init

.gitignore

@@ -0,0 +1,2 @@
+.DS_Store
+*.pdf

csci8980-f23.agda-lib

@@ -0,0 +1,2 @@
+include: bidir
+depend: standard-library

hwk1.typ

@@ -0,0 +1,41 @@
+#import "@preview/prooftrees:0.1.0": *
+
+#let natrec = text[natrec]
+#let suc = text[suc]
+
+= Problem 1
+
+Define `funsplit` in terms of `apply`.
+
+$ "funsplit"(f, d) &equiv d("apply"(f, (x) x)) $
+
+In the case of $f = lambda b$ the following evaluation occurs:
+
+$ "funsplit"(lambda b, d) &equiv d( "apply"(lambda b, (x) x)) \
+&equiv d(((x)x)(b)) \
+&equiv d(b) $
+
+= Problem 2
+
+Assuming that you have Eq sets at your disposal, use only rules (without appealing to the One True Language) to prove:
+
+$ plus.circle(x, 0) = x ∈ NN [x ∈ NN] $
+
+Please be pedantic and explicitly use a rule even for "obvious" steps. You do not have to draw a big derivation tree (which is difficult to typeset), but it should be clear which rule you are using at each step. If you are using an implicit rule that the authors did not explicitly write out, make it clear what it is. If you are not sure what a derivation tree is, whether a particular rule is allowed, or which emoji was just introduced in Emoji 15.1, use the Discord forum immediately.
+
+#{
+    tree(
+        axi[$C(v) "set" [v in NN]$],
+        axi[$x in NN$],
+        axi[$d in C(0)$],
+        axi[$x in NN$],
+        nary(4)[$natrec(x, 0, (u, v) suc(v)) equiv x [Delta tack.r x in NN]$],
+    )
+
+    tree(
+        axi[],
+        uni[$plus.circle(x, 0) equiv natrec(x, 0, (u, v) suc(v)) [Gamma tack.r x in NN]$],
+        axi[$natrec(x, 0, (u, v) suc(v)) equiv x [Delta tack.r x in NN]$],
+        bin[$plus.circle(x, 0) equiv x in NN [(Gamma, Delta) tack.r x in NN]$],
+    )
+}

pmltt-lang/.gitignore

@@ -0,0 +1,30 @@
+# Logs
+logs
+*.log
+npm-debug.log*
+yarn-debug.log*
+yarn-error.log*
+pnpm-debug.log*
+lerna-debug.log*
+
+node_modules
+dist
+dist-ssr
+*.local
+
+# Editor directories and files
+.vscode/*
+!.vscode/extensions.json
+.idea
+.DS_Store
+*.suo
+*.ntvs*
+*.njsproj
+*.sln
+*.sw?
+
+# ReScript
+/lib/
+.bsb.lock
+.merlin
+*.bs.mjs

pmltt-lang/README.md

@@ -0,0 +1,38 @@
+# ReScript / Vite Starter Template
+
+This is a Vite-based template with following setup:
+
+- [ReScript](https://rescript-lang.org) 10.1 with @rescript/react and JSX 4 automatic mode
+- ES6 modules (ReScript code compiled to `.bs.mjs` files)
+- Vite 4 with React Plugin (Fast Refresh)
+- Tailwind 3
+
+## Development
+
+Run ReScript in dev mode:
+
+```sh
+npm run res:dev
+```
+
+In another tab, run the Vite dev server:
+
+```sh
+npm run dev
+```
+
+## Tips
+
+### Fast Refresh & ReScript
+
+Make sure to create interface files (`.resi`) for each `*.res` file.
+
+Fast Refresh requires you to **only export React components**, and it's easy to unintenionally export other values that will disable Fast Refresh (you will see a message in the browser console whenever this happens).
+
+### Why are the generated `.bs.mjs` files tracked in git?
+
+In ReScript, it's a good habit to keep track of the actual JS output the compiler emits. It allows quick sanity checking if we made any changes that actually have an impact on the resulting JS code (especially when doing major compiler upgrades, it's a good way to verify if production code will behave the same way as before the upgrade).
+
+This will also make it easier for your Non-ReScript coworkers to read and understand the changes in Github PRs, and call you out when you are writing inefficient code.
+
+If you want to opt-out, feel free to remove all compiled `.mjs` files within the `src` directory and add `src/**/*.mjs` in your `.gitignore`.

