render agda

.gitignore

@@ -21,3 +21,4 @@ pnpm-debug.log*
 .DS_Store
 
 PragmataPro-Mono-Liga-Regular-Nerd-Font-Complete.woff2
+*.agdai

astro.config.ts

@@ -1,7 +1,6 @@
 import { defineConfig } from "astro/config";
 import mdx from "@astrojs/mdx";
 import sitemap from "@astrojs/sitemap";
-import { astroImageTools } from "astro-imagetools";
 import { rehypeAccessibleEmojis } from "rehype-accessible-emojis";
 
 import remarkReadingTime from "./plugin/remark-reading-time";
@@ -10,24 +9,31 @@ import remarkMermaid from "astro-diagram/remark-mermaid";
 import remarkDescription from "astro-remark-description";
 import remarkAdmonitions from "./plugin/remark-admonitions";
 import remarkMath from "remark-math";
-
 import rehypeKatex from "rehype-katex";
 
+import addProofMacros from "./utils/mzproofs";
+import remarkAgda from "./plugin/remark-agda";
+
 // https://astro.build/config
 export default defineConfig({
   site: "https://mzhang.io",
-  integrations: [mdx(), sitemap(), astroImageTools],
+  integrations: [
+    mdx(),
+    sitemap(),
+    //astroImageTools
+  ],
   markdown: {
     syntaxHighlight: "shiki",
     shikiConfig: { theme: "css-variables" },
     remarkPlugins: [
       remarkAdmonitions,
       remarkReadingTime,
-      remarkMath,
+      remarkAgda,
+      [remarkMath, {}],
       remarkMermaid,
       emoji,
       [remarkDescription, { name: "excerpt" }],
     ],
-    rehypePlugins: [rehypeKatex, rehypeAccessibleEmojis],
+    rehypePlugins: [[rehypeKatex, { macros: addProofMacros({}) }], rehypeAccessibleEmojis],
   },
 });

blog.agda-lib

@@ -0,0 +1,2 @@
+include: src/content/posts
+depend: standard-library

package.json

@@ -34,6 +34,7 @@
   "devDependencies": {
     "@types/lodash-es": "^4.17.9",
     "mdast": "^3.0.0",
+    "mdast-util-from-markdown": "^2.0.0",
     "prettier": "^3.0.3",
     "prettier-plugin-astro": "^0.12.0",
     "sass": "^1.66.1",

plugin/remark-agda.ts

@@ -0,0 +1,54 @@
+import type { RemarkPlugin } from "@astrojs/markdown-remark";
+import { fromMarkdown } from "mdast-util-from-markdown";
+
+import { spawnSync } from "node:child_process";
+import { mkdtempSync, mkdirSync, readFileSync } from "node:fs";
+import { tmpdir } from "node:os";
+import { join, parse } from "node:path";
+
+const remarkAgda: RemarkPlugin = () => {
+  return function (tree, { data }) {
+    const path: string = data.astro.fileURL.pathname;
+    if (!(path.endsWith(".lagda.md") || path.endsWith(".agda"))) return;
+
+    console.log("data", data);
+
+    const tempDir = mkdtempSync(join(tmpdir(), "agdaRender."));
+    const outDir = join(tempDir, "output");
+    mkdirSync(outDir, { recursive: true });
+    console.log("work dir", tempDir);
+
+    const childOutput = spawnSync(
+      "agda",
+      [
+        "--html",
+        `--html-dir=${outDir}`,
+        "--highlight-occurrences",
+        "--html-highlight=code",
+        data.astro.fileURL.pathname,
+      ],
+      {},
+    );
+
+    console.log("output", childOutput.output.toString());
+    const filename = parse(path).base.replace(/\.lagda/, "");
+    console.log();
+    console.log("filename", filename);
+
+    const fullOutputPath = join(outDir, filename);
+    console.log("outDir", fullOutputPath);
+    console.log();
+
+    const doc = readFileSync(fullOutputPath);
+    const tree2 = fromMarkdown(doc);
+    console.log("tree", tree);
+
+    tree.children = tree2.children;
+
+    // visit(tree, "", (node) => {
+    //   console.log("node", node);
+    // });
+  };
+};
+
+export default remarkAgda;

