Start drafting CEK

assets/sass/_content.scss

@@ -124,6 +124,7 @@ a code {
 }
 
 pre > code {
+    color: $text-color;
     display: block;
     padding: 5px;
     overflow-x: auto;
@@ -156,7 +157,56 @@ table.table {
     }
 }
 
-.post-content {
+.post-container {
+    display: flex;
+
+    @media screen and (max-width: 520px) {
+        flex-direction: column;
+        .toc-drawer { display: block; }
+        .toc-list { display: none; }
+    }
+
+    @media screen and (min-width: 520px) {
+        flex-direction: row;
+        align-items: flex-start;
+        gap: 12px;
+
+        .toc-drawer { display: none; }
+        .toc-list {
+            top: 0;
+            display: block;
+            position: sticky;
+            min-width: 160px;
+        }
+    }
+
+    .post-content {
+        min-width: 1px;
+    }
+
+    .toc-draw #TableOfContents, .toc-list #TableOfContents {
+        ul {
+            list-style-type: "\22A2 ";
+            padding-left: 1rem;
+
+            li {
+                margin-bottom: 0.5rem;
+            }
+        }
+
+        li ul {
+            margin-top: 0.5rem;
+        }
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+}
+
+.division .post-content, .post-content {
+    .heading {
+        a {
+            color: $heading-color;
+        }
+    }
+
     > p {
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assets/sass/main.scss

@@ -4,7 +4,8 @@
 
 @font-face {
   font-family: 'PragmataPro Mono Liga';
-  src: url('/fonts/PragmataPro_Mono_R_liga_0829.woff2') format('woff2');
+  src: url("/fonts/PragmataPro_Mono_R_liga_0829.woff2") format("woff2"),
+    url(https://mzhang.io/fonts/PragmataPro_Mono_R_liga_0829.woff2) format("woff2");
 }
 
 $sansfont: "Helvetica", "Arial", "Liberation Sans", sans-serif;
@@ -26,7 +27,7 @@ $monofont: "PragmataPro Mono Liga", "Roboto Mono", "Roboto Mono for Powerline",
 }
 
 @media (prefers-color-scheme: dark) {
-    $background-color: #15202B;
+    $background-color: #151520;
     $faded-background-color: lighten($background-color, 10%);
     $heading-color: #E4E4E4;
     $text-color: #BCBCBC;

config.toml

@@ -9,7 +9,7 @@ language = "languages"
 
 [markup.tableOfContents]
 endLevel = 4
-ordered = true
+ordered = false
 startLevel = 2
 
 [markup.goldmark.renderer]

content/posts/2022-02-02-formal-cek-machine-in-agda/_index.md

@@ -0,0 +1,96 @@
++++
+title = "a formal cek machine in agda"
+draft = true
+date = 2022-02-02
+tags = ["computer-science", "programming-languages", "formal-verification", "lambda-calculus"]
+languages = ["agda"]
+layout = "single"
+toc = true
++++
+
+<!--more-->
+
+Last semester, I took a course on reasoning about programming languages using
+Agda, a dependently typed meta-language. For the term project, we were to
+implement a simply-typed lambda calculus with several extensions, along with
+proofs of certain properties.
+
+My lambda calculus implemented `call/cc` on top of a CEK machine.
+
+## Foreword
+
+**Why is this interesting?** Reasoning about languages is one way of ensuring
+whole-program correctness. Building up these languages from foundations grounded
+in logic helps us achieve our goal with more rigor.
+
+As an example, suppose I wrote a function that takes a list of numbers and
+returns the maximum value. Mathematically speaking, this function would be
+_non-total_; an input consisting of an empty set would not produce reasonable
+output! If this were a library function I'd like to tell people who write code
+that uses this function "don't give me an empty list!"
+
+Unfortunately, just writing this in documentation isn't enough. What we'd really
+like is for a tool (like a compiler) to tell any developer who is trying to pass
+an empty list into our maximum function "You can't do that." Unfortunately, most
+of the popular languages being used today have no way of describing "a list
+that's not empty."
+
+## Lambda calculus
+
+The lambda calculus is a mathematical structure for describing computation. At
+the most basic level, it defines a concept called a _term_. Everything that can
+be represented in a lambda calculus is some combination of terms. A term can
+have several constructors:
+
+- **Var.** This is just a variable, like `x` or `y`. During evaluation, a
+    variable can resolve to a value in the evaluation environment by name. If
+    the environment says `{ x = 5 }`, then evaluating `x` would result in 5.
+
+- **Abstraction, or lambda (λ).** An _abstraction_ is a term that describes some
+    other computation. From an algebraic perspective, it can be thought of as a
+    function with a single argument (i.e f(x) = 2x is an abstraction, although
+    it would be written `(λx.2x)`)
+
+- **Application.** Application is sort of the opposite of abstraction, exposing
+    the computation that was abstracted away. From an algebraic perspective,
+    this is just function application (i.e applying `f(x) = 2x` to 3 would
+    result in 2\*3. Note that only a simple substitution has been done and
+    further evaluation is required to reduce 2*3)
+
+### Why?
+
+The reason it's set up this way is so we can reason about terms inductively. The
+idea is that because terms are just nested constructors, we can describe the
+behavior of any term by just defining the behavior of these 3 constructors.
+
+Interestingly, the lambda calculus is Turing-complete, so any computation can be
+reduced to those 3 constructs. I used numbers liberally in the examples above,
+but in a lambda calculus without numbers, you could define integers recursively
+like this:
+
+- Let `z` represent zero.
+- Let `s` represent a "successor", or increment function. `s(z)` represents 1,
+    `s(s(z))` represents 2, and so on.
+
+In lambda calculus terms, this would look like:
+
+- 0 = `λs.(λz.z)`
+- 1 = `λs.(λz.s(z))`
+- 2 = `λs.(λz.s(s(z)))`
+- 3 = `λs.(λz.s(s(s(z))))`
+
+In practice, many lambda calculus have a set of "base" values from which to
+build off, such as unit values, booleans, and natural numbers (having numbers in
+the language means we don't need the `s` and `z` dance to refer to them).
+
+### Turing completeness
+
+As I noted above, the lambda calculus is _Turing-complete_. One feature of
+Turing complete systems is that they have a (provably!) unsolvable "halting"
+problem.
+
+### Simply-typed lambda calculus (STLC)
+
+## CEK machine
+
+A CEK machine

