476 lines
16 KiB
HTML
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476 lines
16 KiB
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<a href="/20241210233721-brain_moc.html"> <img src="/assets/gr.png" alt="Site Logo" class="banner-logo" /> </a>
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<div id="updated">Updated: 2025-12-28 Sun 19:48</div>
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<article class="stack-pane pane-root" data-url="/20250120113936-afp_lab_1.html">
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</div>
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<h1 class="title">afp<sub>lab</sub><sub>1</sub></h1>
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<div class="title-metadata">
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<span class="metadata-item">
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<span class="metadata-label">planted:</span>
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<span class="metadata-value">2025-01-20</span>
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</span>
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<span class="metadata-item">
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<span class="metadata-label">last tended to:</span>
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<span class="metadata-value">2025-12-28</span>
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</span>
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</div>
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</div>
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<p>
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<span class="timestamp-wrapper"><span class="timestamp"><2025-01-20 Mon> </span></span>
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</p>
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<div id="outline-container-org6ed8c49" class="outline-2">
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<h2 id="org6ed8c49"><a href="#org6ed8c49">Installation of Agda:</a></h2>
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<div class="outline-text-2" id="text-org6ed8c49">
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</div>
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<div id="outline-container-org9d1e75c" class="outline-3">
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<h3 id="org9d1e75c"><a href="#org9d1e75c">Step 1</a></h3>
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<div class="outline-text-3" id="text-org9d1e75c">
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<div class="org-src-container">
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<pre class="src src-eshell">sudo apt-get install zlib1g-dev libncurses5-dev
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</pre>
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</div>
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<p>
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then install ghc
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</p>
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<ul class="org-ul">
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<li><a href="https://www.haskell.org/ghcup/">https://www.haskell.org/ghcup/</a></li>
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</ul>
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<p>
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Now that you have cabal installed, use it to install Agda as a Haskell package:
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</p>
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<div class="org-src-container">
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<pre class="src src-eshell">cabal update
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cabal install Agda
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</pre>
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</div>
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||
</div>
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||
</div>
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<div id="outline-container-orge5f2a86" class="outline-3">
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<h3 id="orge5f2a86"><a href="#orge5f2a86">Step 2</a></h3>
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<div class="outline-text-3" id="text-orge5f2a86">
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<p>
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Most users will want to install the standard library. You can install this as any other Agda library (see Library Management). See the agda-stdlib project’s installation instructions for the steps to take to install the latest version.
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<a href="https://github.com/agda/agda-stdlib">https://github.com/agda/agda-stdlib</a>
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<a href="https://agda.readthedocs.io/en/latest/tools/package-system.html#package-system">https://agda.readthedocs.io/en/latest/tools/package-system.html#package-system</a>
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</p>
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||
</div>
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||
</div>
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||
</div>
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||
<div id="outline-container-org885bf78" class="outline-2">
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<h2 id="org885bf78"><a href="#org885bf78">Exercises:</a></h2>
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<div class="outline-text-2" id="text-org885bf78">
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<p>
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<a href="file:///home/zaine/master-folder/Uni/ADVFUNC/afp-learning-2024-2025/files/LectureNotes/files/exercises/my-lab1.lagda.md">my lab1</a>
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</p>
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<p>
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```agda
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data Bool : Type where
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true false : Bool
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```
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</p>
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<p>
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In Agda, the snippet `data Bool : Type where true false : Bool` is a definition of a simple data type named `Bool`. Let’s break down and explain all the components and words in this snippet:
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</p>
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<p>
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—
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</p>
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<p>
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### 1. <b><b>`data`</b></b>
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</p>
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<ul class="org-ul">
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<li><b><b>What it means:</b></b> This keyword introduces a new <b>data type</b> definition in Agda.</li>
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<li><b><b>Purpose:</b></b> Defines a type that consists of one or more <b>constructors</b>, which are used to create values of the type.</li>
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<li><b><b>In this case:</b></b> The `data` keyword is used to define the `Bool` type.</li>
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</ul>
