <code>Maybe</code>, <code>Reader</code>, <code>Error</code>, <code>State</code>, …</p>
<p>See <a href="https://jespercockx.github.io/ohrid19-agda/src/html/Library.Error.html">Library/Error.agda</a></p>
</section><section id="do-notation" class="slide level2">
<h2><code>do</code> notation</h2>
<p><code>do</code> is syntactic sugar for repeated binds: instead of</p>
<!--
<pre class="Agda"><a id="2740" class="Keyword">open</a> <a id="2745" class="Keyword">import</a> <a id="2752" href="Data.Vec.html" class="Module">Data.Vec</a> <a id="2761" class="Keyword">using</a> <a id="2767" class="Symbol">(</a><a id="2768" href="Data.Vec.Base.html#935" class="Datatype">Vec</a><a id="2771" class="Symbol">)</a>
<a id="2773" class="Keyword">open</a> <a id="2778" class="Keyword">import</a> <a id="2785" href="Library.html" class="Module">Library</a> <a id="2793" class="Keyword">hiding</a> <a id="2800" class="Symbol">(</a><a id="2801" href="Data.List.Relation.Unary.All.html#1176" class="Datatype">All</a><a id="2804" class="Symbol">;</a> <a id="2806" href="Library.Monad.html#867" class="Record">IMonad</a><a id="2812" class="Symbol">;</a> <a id="2814" href="Library.Monad.html#1110" class="Function">return</a><a id="2820" class="Symbol">;</a> <a id="2822" href="Library.Monad.html#1002" class="Field Operator">_>>=_</a><a id="2827" class="Symbol">)</a>
<a id="2829" class="Keyword">module</a> <a id="2836" href="slides3.html#2836" class="Module">_</a> <a id="2838" class="Keyword">where</a>
<a id="2846" class="Keyword">open</a> <a id="2851" class="Keyword">import</a> <a id="2858" href="Library.html" class="Module">Library</a> <a id="2866" class="Keyword">hiding</a> <a id="2873" class="Symbol">(</a><a id="2874" href="Data.List.Relation.Unary.All.html#1176" class="Datatype">All</a><a id="2877" class="Symbol">;</a> <a id="2879" href="Library.Monad.html#867" class="Record">IMonad</a><a id="2885" class="Symbol">)</a>
</pre>-->
<pre class="Agda"> <a id="2902" href="slides3.html#2902" class="Function">_</a> <a id="2904" class="Symbol">:</a> <a id="2906" href="Data.Maybe.Base.html#795" class="Datatype">Maybe</a> <a id="2912" href="Agda.Builtin.Int.html#219" class="Datatype">ℤ</a>
<a id="2916" class="Symbol">_</a> <a id="2918" class="Symbol">=</a> <a id="2920" class="Symbol">(</a><a id="2921" href="Data.Maybe.Base.html#829" class="InductiveConstructor">just</a> <a id="2926" class="Symbol">(</a><a id="2927" href="Agda.Builtin.Int.html#264" class="InductiveConstructor Operator">-[1+</a> <a id="2932" class="Number">3</a> <a id="2934" href="Agda.Builtin.Int.html#264" class="InductiveConstructor Operator">]</a><a id="2935" class="Symbol">))</a> <a id="2938" href="Library.Monad.html#1002" class="Field Operator">>>=</a> <a id="2942" class="Symbol">λ</a> <a id="2944" href="slides3.html#2944" class="Bound">x</a> <a id="2946" class="Symbol">→</a>
<a id="2954" class="Symbol">(</a><a id="2955" href="Data.Maybe.Base.html#829" class="InductiveConstructor">just</a> <a id="2960" class="Symbol">(</a><a id="2961" href="Agda.Builtin.Int.html#237" class="InductiveConstructor Operator">+</a> <a id="2963" class="Number">5</a><a id="2964" class="Symbol">)</a> <a id="2970" class="Symbol">)</a> <a id="2972" href="Library.Monad.html#1002" class="Field Operator">>>=</a> <a id="2976" class="Symbol">λ</a> <a id="2978" href="slides3.html#2978" class="Bound">y</a> <a id="2980" class="Symbol">→</a>