pmltt-lang/bsconfig.json

@@ -0,0 +1,27 @@
+{
+  "name": "pmltt-lang",
+  "sources": [
+    {
+      "dir": "src",
+      "subdirs": true
+    }
+  ],
+  "package-specs": [
+    {
+      "module": "es6",
+      "in-source": true
+    }
+  ],
+  "suffix": ".bs.mjs",
+  "bs-dependencies": [
+    "@rescript/react",
+    "@rescript/core"
+  ],
+  "jsx": {
+    "version": 4,
+    "mode": "automatic"
+  },
+  "bsc-flags": [
+    "-open RescriptCore"
+  ]
+}

pmltt-lang/index.html

@@ -0,0 +1,16 @@
+<!DOCTYPE html>
+<html lang="en">
+
+<head>
+  <meta charset="UTF-8" />
+  <link rel="icon" type="image/svg+xml" href="/vite.svg" />
+  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+  <title>ReScript + Vite + React</title>
+</head>
+
+<body>
+  <div id="root"></div>
+  <script type="module" src="/src/Main.bs.mjs"></script>
+</body>
+
+</html>

pmltt-lang/package.json

@@ -0,0 +1,28 @@
+{
+  "name": "pmltt-lang",
+  "private": true,
+  "version": "0.0.0",
+  "type": "module",
+  "scripts": {
+    "res:build": "rescript",
+    "res:clean": "rescript clean",
+    "res:dev": "rescript build -w",
+    "dev": "vite",
+    "build": "vite build",
+    "preview": "vite preview"
+  },
+  "dependencies": {
+    "@rescript/core": "^0.5.0",
+    "@rescript/react": "^0.11.0",
+    "react": "^18.2.0",
+    "react-dom": "^18.2.0",
+    "rescript": "10.1"
+  },
+  "devDependencies": {
+    "@vitejs/plugin-react": "4.0.0",
+    "autoprefixer": "^10.4.15",
+    "postcss": "^8.4.28",
+    "tailwindcss": "^3.3.3",
+    "vite": "^4.4.9"
+  }
+}

pmltt-lang/postcss.config.cjs

@@ -0,0 +1,6 @@
+module.exports = {
+  plugins: {
+    tailwindcss: {},
+    autoprefixer: {},
+  },
+};

pmltt-lang/public/vite.svg

@@ -0,0 +1 @@
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" class="iconify iconify--logos" width="31.88" height="32" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 257"><defs><linearGradient id="IconifyId1813088fe1fbc01fb466" x1="-.828%" x2="57.636%" y1="7.652%" y2="78.411%"><stop offset="0%" stop-color="#41D1FF"></stop><stop offset="100%" stop-color="#BD34FE"></stop></linearGradient><linearGradient id="IconifyId1813088fe1fbc01fb467" x1="43.376%" x2="50.316%" y1="2.242%" y2="89.03%"><stop offset="0%" stop-color="#FFEA83"></stop><stop offset="8.333%" stop-color="#FFDD35"></stop><stop offset="100%" stop-color="#FFA800"></stop></linearGradient></defs><path fill="url(#IconifyId1813088fe1fbc01fb466)" d="M255.153 37.938L134.897 252.976c-2.483 4.44-8.862 4.466-11.382.048L.875 37.958c-2.746-4.814 1.371-10.646 6.827-9.67l120.385 21.517a6.537 6.537 0 0 0 2.322-.004l117.867-21.483c5.438-.991 9.574 4.796 6.877 9.62Z"></path><path fill="url(#IconifyId1813088fe1fbc01fb467)" d="M185.432.063L96.44 17.501a3.268 3.268 0 0 0-2.634 3.014l-5.474 92.456a3.268 3.268 0 0 0 3.997 3.378l24.777-5.718c2.318-.535 4.413 1.507 3.936 3.838l-7.361 36.047c-.495 2.426 1.782 4.5 4.151 3.78l15.304-4.649c2.372-.72 4.652 1.36 4.15 3.788l-11.698 56.621c-.732 3.542 3.979 5.473 5.943 2.437l1.313-2.028l72.516-144.72c1.215-2.423-.88-5.186-3.54-4.672l-25.505 4.922c-2.396.462-4.435-1.77-3.759-4.114l16.646-57.705c.677-2.35-1.37-4.583-3.769-4.113Z"></path></svg>