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<p>
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—
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</p>
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<p>
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### 2. <b><b>`Bool`</b></b>
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</p>
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<ul class="org-ul">
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<li><b><b>What it is:</b></b> The name of the data type being defined.</li>
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<li><b><b>Purpose:</b></b> Represents a type that has exactly two possible values: `true` and `false`.</li>
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<li><b><b>In this case:</b></b> `Bool` is a common type used to represent truth values in logic (true or false).</li>
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</ul>
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<p>
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—
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</p>
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<p>
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### 3. <b><b>`:` (colon)</b></b>
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</p>
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<ul class="org-ul">
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<li><b><b>What it means:</b></b> Indicates a type declaration in Agda.</li>
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<li><b><b>Purpose:</b></b> Separates the name of the data type (`Bool`) from its type (`Type`).</li>
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<li><b><b>In this case:</b></b> `Bool : Type` declares that `Bool` is a type itself (i.e., a type of values).</li>
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</ul>
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<p>
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||
—
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||
</p>
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<p>
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### 4. <b><b>`Type`</b></b>
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</p>
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<ul class="org-ul">
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<li><b><b>What it is:</b></b> The universe of all types in Agda.</li>
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<li><b><b>Purpose:</b></b> In Agda, types are first-class citizens, and `Type` represents the “type of types.” For instance:
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<ul class="org-ul">
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<li>`Bool : Type` means `Bool` is a type.</li>
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<li>If you define a type `ℕ : Type` for natural numbers, it also belongs to `Type`.</li>
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</ul></li>
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<li><b><b>In this case:</b></b> `Bool` is defined as a type that belongs to this universe.</li>
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</ul>
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<p>
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—
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</p>
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<p>
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### 5. <b><b>`where`</b></b>
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</p>
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<ul class="org-ul">
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<li><b><b>What it means:</b></b> Introduces the constructors (values) of the type.</li>
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<li><b><b>Purpose:</b></b> Lists the specific ways you can construct or create values of the newly defined type.</li>
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<li><b><b>In this case:</b></b> `where` introduces the two constructors, `true` and `false`, which are the only possible values of the `Bool` type.</li>
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</ul>
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<p>
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—
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</p>
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<p>
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### 6. <b><b>`true false`</b></b>
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</p>
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<ul class="org-ul">
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<li><b><b>What they are:</b></b> The <b>constructors</b> of the `Bool` type.</li>
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<li><b><b>Purpose:</b></b> Constructors are functions (or constants) that produce values of the type. Here:
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<ul class="org-ul">
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<li>`true : Bool` means `true` is a value of type `Bool`.</li>
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<li>`false : Bool` means `false` is a value of type `Bool`.</li>
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</ul></li>
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<li><b><b>In this case:</b></b> These two constructors define all possible values of `Bool`.</li>
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</ul>
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<p>
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—
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</p>
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<p>
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### 7. <b><b>`Bool` after the `:`</b></b>
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</p>
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<ul class="org-ul">
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<li><b><b>What it means:</b></b> Specifies the type of each constructor.</li>
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<li><b><b>Purpose:</b></b> Ensures that each constructor produces a value of the correct type (`Bool` in this case).</li>
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<li><b><b>In this case:</b></b> Both `true` and `false` are of type `Bool`.</li>
|
||
</ul>
|
||
|
||
<p>
|
||
—
|
||
</p>
|
||
|
||
<p>
|
||
### Complete Meaning
|
||
The entire definition can be read as:
|
||
</p>
|
||
<ol class="org-ol">
|
||
<li>Define a new type called `Bool`.</li>
|
||
<li>`Bool` belongs to the universe of types (`Type`).</li>
|
||
<li>The `Bool` type has two constructors:
|
||
<ul class="org-ul">
|
||
<li>`true` (a value of type `Bool`).</li>
|
||
<li>`false` (a value of type `Bool`).</li>
|
||
</ul></li>
|
||
</ol>
|
||
|
||
<p>
|
||
—
|
||
</p>
|
||
|
||
<p>
|
||
### Example Usage in Agda
|
||
You can use `Bool` in various ways:
|
||
```agda
|
||
– A function that negates a Bool
|
||
not : Bool → Bool
|
||
not true = false
|
||
not false = true
|
||
</p>
|
||
|
||
<p>
|
||
– A value of type Bool
|
||
myBool : Bool
|
||
myBool = true
|
||
```
|
||
</p>
|
||
|
||
<p>
|
||
This showcases how the `Bool` type and its constructors (`true` and `false`) can be used in programs.
|
||
</p>
|
||
|
||
<p class="backlinks-section" id="backlinks">
|
||
Backlinks
|
||
</p>
|
||
<ul class="org-ul backlinks-list">
|
||
<li><a href="20250120111047-afp_week1.html#ID-6c272430-aff5-468b-90d3-5ff3a96152cf">afp<sub>week1</sub></a></li>
|
||
</ul>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
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