commit 1f0b6bba514d4df2ee2c9a6af2040062846badf8
Author: Michael Zhang <mail@mzhang.io>
Date:   Wed Jul 31 19:57:35 2024 -0500

    Implement

diff --git a/.gitignore b/.gitignore
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index 0000000..72c59a9
--- /dev/null
+++ b/.gitignore
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+# Based on https://raw.githubusercontent.com/github/gitignore/main/Node.gitignore
+
+# Logs
+
+logs
+_.log
+npm-debug.log_
+yarn-debug.log*
+yarn-error.log*
+lerna-debug.log*
+.pnpm-debug.log*
+
+# Caches 
+
+.cache
+
+# Diagnostic reports (https://nodejs.org/api/report.html)
+
+report.[0-9]_.[0-9]_.[0-9]_.[0-9]_.json
+
+# Runtime data
+
+pids
+_.pid
+_.seed
+*.pid.lock
+
+# Directory for instrumented libs generated by jscoverage/JSCover
+
+lib-cov
+
+# Coverage directory used by tools like istanbul
+
+coverage
+*.lcov
+
+# nyc test coverage
+
+.nyc_output
+
+# Grunt intermediate storage (https://gruntjs.com/creating-plugins#storing-task-files)
+
+.grunt
+
+# Bower dependency directory (https://bower.io/)
+
+bower_components
+
+# node-waf configuration
+
+.lock-wscript
+
+# Compiled binary addons (https://nodejs.org/api/addons.html)
+
+build/Release
+
+# Dependency directories
+
+node_modules/
+jspm_packages/
+
+# Snowpack dependency directory (https://snowpack.dev/)
+
+web_modules/
+
+# TypeScript cache
+
+*.tsbuildinfo
+
+# Optional npm cache directory
+
+.npm
+
+# Optional eslint cache
+
+.eslintcache
+
+# Optional stylelint cache
+
+.stylelintcache
+
+# Microbundle cache
+
+.rpt2_cache/
+.rts2_cache_cjs/
+.rts2_cache_es/
+.rts2_cache_umd/
+
+# Optional REPL history
+
+.node_repl_history
+
+# Output of 'npm pack'
+
+*.tgz
+
+# Yarn Integrity file
+
+.yarn-integrity
+
+# dotenv environment variable files
+
+.env
+.env.development.local
+.env.test.local
+.env.production.local
+.env.local
+
+# parcel-bundler cache (https://parceljs.org/)
+
+.parcel-cache
+
+# Next.js build output
+
+.next
+out
+
+# Nuxt.js build / generate output
+
+.nuxt
+dist
+
+# Gatsby files
+
+# Comment in the public line in if your project uses Gatsby and not Next.js
+
+# https://nextjs.org/blog/next-9-1#public-directory-support
+
+# public
+
+# vuepress build output
+
+.vuepress/dist
+
+# vuepress v2.x temp and cache directory
+
+.temp
+
+# Docusaurus cache and generated files
+
+.docusaurus
+
+# Serverless directories
+
+.serverless/
+
+# FuseBox cache
+
+.fusebox/
+
+# DynamoDB Local files
+
+.dynamodb/
+
+# TernJS port file
+
+.tern-port
+
+# Stores VSCode versions used for testing VSCode extensions
+
+.vscode-test
+
+# yarn v2
+
+.yarn/cache
+.yarn/unplugged
+.yarn/build-state.yml
+.yarn/install-state.gz
+.pnp.*
+
+# IntelliJ based IDEs
+.idea
+
+# Finder (MacOS) folder config
+.DS_Store
+
+*.ohm-bundle.*
\ No newline at end of file
diff --git a/biome.json b/biome.json
new file mode 100644
index 0000000..0d449a7
--- /dev/null
+++ b/biome.json
@@ -0,0 +1,18 @@
+{
+  "$schema": "https://biomejs.dev/schemas/1.4.1/schema.json",
+  "organizeImports": {
+    "enabled": true
+  },
+  "formatter": {
+    "enabled": true,
+    "indentWidth": 2,
+    "indentStyle": "space",
+    "lineWidth": 80
+  },
+  "linter": {
+    "enabled": true,
+    "rules": {
+      "recommended": true
+    }
+  }
+}
diff --git a/main.ts b/main.ts
new file mode 100644
index 0000000..74a0369
--- /dev/null
+++ b/main.ts
@@ -0,0 +1,225 @@
+import isEqual from "lodash.isequal";