src/content/posts/2023-10-10-dtt-project.lagda.md

@@ -0,0 +1,154 @@
+---
+title: DTT Project
+date: 2023-10-11T04:05:23.082Z
+draft: true
+toc: true
+tags:
+  - type-theory
+---
+
+References:
+
+- https://www.cl.cam.ac.uk/~nk480/bidir.pdf
+
+<details>
+  <summary>
+    Agda Imports
+    <small>for the purpose of type-checking</small>
+  </summary>
+
+```agda
+{-# OPTIONS --allow-unsolved-metas --allow-incomplete-matches #-}
+open import Data.Nat
+open import Data.Product
+open import Data.String hiding (_<_)
+open import Relation.Nullary using (Dec)
+open import Relation.Nullary.Decidable using (True; toWitness)
+```
+
+</details>
+
+## Damas-Hindley-Milner type inference
+
+Unification-based algorithm for lambda calculus.
+
+## First try
+
+Implement terms, monotypes, and polytypes:
+
+```agda
+data Term : Set
+data Type : Set
+data Monotype : Set
+```
+
+Regular lambda calculus terms:
+
+$e ::= x \mid () \mid \lambda x. e \mid e e \mid (e : A)$
+
+```agda
+data Term where
+    Unit : Term
+    Var : String → Term
+    Lambda : String → Term → Term
+    App : Term → Term → Term
+    Annot : Term → Type → Term
+```
+
+Polytypes are types that may include universal quantifiers ($\forall$)
+
+$A, B, C ::= 1 \mid \alpha \mid \forall \alpha. A \mid A \rightarrow B$
+
+```agda
+data Type where
+    Unit : Type
+    Var : String → Type
+    Existential : String → Type
+    Forall : String → Type → Type
+    Arrow : Type → Type → Type
+```
+
+Monotypes (usually denoted $\tau$) are types that aren't universally quantified.
+
+> [!NOTE]
+> In the declarative version of this algorithm, monotypes don't have existential quantifiers either,
+> but the algorithmic type system includes it.
+> TODO: Explain why
+
+```agda
+data Monotype where
+    Unit : Monotype
+    Var : String → Monotype
+    Existential : String → Monotype
+    Arrow : Monotype → Monotype → Monotype
+```
+
+### Contexts
+
+```agda
+data Context : Set where
+    Nil : Context
+    Var : Context → String → Context
+    Annot : Context → String → Type → Context
+    UnsolvedExistential : Context → String → Context
+    SolvedExistential : Context → String → Monotype → Context
+    Marker : Context → String → Context
+
+contextLength : Context → ℕ
+contextLength Nil = zero
+contextLength (Var Γ _) = suc (contextLength Γ)
+contextLength (Annot Γ _ _) = suc (contextLength Γ)
+contextLength (UnsolvedExistential Γ _) = suc (contextLength Γ)
+contextLength (SolvedExistential Γ _ _) = suc (contextLength Γ)
+contextLength (Marker Γ _) = suc (contextLength Γ)
+
+-- https://plfa.github.io/DeBruijn/#abbreviating-de-bruijn-indices
+postulate
+    lookupVar : (Γ : Context) → (n : ℕ) → (p : n < contextLength Γ) → Set
+-- lookupVar (Var Γ x) n p = {!   !}
+-- lookupVar (Annot Γ x x₁) n p = {!   !}
+-- lookupVar (UnsolvedExistential Γ x) n p = {!   !}
+-- lookupVar (SolvedExistential Γ x x₁) n p = {!   !}
+-- lookupVar (Marker Γ x) n p = {!   !}
+
+data CompleteContext : Set where
+    Nil : CompleteContext
+    Var : CompleteContext → String → CompleteContext
+    Annot : CompleteContext → String → Type → CompleteContext
+    SolvedExistential : CompleteContext → String → Monotype → CompleteContext
+    Marker : CompleteContext → String → CompleteContext
+```
+
+### Type checking
+
+```agda
+postulate
+    check : (Γ : Context) → (e : Term) → (A : Type) → Context
+```
+
+```agda
+-- check Γ Unit A = Γ
+```
+
+```agda
+-- check Γ (Var x) A = {!   !}
+-- check Γ (Lambda x e) A = {!   !}
+-- check Γ (App e e₁) A = {!   !}
+-- check Γ (Annot e x) A = {!   !}
+```
+
+### Type synthesizing
+
+```js
+const x = () => {};
+```
+
+```agda
+postulate
+    synthesize : (Γ : Context) → (e : Term) → (Type × Context)
+-- synthesize Γ Unit = Unit , Γ
+-- synthesize Γ (Var x) = {!   !}
+-- synthesize Γ (Lambda x e) = {!   !}
+-- synthesize Γ (App e e₁) = {!   !}
+-- synthesize Γ (Annot e x) = {!   !}
+```