pmltt-lang/src/App.res

@@ -0,0 +1,22 @@
+open React
+open ReactEvent.Form
+
+@react.component
+let make = () => {
+  let (inputExpr, setInputExpr) = useState(() => "")
+
+  let (interp, setInterp) = useState(() => OneTruth.make())
+
+  <div className="p-6">
+    <h1 className="text-3xl font-semibold"> {"What is this about?"->React.string} </h1>
+    <div>
+      <input
+        className="bg-gray-50 border border-gray-300 text-gray-900 text-sm rounded-lg focus:ring-blue-500 focus:border-blue-500 block w-full p-2.5 dark:bg-gray-700 dark:border-gray-600 dark:placeholder-gray-400 dark:text-white dark:focus:ring-blue-500 dark:focus:border-blue-500"
+        type_="text"
+        value={inputExpr}
+        onChange={event => setInputExpr(currentTarget(event)["value"])}
+      />
+      <pre> {interp->JSON.stringifyAnyWithIndent(2)->Option.getWithDefault("")->string} </pre>
+    </div>
+  </div>
+}

pmltt-lang/src/App.resi

@@ -0,0 +1,2 @@
+@react.component
+let make: unit => Jsx.element

pmltt-lang/src/Button.res

@@ -0,0 +1,7 @@
+// Styling from https://tailwind-elements.com/docs/standard/components/buttons/
+let make = props =>
+  <button
+    {...
+    props}
+    className="inline-block px-6 py-2.5 bg-blue-600 text-white font-medium text-xs leading-tight uppercase rounded shadow-md hover:bg-blue-700 hover:shadow-lg focus:bg-blue-700 focus:shadow-lg focus:outline-none focus:ring-0 active:bg-blue-800 active:shadow-lg transition duration-150 ease-in-out"
+  />

pmltt-lang/src/Button.resi

@@ -0,0 +1 @@
+let make: JsxDOM.domProps => Jsx.element

pmltt-lang/src/Main.res

@@ -0,0 +1,11 @@
+%%raw("import './index.css'")
+
+switch ReactDOM.querySelector("#root") {
+| Some(domElement) =>
+  ReactDOM.Client.createRoot(domElement)->ReactDOM.Client.Root.render(
+    <React.StrictMode>
+      <App />
+    </React.StrictMode>,
+  )
+| None => ()
+}