<a id="2988" href="Library.Monad.html#1110" class="Function">return</a> <a id="2995" class="Symbol">(</a><a id="2996" href="slides3.html#2944" class="Bound">x</a> <a id="2998" href="Data.Integer.Base.html#2950" class="Function Operator">+</a> <a id="3000" href="slides3.html#2978" class="Bound">y</a><a id="3001" class="Symbol">)</a>
</pre>
you can write:
<pre class="Agda"> <a id="3028" href="slides3.html#3028" class="Function">_</a> <a id="3030" class="Symbol">:</a> <a id="3032" href="Data.Maybe.Base.html#795" class="Datatype">Maybe</a> <a id="3038" href="Agda.Builtin.Int.html#219" class="Datatype">ℤ</a>
<a id="3042" class="Symbol">_</a> <a id="3044" class="Symbol">=</a> <a id="3046" class="Keyword">do</a>
<a id="3053" href="slides3.html#3053" class="Bound">x</a> <a id="3055" href="Library.Monad.html#1002" class="Field Operator">←</a> <a id="3057" href="Data.Maybe.Base.html#829" class="InductiveConstructor">just</a> <a id="3062" class="Symbol">(</a><a id="3063" href="Agda.Builtin.Int.html#264" class="InductiveConstructor Operator">-[1+</a> <a id="3068" class="Number">3</a> <a id="3070" href="Agda.Builtin.Int.html#264" class="InductiveConstructor Operator">]</a><a id="3071" class="Symbol">)</a>
<a id="3077" href="slides3.html#3077" class="Bound">y</a> <a id="3079" href="Library.Monad.html#1002" class="Field Operator">←</a> <a id="3081" href="Data.Maybe.Base.html#829" class="InductiveConstructor">just</a> <a id="3086" class="Symbol">(</a><a id="3087" href="Agda.Builtin.Int.html#237" class="InductiveConstructor Operator">+</a> <a id="3089" class="Number">5</a><a id="3090" class="Symbol">)</a>
<a id="3096" href="Library.Monad.html#1110" class="Function">return</a> <a id="3103" class="Symbol">(</a><a id="3104" href="slides3.html#3053" class="Bound">x</a> <a id="3106" href="Data.Integer.Base.html#2950" class="Function Operator">+</a> <a id="3108" href="slides3.html#3077" class="Bound">y</a><a id="3109" class="Symbol">)</a>
</pre>
</section><section id="pattern-matching-with-do" class="slide level2">
<h2>Pattern matching with <code>do</code></h2>
<p>There can be a <em>pattern</em> to the left of a <code>←</code>, alternative cases can be handled in a local <code>where</code></p>
<pre class="Agda"> <a id="3253" href="slides3.html#3253" class="Function">pred</a> <a id="3258" class="Symbol">:</a> <a id="3260" href="Agda.Builtin.Nat.html#165" class="Datatype">ℕ</a> <a id="3262" class="Symbol">→</a> <a id="3264" href="Data.Maybe.Base.html#795" class="Datatype">Maybe</a> <a id="3270" href="Agda.Builtin.Nat.html#165" class="Datatype">ℕ</a>
<a id="3274" href="slides3.html#3253" class="Function">pred</a> <a id="3279" href="slides3.html#3279" class="Bound">n</a> <a id="3281" class="Symbol">=</a> <a id="3283" class="Keyword">do</a>
<a id="3290" href="Agda.Builtin.Nat.html#196" class="InductiveConstructor">suc</a> <a id="3294" href="slides3.html#3294" class="Bound">m</a> <a id="3296" href="Library.Monad.html#1002" class="Field Operator">←</a> <a id="3298" href="Data.Maybe.Base.html#829" class="InductiveConstructor">just</a> <a id="3303" href="slides3.html#3279" class="Bound">n</a>
<a id="3311" class="Keyword">where</a> <a id="3317" href="Agda.Builtin.Nat.html#183" class="InductiveConstructor">zero</a> <a id="3322" class="Symbol">→</a> <a id="3324" href="Data.Maybe.Base.html#859" class="InductiveConstructor">nothing</a>