+import { match, P } from "ts-pattern";
+
+export type expr =
+  | { kind: "var"; x: variable }
+  | { kind: "universe"; level: number }
+  | { kind: "pi"; abs: abstraction }
+  | { kind: "lambda"; abs: abstraction }
+  | { kind: "app"; left: expr; right: expr };
+
+export interface abstraction {
+  x: variable;
+  type: expr;
+  body: expr;
+}
+
+// =============================================================================
+// Substitution
+
+export type variable =
+  | { kind: "string"; name: string }
+  | { kind: "gensym"; name: string; n: number }
+  | { kind: "dummy" };
+
+export const dummy = (): variable => ({ kind: "dummy" });
+
+export interface Substitution {
+  x: variable;
+  repl: expr;
+}
+
+let ctr = 0;
+export function refresh(v: variable): variable {
+  const n = ctr + 1;
+  ctr += 1;
+  switch (v.kind) {
+    case "gensym":
+    case "string": {
+      return { kind: "gensym", name: v.name, n };
+    }
+    case "dummy":
+      return { kind: "gensym", name: "_", n };
+  }
+}
+
+export function subst(s: Substitution[], e: expr): expr {
+  switch (e.kind) {
+    case "var":
+      return s.find((sub) => isEqual(sub.x, e.x))?.repl ?? e;
+    case "universe":
+      return e;
+    case "pi":
+      return { kind: "pi", abs: substAbstraction(s, e.abs) };
+    case "lambda":
+      return { kind: "lambda", abs: substAbstraction(s, e.abs) };
+    case "app":
+      return { kind: "app", left: subst(s, e.left), right: subst(s, e.right) };
+  }
+}
+
+export function substAbstraction(
+  s: Substitution[],
+  { x, type, body }: abstraction,
+): abstraction {
+  const x2 = refresh(x);
+  return {
+    x: x,
+    type: subst(s, type),
+    body: subst([{ x, repl: { kind: "var", x: x2 } }, ...s], body),
+  };
+}
+
+// =============================================================================
+// Type inference
+
+export type context = ContextEntry[];
+
+export interface ContextEntry {
+  x: variable;
+  type: expr;
+  value?: expr | undefined;
+}
+
+/** Returns the type of the definition associated with `x` inside the context `ctx` */
+export function lookupTy(x: variable, ctx: context): expr | null {
+  return ctx.find((entry) => isEqual(entry.x, x))?.type ?? null;
+}
+
+/** Returns the value of the definition associated with `x` inside the context `ctx` */
+export function lookupValue(x: variable, ctx: context): expr | null {
+  return ctx.find((entry) => isEqual(entry.x, x))?.value ?? null;
+}
+
+export function extend(
+  x: variable,
+  t: expr,
+  value: expr | undefined,
+  ctx: context,
+): context {
+  return [...ctx, { x: x, type: t, value }];
+}
+
+/** Infer the type of the expression `e` in context `ctx` */
+export function inferType(ctx: context, e: expr): expr {
+  switch (e.kind) {
+    case "var": {
+      const ty = lookupTy(e.x, ctx);
+      if (ty === null) throw new Error(`unknown identifier ${e.x}`);
+      return ty;
+    }
+    case "universe":
+      return { kind: "universe", level: e.level + 1 };
+    case "pi": {
+      const { x, type, body } = e.abs;
+      const k1 = inferUniverse(ctx, type);
+      const k2 = inferUniverse(extend(x, type, undefined, ctx), e.abs.body);
+      return { kind: "universe", level: Math.max(k1, k2) };
+    }
+    case "lambda": {
+      const { x, type, body } = e.abs;
+      const te = inferType(extend(x, type, undefined, ctx), body);