src/styles/_colors.scss

@@ -76,3 +76,126 @@
     --astro-code-token-link: black;
   }
 }
+
+pre.Agda {
+  a {
+    color: var(--astro-code-color-text);
+  }
+
+  //   .Keyword {
+  //     color: var(--astro-code-token-keyword);
+  //   }
+
+  //   .Comment {
+  //     color: var(--astro-code-token-comment);
+  //   }
+
+  //   .Symbol {
+  //     color: var(--astro-code-token-punctuation);
+  //   }
+
+  //   .Function {
+  //     color: var(--astro-code-token-function);
+  //   }
+}
+
+/* Aspects. */
+.Agda .Comment {
+  color: #b22222;
+}
+.Agda .Background {
+}
+.Agda .Markup {
+  color: #000000;
+}
+.Agda .Keyword {
+  color: #cd6600;
+}
+.Agda .String {
+  color: #b22222;
+}
+.Agda .Number {
+  color: #a020f0;
+}
+.Agda .Symbol {
+  color: #404040;
+}
+.Agda .PrimitiveType {
+  color: #0000cd;
+}
+.Agda .Pragma {
+  color: black;
+}
+.Agda .Operator {
+}
+
+/* NameKinds. */
+.Agda .Bound {
+  color: black;
+}
+.Agda .Generalizable {
+  color: black;
+}
+.Agda .InductiveConstructor {
+  color: #008b00;
+}
+.Agda .CoinductiveConstructor {
+  color: #8b7500;
+}
+.Agda .Datatype {
+  color: #0000cd;
+}
+.Agda .Field {
+  color: #ee1289;
+}
+.Agda .Function {
+  color: #0000cd;
+}
+.Agda .Module {
+  color: #a020f0;
+}
+.Agda .Postulate {
+  color: #0000cd;
+}
+.Agda .Primitive {
+  color: #0000cd;
+}
+.Agda .Record {
+  color: #0000cd;
+}
+
+/* OtherAspects. */
+.Agda .DottedPattern {
+}
+.Agda .UnsolvedMeta {
+  color: black;
+  background: yellow;
+}
+.Agda .UnsolvedConstraint {
+  color: black;
+  background: yellow;
+}
+.Agda .TerminationProblem {
+  color: black;
+  background: #ffa07a;
+}
+.Agda .IncompletePattern {
+  color: black;
+  background: #f5deb3;
+}
+.Agda .Error {
+  color: red;
+  text-decoration: underline;
+}
+.Agda .TypeChecks {
+  color: black;
+  background: #add8e6;
+}
+
+/* Standard attributes. */
+.Agda a {
+  text-decoration: none;
+}
+// .Agda a[href]:hover {
+//   background-color: #b4eeb4;
+// }

src/styles/global.scss

@@ -46,17 +46,19 @@ code {
   font-family: var(--monofont);
   box-sizing: border-box;
   padding: 1px 5px;
-  background-color: var(--faded-background-color);
+  //   background-color: var(--faded-background-color);
   // color: $code-color;
 }
 
-pre > code {
+pre > code,
+pre.Agda {
   color: var(--text-color);
   display: block;
   padding: 5px;
   overflow-x: auto;
   font-family: var(--monofont);
   line-height: 1.15rem;
+  background-color: var(--faded-background-color);
 }
 
 a code {

src/styles/post.scss

@@ -52,10 +52,23 @@
     border: 1px solid var(--hr-color);
   }
 
-  pre > code {
+  pre > code,
+  pre.Agda {
     padding: 12px;
     border-radius: 8px;
     border: 1px solid var(--hr-color);
+    // background-color: var(--astro-code-color-background);
+
+    a {
+      background-color: unset;
+
+      &:not([href]):hover {
+      }
+
+      &[href]:hover {
+        text-decoration: underline;
+      }
+    }
   }
 
   /*