<a id="3336" href="Library.Monad.html#1110" class="Function">return</a> <a id="3343" href="slides3.html#3294" class="Bound">m</a>
</pre>
</section><section id="dependent-pattern-matching-with-do" class="slide level2">
<h2>Dependent pattern matching with <code>do</code></h2>
<pre class="Agda"> <a id="3397" class="Keyword">postulate</a>
<a id="3411" href="slides3.html#3411" class="Postulate">test</a> <a id="3416" class="Symbol">:</a> <a id="3418" class="Symbol">(</a><a id="3419" href="slides3.html#3419" class="Bound">m</a> <a id="3421" href="slides3.html#3421" class="Bound">n</a> <a id="3423" class="Symbol">:</a> <a id="3425" href="Agda.Builtin.Nat.html#165" class="Datatype">ℕ</a><a id="3426" class="Symbol">)</a> <a id="3428" class="Symbol">→</a> <a id="3430" href="Data.Maybe.Base.html#795" class="Datatype">Maybe</a> <a id="3436" class="Symbol">(</a><a id="3437" href="slides3.html#3419" class="Bound">m</a> <a id="3439" href="Agda.Builtin.Equality.html#125" class="Datatype Operator">≡</a> <a id="3441" href="slides3.html#3421" class="Bound">n</a><a id="3442" class="Symbol">)</a>
<a id="3447" href="slides3.html#3447" class="Function">cast</a> <a id="3452" class="Symbol">:</a> <a id="3454" class="Symbol">(</a><a id="3455" href="slides3.html#3455" class="Bound">m</a> <a id="3457" href="slides3.html#3457" class="Bound">n</a> <a id="3459" class="Symbol">:</a> <a id="3461" href="Agda.Builtin.Nat.html#165" class="Datatype">ℕ</a><a id="3462" class="Symbol">)</a> <a id="3464" class="Symbol">→</a> <a id="3466" href="Data.Vec.Base.html#935" class="Datatype">Vec</a> <a id="3470" href="Agda.Builtin.Int.html#219" class="Datatype">ℤ</a> <a id="3472" href="slides3.html#3455" class="Bound">m</a> <a id="3474" class="Symbol">→</a> <a id="3476" href="Data.Maybe.Base.html#795" class="Datatype">Maybe</a> <a id="3482" class="Symbol">(</a><a id="3483" href="Data.Vec.Base.html#935" class="Datatype">Vec</a> <a id="3487" href="Agda.Builtin.Int.html#219" class="Datatype">ℤ</a> <a id="3489" href="slides3.html#3457" class="Bound">n</a><a id="3490" class="Symbol">)</a>
<a id="3494" href="slides3.html#3447" class="Function">cast</a> <a id="3499" href="slides3.html#3499" class="Bound">m</a> <a id="3501" href="slides3.html#3501" class="Bound">n</a> <a id="3503" href="slides3.html#3503" class="Bound">xs</a> <a id="3506" class="Symbol">=</a> <a id="3508" class="Keyword">do</a>
<a id="3515" href="Agda.Builtin.Equality.html#182" class="InductiveConstructor">refl</a> <a id="3520" href="Library.Monad.html#1002" class="Field Operator">←</a> <a id="3522" href="slides3.html#3411" class="Postulate">test</a> <a id="3527" href="slides3.html#3499" class="Bound">m</a> <a id="3529" href="slides3.html#3501" class="Bound">n</a>
<a id="3535" href="Library.Monad.html#1110" class="Function">return</a> <a id="3542" href="slides3.html#3503" class="Bound">xs</a>
</pre>
<p>Pattern matching allows typechecker to learn new facts!</p>
</section><section id="type-checking-expressions" class="slide level2">
<h2>Type-checking expressions</h2>
<p>See <a href="https://jespercockx.github.io/ohrid19-agda/src/html/V1/V1.TypeChecker.html">V1/TypeChecker.agda</a>.</p>
<p>Exercise: extend the typechecker with rules for the new syntactic constructions you added before</p>
</section></section>