pmltt-lang/src/assets/react.svg

@@ -0,0 +1 @@
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" role="img" class="iconify iconify--logos" width="35.93" height="32" preserveAspectRatio="xMidYMid meet" viewBox="0 0 256 228"><path fill="#00D8FF" d="M210.483 73.824a171.49 171.49 0 0 0-8.24-2.597c.465-1.9.893-3.777 1.273-5.621c6.238-30.281 2.16-54.676-11.769-62.708c-13.355-7.7-35.196.329-57.254 19.526a171.23 171.23 0 0 0-6.375 5.848a155.866 155.866 0 0 0-4.241-3.917C100.759 3.829 77.587-4.822 63.673 3.233C50.33 10.957 46.379 33.89 51.995 62.588a170.974 170.974 0 0 0 1.892 8.48c-3.28.932-6.445 1.924-9.474 2.98C17.309 83.498 0 98.307 0 113.668c0 15.865 18.582 31.778 46.812 41.427a145.52 145.52 0 0 0 6.921 2.165a167.467 167.467 0 0 0-2.01 9.138c-5.354 28.2-1.173 50.591 12.134 58.266c13.744 7.926 36.812-.22 59.273-19.855a145.567 145.567 0 0 0 5.342-4.923a168.064 168.064 0 0 0 6.92 6.314c21.758 18.722 43.246 26.282 56.54 18.586c13.731-7.949 18.194-32.003 12.4-61.268a145.016 145.016 0 0 0-1.535-6.842c1.62-.48 3.21-.974 4.76-1.488c29.348-9.723 48.443-25.443 48.443-41.52c0-15.417-17.868-30.326-45.517-39.844Zm-6.365 70.984c-1.4.463-2.836.91-4.3 1.345c-3.24-10.257-7.612-21.163-12.963-32.432c5.106-11 9.31-21.767 12.459-31.957c2.619.758 5.16 1.557 7.61 2.4c23.69 8.156 38.14 20.213 38.14 29.504c0 9.896-15.606 22.743-40.946 31.14Zm-10.514 20.834c2.562 12.94 2.927 24.64 1.23 33.787c-1.524 8.219-4.59 13.698-8.382 15.893c-8.067 4.67-25.32-1.4-43.927-17.412a156.726 156.726 0 0 1-6.437-5.87c7.214-7.889 14.423-17.06 21.459-27.246c12.376-1.098 24.068-2.894 34.671-5.345a134.17 134.17 0 0 1 1.386 6.193ZM87.276 214.515c-7.882 2.783-14.16 2.863-17.955.675c-8.075-4.657-11.432-22.636-6.853-46.752a156.923 156.923 0 0 1 1.869-8.499c10.486 2.32 22.093 3.988 34.498 4.994c7.084 9.967 14.501 19.128 21.976 27.15a134.668 134.668 0 0 1-4.877 4.492c-9.933 8.682-19.886 14.842-28.658 17.94ZM50.35 144.747c-12.483-4.267-22.792-9.812-29.858-15.863c-6.35-5.437-9.555-10.836-9.555-15.216c0-9.322 13.897-21.212 37.076-29.293c2.813-.98 5.757-1.905 8.812-2.773c3.204 10.42 7.406 21.315 12.477 32.332c-5.137 11.18-9.399 22.249-12.634 32.792a134.718 134.718 0 0 1-6.318-1.979Zm12.378-84.26c-4.811-24.587-1.616-43.134 6.425-47.789c8.564-4.958 27.502 2.111 47.463 19.835a144.318 144.318 0 0 1 3.841 3.545c-7.438 7.987-14.787 17.08-21.808 26.988c-12.04 1.116-23.565 2.908-34.161 5.309a160.342 160.342 0 0 1-1.76-7.887Zm110.427 27.268a347.8 347.8 0 0 0-7.785-12.803c8.168 1.033 15.994 2.404 23.343 4.08c-2.206 7.072-4.956 14.465-8.193 22.045a381.151 381.151 0 0 0-7.365-13.322Zm-45.032-43.861c5.044 5.465 10.096 11.566 15.065 18.186a322.04 322.04 0 0 0-30.257-.006c4.974-6.559 10.069-12.652 15.192-18.18ZM82.802 87.83a323.167 323.167 0 0 0-7.227 13.238c-3.184-7.553-5.909-14.98-8.134-22.152c7.304-1.634 15.093-2.97 23.209-3.984a321.524 321.524 0 0 0-7.848 12.897Zm8.081 65.352c-8.385-.936-16.291-2.203-23.593-3.793c2.26-7.3 5.045-14.885 8.298-22.6a321.187 321.187 0 0 0 7.257 13.246c2.594 4.48 5.28 8.868 8.038 13.147Zm37.542 31.03c-5.184-5.592-10.354-11.779-15.403-18.433c4.902.192 9.899.29 14.978.29c5.218 0 10.376-.117 15.453-.343c-4.985 6.774-10.018 12.97-15.028 18.486Zm52.198-57.817c3.422 7.8 6.306 15.345 8.596 22.52c-7.422 1.694-15.436 3.058-23.88 4.071a382.417 382.417 0 0 0 7.859-13.026a347.403 347.403 0 0 0 7.425-13.565Zm-16.898 8.101a358.557 358.557 0 0 1-12.281 19.815a329.4 329.4 0 0 1-23.444.823c-7.967 0-15.716-.248-23.178-.732a310.202 310.202 0 0 1-12.513-19.846h.001a307.41 307.41 0 0 1-10.923-20.627a310.278 310.278 0 0 1 10.89-20.637l-.001.001a307.318 307.318 0 0 1 12.413-19.761c7.613-.576 15.42-.876 23.31-.876H128c7.926 0 15.743.303 23.354.883a329.357 329.357 0 0 1 12.335 19.695a358.489 358.489 0 0 1 11.036 20.54a329.472 329.472 0 0 1-11 20.722Zm22.56-122.124c8.572 4.944 11.906 24.881 6.52 51.026c-.344 1.668-.73 3.367-1.15 5.09c-10.622-2.452-22.155-4.275-34.23-5.408c-7.034-10.017-14.323-19.124-21.64-27.008a160.789 160.789 0 0 1 5.888-5.4c18.9-16.447 36.564-22.941 44.612-18.3ZM128 90.808c12.625 0 22.86 10.235 22.86 22.86s-10.235 22.86-22.86 22.86s-22.86-10.235-22.86-22.86s10.235-22.86 22.86-22.86Z"></path></svg>