layouts/_default/_markup/render-heading.html

@@ -0,0 +1,3 @@
+<h{{ .Level }} id="{{ .Anchor | safeURL }}" class="heading">
+  <a href="#{{ .Anchor | safeURL }}">{{ .Text | safeHTML }}</a>
+</h{{ .Level }}>

layouts/partials/post-list.html

@@ -1,19 +1,21 @@
 <table style="width: 100%;">
     {{- range .Pages -}}
-        <tr class="postlisting-row">
+        {{ if not .Draft }}
-            <td>
+            <tr class="postlisting-row">
-                <span class="title">
+                <td>
-                    <a href="{{ .RelPermalink }}" class="brand-colorlink">{{ .Title }}</a>
+                    <span class="title">
-                </span>
+                        <a href="{{ .RelPermalink }}" class="brand-colorlink">{{ .Title }}</a>
-                <br />
+                    </span>
-                <small>
+                    <br />
-                    {{ .ReadingTime }} min read -
+                    <small>
+                        {{ .ReadingTime }} min read -
 
-                    {{ .Date.Format "Mon Jan 02, 2006" }}
+                        {{ .Date.Format "Mon Jan 02, 2006" }}
-                </small>
+                    </small>
 
-                <br />
+                    <br />
-            </td>
+                </td>
-        </tr>
+            </tr>
+        {{ end }}
     {{- end -}}
 </table>

layouts/posts/single.html

@@ -18,24 +18,28 @@
     - {{ .ReadingTime }} min read
 </small>
 
-{{ if .Params.toc }}
+<div class="post-container">
-<div class="toc">
+    {{ if .Params.toc }}
-    <details>
+        <div class="toc-drawer">
-        <summary>Table of Contents</summary>
+            <details>
-        {{ .TableOfContents }}
+                <summary>Table of Contents</summary>
-    </details>
+                {{ .TableOfContents }}
+            </details>
+        </div>
+        <div class="toc-list">
+            {{ .TableOfContents }}
+        </div>
+    {{ end }}
+    <div id="content" class="post-content">{{ .Content }}</div>
 </div>
-{{ end }}
-
-<div id="content" class="post-content">{{ .Content }}</div>
 
 <hr />
 
 <small>
     Thanks for reading!
-    {{ if .Params.mastodon }}
+
-        Have comments? Discuss this post on <a href="{{ .Params.mastodon }}" target="_blank">Mastodon</a>.
+    Have comments? Discuss this post by sending me a
-    {{ end }}
+    <a href="mailto:~mzhang/public-inbox@lists.sr.ht?subject=Re:+{{ .Title }}">public email</a>.
 </small>
 
 {{- end -}}