<section><section id="indexed-monads" class="title-slide slide level1"><h1>Indexed monads</h1></section><section id="typechecking-variable-declarations" class="slide level2">
<h2>Typechecking variable declarations</h2>
<p>For type-checking variables, we need the following side-effects:</p>
<ul>
<li>For checking <em>expressions</em>: find variable with given name (⇒ read-only access)</li>
<li>For checking <em>declarations</em>: add new variable with given name (⇒ read-write access)</li>
</ul>
<p>How to ensure <strong>statically</strong> that each variable in scope has a name?</p>
</section><section id="reminder-the-all-type" class="slide level2">
<h2>Reminder: The <code>All</code> type</h2>
For <code>P : A → Set</code> and <code>xs : List A</code>, <code>All P xs</code> associates an element of <code>P x</code> to each <code>x ∈ xs</code>:
<pre class="Agda"><a id="4330" class="Keyword">data</a> <a id="All"></a><a id="4335" href="slides3.html#4335" class="Datatype">All</a> <a id="4339" class="Symbol">{</a><a id="4340" href="slides3.html#4340" class="Bound">A</a> <a id="4342" class="Symbol">:</a> <a id="4344" class="PrimitiveType">Set</a><a id="4347" class="Symbol">}</a> <a id="4349" class="Symbol">(</a><a id="4350" href="slides3.html#4350" class="Bound">P</a> <a id="4352" class="Symbol">:</a> <a id="4354" href="slides3.html#4340" class="Bound">A</a> <a id="4356" class="Symbol">→</a> <a id="4358" class="PrimitiveType">Set</a><a id="4361" class="Symbol">)</a> <a id="4363" class="Symbol">:</a> <a id="4365" href="Agda.Builtin.List.html#121" class="Datatype">List</a> <a id="4370" href="slides3.html#4340" class="Bound">A</a> <a id="4372" class="Symbol">→</a> <a id="4374" class="PrimitiveType">Set</a> <a id="4378" class="Keyword">where</a>
<a id="All.[]"></a><a id="4386" href="slides3.html#4386" class="InductiveConstructor">[]</a> <a id="4390" class="Symbol">:</a> <a id="4392" href="slides3.html#4335" class="Datatype">All</a> <a id="4396" href="slides3.html#4350" class="Bound">P</a> <a id="4398" href="Agda.Builtin.List.html#158" class="InductiveConstructor">[]</a>
<a id="All._∷_"></a><a id="4403" href="slides3.html#4403" class="InductiveConstructor Operator">_∷_</a> <a id="4407" class="Symbol">:</a> <a id="4409" class="Symbol">∀</a> <a id="4411" class="Symbol">{</a><a id="4412" href="slides3.html#4412" class="Bound">x</a> <a id="4414" href="slides3.html#4414" class="Bound">xs</a><a id="4416" class="Symbol">}</a> <a id="4418" class="Symbol">→</a> <a id="4420" href="slides3.html#4350" class="Bound">P</a> <a id="4422" href="slides3.html#4412" class="Bound">x</a> <a id="4424" class="Symbol">→</a> <a id="4426" href="slides3.html#4335" class="Datatype">All</a> <a id="4430" href="slides3.html#4350" class="Bound">P</a> <a id="4432" href="slides3.html#4414" class="Bound">xs</a> <a id="4435" class="Symbol">→</a> <a id="4437" href="slides3.html#4335" class="Datatype">All</a> <a id="4441" href="slides3.html#4350" class="Bound">P</a> <a id="4443" class="Symbol">(</a><a id="4444" href="slides3.html#4412" class="Bound">x</a> <a id="4446" href="Agda.Builtin.List.html#173" class="InductiveConstructor Operator">∷</a> <a id="4448" href="slides3.html#4414" class="Bound">xs</a><a id="4450" class="Symbol">)</a>
</pre>
<ul>
<li>Value for each variable: <code>Env Γ = All Val Γ</code></li>
<li>Name for each variable: <code>TCCxt Γ = All (\_ → Name) Γ</code></li>
</ul>
</section><section id="adding-new-variables-to-the-typechecking-context" class="slide level2">