pmltt-lang/src/index.css

@@ -0,0 +1,3 @@
+@tailwind base;
+@tailwind components;
+@tailwind utilities;

pmltt-lang/src/lang/Core.res

@@ -0,0 +1,20 @@
+type rec arity =
+  | Zero
+  | Combined(array<arity>)
+  | Arrow(arity, arity)
+
+type rec expr =
+  | Var(string)
+  | Abs(string, expr)
+  | App(expr, expr)
+
+type judgment =
+  // Base judgments
+  | IsSet(expr)
+  | AreEqualSets(expr, expr)
+  | InSet(expr, expr)
+  | AreEqualElementsInSet(expr, expr, expr)
+
+  // Proposition stuff
+  | IsProp(expr)
+  | IsTrue(expr)

pmltt-lang/src/lang/Interp.res

@@ -0,0 +1,50 @@
+open Core
+
+type context = {judgments: array<judgment>}
+
+type t = {
+  context: context,
+  knownNames: Map.t<string, expr>,
+  knownSets: Set.t<string>,
+}
+
+// Something that appears in the top or bottom of a derivation
+type hypotheticalJudgment = {
+  assumptions?: context,
+  judgment: judgment,
+}
+
+type rule = {
+  premises: array<hypotheticalJudgment>,
+  conclusions: array<hypotheticalJudgment>,
+}
+
+let makeWithRules = (initialRules: array<rule>) => {
+  let knownSets = ref(Set.make())
+  let knownNames = ref(Map.make())
+  let context = {judgments: []}
+
+  // Evaluate some shit
+  initialRules->Array.forEach(rule => {
+    Js.log2("helloge", rule)
+    ()
+  })
+
+  {
+    context,
+    knownSets: knownSets.contents,
+    knownNames: knownNames.contents,
+  }
+}
+
+// Evaluate an expression without changing the interpreter state
+let eval = (state: t, expr: expr) => {
+  let stop = ref(false)
+  while !stop.contents {
+    stop := true
+    state.context.judgments->Array.forEach(rule => ())
+  }
+
+  //
+  state
+}

pmltt-lang/src/lang/OneTruth.res

@@ -0,0 +1,22 @@
+open Interp
+
+let make = () =>
+  makeWithRules([
+    {
+      premises: [{judgment: InSet(Var("a"), Var("A"))}],
+      conclusions: [{judgment: IsTrue(Var("A"))}],
+    },
+    // Bool
+    {
+      premises: [],
+      conclusions: [{judgment: IsSet(Var("Bool"))}],
+    },
+    {
+      premises: [],
+      conclusions: [{judgment: InSet(Var("true"), Var("Bool"))}],
+    },
+    {
+      premises: [],
+      conclusions: [{judgment: InSet(Var("false"), Var("Bool"))}],
+    },
+  ])

pmltt-lang/tailwind.config.cjs

@@ -0,0 +1,8 @@
+/** @type {import('tailwindcss').Config} */
+module.exports = {
+  content: ["./index.html", "./src/**/*.bs.mjs"],
+  theme: {
+    extend: {},
+  },
+  plugins: [],
+};

pmltt-lang/vite.config.js

@@ -0,0 +1,11 @@
+import { defineConfig } from 'vite'
+import react from '@vitejs/plugin-react'
+
+// https://vitejs.dev/config/
+export default defineConfig({
+  plugins: [
+    react({
+      include: ['**/*.bs.mjs'],
+    }),
+  ],
+});