add rss feed

assets/sass/_content.scss

@@ -1,5 +1,7 @@
 @import "footer";
 
+$breakpoint: 720px;
+
 html {
     min-height: 100vh;
     margin: 0;
@@ -68,7 +70,8 @@ footer {
 
 .side-nav .side-nav-content {
     display: flex;
-    justify-content: space-evenly;
+    justify-content: center;
+    gap: 20px;
 
     .me {
         display: flex;
@@ -91,7 +94,7 @@ footer {
     }
 }
 
-@media screen and (max-width: 672px) {
+@media screen and (max-width: $breakpoint) {
     .flex-wrapper {
         flex-direction: column;
         .container {
@@ -116,6 +119,7 @@ footer {
             .portrait {
                 max-height: 80px;
             }
+
             .bio {
                 display: none;
             }
@@ -123,7 +127,7 @@ footer {
     }
 }
 
-@media screen and (min-width: 672px) {
+@media screen and (min-width: $breakpoint) {
     .flex-wrapper {
         flex-direction: row;
         .container {
@@ -137,7 +141,8 @@ footer {
         left: 0;
         top: 0;
         // Capital Min to avoid invoking SCSS min
-        max-width: Min(30%, 30em);
+        width: 30%;
+        min-width: 300px;
 
         .side-nav-content {
             padding-top: 32px;

blog.agda-lib

@@ -1,3 +1,3 @@
 name: blog
-depend: standard-library
+depend: standard-library cubical
 include: content/posts

content/posts/2023-02-04-proving-true-from-false.lagda.md

@@ -0,0 +1,75 @@
++++
+title = "Proving true from false"
+slug = "proving-true-from-false"
+date = 2023-02-04
+tags = ["type-theory"]
+math = true
+draft = true
++++
+
+<details>
+<summary>Imports</summary>
+
+These are some imports that are required for code on this page to work properly.
+
+```agda
+{-# OPTIONS --cubical #-}
+
+open import Cubical.Foundations.Prelude
+open import Data.Bool
+open import Data.Unit
+open import Data.Empty
+
+¬_ : Set → Set
+¬ A = A → ⊥
+
+_≢_ : ∀ {A : Set} → A → A → Set
+x ≢ y  =  ¬ (x ≡ y)
+```
+</details>
+
+Let's say you wanted to prove that `true` and `false` diverge, a.k.a are not
+equal to each other. In a theorem prover like Agda, you could write this
+statement as something like this:
+
+```
+true≢false : true ≢ false
+```
+
+For many "obvious" statements, it suffices to just write `refl` since the two
+sides are trivially true via rewriting. For example:
+
+```
+open import Data.Nat
+1+2≡3 : 1 + 2 ≡ 3
+1+2≡3 = refl
+```
+
+However, in cubical Agda, this following statement doesn't work. I've commented
+it out so the code on this page can continue to compile.
+
+```
+-- true≢false = refl
+```
+
+It looks like it's not obvious to the interpreter that this statement is
+actually true. Why is this?
+
+Well, in homotopy type theory, TODO
+
+The strategy here is we define some kind of "type-map". Every time we see true,
+we'll map it to some type, and every time we see false, we'll map it to empty.
+
+Because the `≢` type actually means "having `a ≡ b` can produce `⊥`", all we
+need to do is to produce an empty type. To do this, we need to do something
+called _transport_.
+
+In homotopy type theory, is a way of generating functions out of paths.
+
+```
+bool-map : Bool → Type
+bool-map true = ⊤
+bool-map false = ⊥
+
+true≢false p = transport (λ i → bool-map (p i)) tt
+```

layouts/_default/baseof.html

@@ -10,6 +10,7 @@
 
         {{ if .IsHome }}
             <link rel="me" href="https://fosstodon.org/@mzhang" />
+            <link rel="alternate" type="application/rss+xml" title="RSS Feed" href="/index.xml" />
         {{ end }}
 
         {{ $style := resources.Get "sass/main.scss" | resources.ToCSS }}

layouts/partials/left-nav.html

@@ -13,6 +13,7 @@
                 {{ end }}
             </div>
         </div>
+
         <div class="bio">
             {{ os.ReadFile "layouts/partials/left-nav.md" | .RenderString }}