<h2>Adding new variables to the typechecking context</h2>
<p>We need to <em>modify</em> both <code>Γ : Cxt</code> and <code>ρ : TCCxt Γ</code>!</p>
<p>Possible solutions:</p>
<ul>
<li>decouple names from the context?</li>
<li>use state of type <code>Σ Cxt TCCxt</code>?</li>
<li><strong>index</strong> the monad by the context Γ!</li>
</ul>
</section><section id="indexed-monads-1" class="slide level2">
<h2>Indexed monads</h2>
<p>An <strong>indexed monad</strong> = a monad with two extra parameters for the (static) <em>input</em> and <em>output</em> states</p>
<pre class="Agda"><a id="4927" class="Keyword">record</a> <a id="IMonad"></a><a id="4934" href="slides3.html#4934" class="Record">IMonad</a> <a id="4941" class="Symbol">{</a><a id="4942" href="slides3.html#4942" class="Bound">I</a> <a id="4944" class="Symbol">:</a> <a id="4946" class="PrimitiveType">Set</a><a id="4949" class="Symbol">}</a> <a id="4951" class="Symbol">(</a><a id="4952" href="slides3.html#4952" class="Bound">M</a> <a id="4954" class="Symbol">:</a> <a id="4956" href="slides3.html#4942" class="Bound">I</a> <a id="4958" class="Symbol">→</a> <a id="4960" href="slides3.html#4942" class="Bound">I</a> <a id="4962" class="Symbol">→</a> <a id="4964" class="PrimitiveType">Set</a> <a id="4968" class="Symbol">→</a> <a id="4970" class="PrimitiveType">Set</a><a id="4973" class="Symbol">)</a> <a id="4975" class="Symbol">:</a> <a id="4977" class="PrimitiveType">Set₁</a> <a id="4982" class="Keyword">where</a>
<a id="4990" class="Keyword">field</a>
<a id="IMonad.return"></a><a id="5000" href="slides3.html#5000" class="Field">return</a> <a id="5007" class="Symbol">:</a> <a id="5009" class="Symbol">∀</a> <a id="5011" class="Symbol">{</a><a id="5012" href="slides3.html#5012" class="Bound">A</a> <a id="5014" href="slides3.html#5014" class="Bound">i</a><a id="5015" class="Symbol">}</a> <a id="5017" class="Symbol">→</a> <a id="5019" href="slides3.html#5012" class="Bound">A</a> <a id="5021" class="Symbol">→</a> <a id="5023" href="slides3.html#4952" class="Bound">M</a> <a id="5025" href="slides3.html#5014" class="Bound">i</a> <a id="5027" href="slides3.html#5014" class="Bound">i</a> <a id="5029" href="slides3.html#5012" class="Bound">A</a>
<a id="IMonad._>>=_"></a><a id="5035" href="slides3.html#5035" class="Field Operator">_>>=_</a> <a id="5042" class="Symbol">:</a> <a id="5044" class="Symbol">∀</a> <a id="5046" class="Symbol">{</a><a id="5047" href="slides3.html#5047" class="Bound">A</a> <a id="5049" href="slides3.html#5049" class="Bound">B</a> <a id="5051" href="slides3.html#5051" class="Bound">i</a> <a id="5053" href="slides3.html#5053" class="Bound">j</a> <a id="5055" href="slides3.html#5055" class="Bound">k</a><a id="5056" class="Symbol">}</a>
<a id="5069" class="Symbol">→</a> <a id="5071" href="slides3.html#4952" class="Bound">M</a> <a id="5073" href="slides3.html#5051" class="Bound">i</a> <a id="5075" href="slides3.html#5053" class="Bound">j</a> <a id="5077" href="slides3.html#5047" class="Bound">A</a> <a id="5079" class="Symbol">→</a> <a id="5081" class="Symbol">(</a><a id="5082" href="slides3.html#5047" class="Bound">A</a> <a id="5084" class="Symbol">→</a> <a id="5086" href="slides3.html#4952" class="Bound">M</a> <a id="5088" href="slides3.html#5053" class="Bound">j</a> <a id="5090" href="slides3.html#5055" class="Bound">k</a> <a id="5092" href="slides3.html#5049" class="Bound">B</a><a id="5093" class="Symbol">)</a> <a id="5095" class="Symbol">→</a> <a id="5097" href="slides3.html#4952" class="Bound">M</a> <a id="5099" href="slides3.html#5051" class="Bound">i</a> <a id="5101" href="slides3.html#5055" class="Bound">k</a> <a id="5103" href="slides3.html#5049" class="Bound">B</a>