+      return { kind: "pi", abs: { x, type, body: te } };
+    }
+    case "app": {
+      const { x, type, body } = inferPi(ctx, e.left);
+      const te = inferType(ctx, e.right);
+      checkEqual(ctx, type, te);
+      return subst([{ x, repl: e.right }], body);
+    }
+  }
+}
+
+export function inferUniverse(ctx: context, t: expr): number {
+  const u = inferType(ctx, t);
+  const n = normalize(ctx, u);
+  switch (n.kind) {
+    case "universe":
+      return n.level;
+    default:
+      throw new Error("type expected.");
+  }
+}
+
+export function inferPi(ctx: context, e: expr): abstraction {
+  const t = inferType(ctx, e);
+  const n = normalize(ctx, t);
+  switch (n.kind) {
+    case "pi":
+      return n.abs;
+    default:
+      throw new Error("function expected");
+  }
+}
+
+export function checkEqual(ctx: context, e1: expr, e2: expr) {
+  if (!equal(ctx, e1, e2))
+    throw new Error(`expressions ${e1} and ${e2} not equal`);
+}
+
+// =============================================================================
+// Normalization and equality
+
+export function normalize(ctx: context, e: expr): expr {
+  switch (e.kind) {
+    case "var": {
+      const n = lookupTy(e.x, ctx);
+      if (!n) throw new Error(`unknown identifier ${e.x}`);
+      return n;
+    }
+    case "app": {
+      const e2 = normalize(ctx, e.right);
+      const e1 = normalize(ctx, e.left);
+      switch (e1.kind) {
+        case "lambda":
+          return normalize(
+            ctx,
+            subst([{ x: e1.abs.x, repl: e2 }], e1.abs.body),
+          );
+        default:
+          return { kind: "app", left: e1, right: e2 };
+      }
+    }
+    case "universe":
+      return e;
+    case "pi":
+      return { kind: "pi", abs: normalizeAbstraction(ctx, e.abs) };
+    case "lambda":
+      return { kind: "lambda", abs: normalizeAbstraction(ctx, e.abs) };
+  }
+}
+
+export function normalizeAbstraction(
+  ctx: context,
+  { x, type, body }: abstraction,
+): abstraction {
+  const t = normalize(ctx, type);
+  return { x, type: t, body: normalize(extend(x, t, undefined, ctx), body) };
+}
+
+export function equal(ctx: context, e1: expr, e2: expr): boolean {
+  function equalHelper(e1: expr, e2: expr): boolean {
+    if (e1.kind === "var" && e2.kind === "var") return isEqual(e1.x, e2.x);
+    if (e1.kind === "app" && e2.kind === "app")
+      return equalHelper(e1.left, e2.left) && equalHelper(e1.right, e2.right);
+    if (e1.kind === "universe" && e2.kind === "universe")
+      return e1.level === e2.level;
+    if (e1.kind === "pi" && e2.kind === "pi")
+      return equalAbstraction(e1.abs, e2.abs);
+    if (e1.kind === "lambda" && e2.kind === "lambda")
+      return equalAbstraction(e1.abs, e2.abs);
+    return false;
+  }
+
+  function equalAbstraction(
+    { x, type: type1, body: body1 }: abstraction,
+    { x: y, type: type2, body: body2 }: abstraction,
+  ): boolean {
+    return (
+      equalHelper(type1, type2) &&
+      equalHelper(body1, subst([{ x: y, repl: { kind: "var", x } }], body2))
+    );
+  }
+
+  return equalHelper(normalize(ctx, e1), normalize(ctx, e2));
+}
diff --git a/tsconfig.json b/tsconfig.json
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--- /dev/null
+++ b/tsconfig.json
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+{
+  "compilerOptions": {
+    "strict": true,
+    "esModuleInterop": true,
+    "skipLibCheck": true,
+  },
+}