</pre>
<p>Examples:</p>
<ul>
<li><code>TCDecl</code> monad (see <a href="https://jespercockx.github.io/ohrid19-agda/src/html/V2/V2.TypeChecker.html">V2/TypeChecker.agda</a>).</li>
<li><code>Exec</code> monad (see <a href="https://jespercockx.github.io/ohrid19-agda/src/html/V3/V3.TypeChecker.html">V3/Interpreter.agda</a>).</li>
</ul>
</section></section>
<section><section id="haskell-ffi" class="title-slide slide level1"><h1>Haskell FFI</h1></section><section id="why-use-an-ffi" class="slide level2">
<h2>Why use an FFI?</h2>
<p>We now have a correct-by-construction typechecker + interpreter.</p>
<p>However, some things are still missing:</p>
<ul>
<li>Parser</li>
<li>Pretty printer</li>
</ul>
<p><strong>Goal.</strong> Use Haskell library for generating these <em>automatically</em></p>
<!--
<pre class="Agda"><a id="5615" class="Keyword">module</a> <a id="5622" href="slides3.html#5622" class="Module">_</a> <a id="5624" class="Keyword">where</a>
<a id="5631" class="Keyword">module</a> <a id="FFI"></a><a id="5638" href="slides3.html#5638" class="Module">FFI</a> <a id="5642" class="Keyword">where</a>
</pre>-->
</section><section id="haskell-ffi-basics" class="slide level2">
<h2>Haskell FFI: basics</h2>
<p>Import a Haskell module:</p>
<pre class="Agda"> <a id="5719" class="Symbol">{-#</a> <a id="5723" class="Keyword">FOREIGN</a> <a id="5731" class="Pragma">GHC</a> <a id="5735" class="Pragma">import</a> <a id="5742" class="Pragma">HaskellModule.hs</a> <a id="5759" class="Symbol">#-}</a>
</pre>
<p>Bind Haskell function to Agda name:</p>
<!--
<pre class="Agda"> <a id="5816" class="Keyword">postulate</a> <a id="FFI.AgdaType"></a><a id="5826" href="slides3.html#5826" class="Postulate">AgdaType</a> <a id="5835" class="Symbol">:</a> <a id="5837" class="PrimitiveType">Set</a>
</pre>-->
<pre class="Agda"> <a id="5860" class="Keyword">postulate</a> <a id="FFI.agdaName"></a><a id="5870" href="slides3.html#5870" class="Postulate">agdaName</a> <a id="5879" class="Symbol">:</a> <a id="5881" href="slides3.html#5826" class="Postulate">AgdaType</a>
<a id="5892" class="Symbol">{-#</a> <a id="5896" class="Keyword">COMPILE</a> <a id="5904" class="Pragma">GHC</a> <a id="5908" href="slides3.html#5870" class="Postulate">agdaName</a> <a id="5917" class="Pragma">=</a> <a id="5919" class="Pragma">haskellCode</a> <a id="5931" class="Symbol">#-}</a>
</pre>
<p>Bind Haskell datatype to Agda datatype:</p>
<pre class="Agda"> <a id="5987" class="Keyword">data</a> <a id="FFI.D"></a><a id="5992" href="slides3.html#5992" class="Datatype">D</a> <a id="5994" class="Symbol">:</a> <a id="5996" class="PrimitiveType">Set</a> <a id="6000" class="Keyword">where</a> <a id="FFI.D.c₁"></a><a id="6006" href="slides3.html#6006" class="InductiveConstructor">c₁</a> <a id="FFI.D.c₂"></a><a id="6009" href="slides3.html#6009" class="InductiveConstructor">c₂</a> <a id="6012" class="Symbol">:</a> <a id="6014" href="slides3.html#5992" class="Datatype">D</a>
<a id="6018" class="Symbol">{-#</a> <a id="6022" class="Keyword">COMPILE</a> <a id="6030" class="Pragma">GHC</a> <a id="6034" href="slides3.html#5992" class="Datatype">D</a> <a id="6036" class="Pragma">=</a> <a id="6038" class="Pragma">data</a> <a id="6043" class="Pragma">hsData</a> <a id="6050" class="Pragma">(hsCon₁</a> <a id="6058" class="Pragma">|</a> <a id="6060" class="Pragma">hsCon₂)</a> <a id="6068" class="Symbol">#-}</a>
</pre>
</section><section id="haskell-ffi-example" class="slide level2">
<h2>Haskell FFI example:</h2>
<div class="sourceCode" id="cb1"><pre class="sourceCode haskell"><code class="sourceCode haskell"><a class="sourceLine" id="cb1-1" data-line-number="1"> <span class="co">-- In file `While/V1/Abs.hs`:</span></a>
<a class="sourceLine" id="cb1-2" data-line-number="2"> <span class="kw">data</span> <span class="dt">Type</span> <span class="fu">=</span> <span class="dt">TBool</span> <span class="fu">|</span> <span class="dt">TInt</span></a></code></pre></div>
<pre class="Agda"> <a id="6185" class="Comment">-- In file `AST.agda`:</a>
<a id="6210" class="Symbol">{-#</a> <a id="6214" class="Keyword">FOREIGN</a> <a id="6222" class="Pragma">GHC</a> <a id="6226" class="Pragma">import</a> <a id="6233" class="Pragma">While.Abs</a> <a id="6243" class="Symbol">#-}</a>
<a id="6249" class="Keyword">data</a> <a id="FFI.Type"></a><a id="6254" href="slides3.html#6254" class="Datatype">Type</a> <a id="6259" class="Symbol">:</a> <a id="6261" class="PrimitiveType">Set</a> <a id="6265" class="Keyword">where</a>
<a id="FFI.Type.bool"></a><a id="6275" href="slides3.html#6275" class="InductiveConstructor">bool</a> <a id="FFI.Type.int"></a><a id="6280" href="slides3.html#6280" class="InductiveConstructor">int</a> <a id="6284" class="Symbol">:</a> <a id="6286" href="slides3.html#6254" class="Datatype">Type</a>
<a id="6294" class="Symbol">{-#</a> <a id="6298" class="Keyword">COMPILE</a> <a id="6306" class="Pragma">GHC</a> <a id="6310" href="slides3.html#6254" class="Datatype">Type</a> <a id="6315" class="Pragma">=</a> <a id="6317" class="Pragma">data</a> <a id="6322" class="Pragma">Type</a>
<a id="6331" class="Pragma">(</a> <a id="6333" class="Pragma">TBool</a>
<a id="6343" class="Pragma">|</a> <a id="6345" class="Pragma">TInt</a>
<a id="6354" class="Pragma">)</a> <a id="6356" class="Symbol">#-}</a>
</pre>
</section><section id="bnfc-the-backus-naur-form-compiler" class="slide level2">
<h2>BNFC: the Backus-Naur Form Compiler</h2>
<p>BNFC is a Haskell library for generating Haskell code from a grammar:</p>
<ul>
<li>Datatypes for abstract syntax</li>
<li>Parser</li>
<li>Pretty-printer</li>
</ul>
<p>See <a href="https://jespercockx.github.io/ohrid19-agda/src/V1/While.cf">While.cf</a> for the grammar of WHILE.</p>
</section><section id="exercises" class="slide level2">
<h2>Exercises</h2>
<p>Extend the typechecker and the BNFC grammar with the new syntactic constructions you added.</p>
<p>Don’t forget to update the Haskell bindings in <a href="https://jespercockx.github.io/ohrid19-agda/src/V1/html/V1.AST.html">AST.agda</a>!</p>
<p>Running the test suite:</p>
<p> <code>make parser</code>: compile the parser and run it on <a href="https://jespercockx.github.io/ohrid19-agda/test/gcd.c">/test/gcd.c</a>. - <code>make test</code>: compile the whole typechecker and run it on the examples in <code>/test</code></p>
</section></section>
</div>
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