Merge pull request #3 from Simponic/godel

L-Program and Godel Numbers
2023-11-17 12:13:30 -07:00 · 2023-11-17 12:13:30 -07:00 · eaca9073eb
commit eaca9073eb
parent 1aefa0f9b1 57a4d43984
14 changed files with 12156 additions and 0 deletions
--- a/.gitignore
+++ b/.gitignore
@ -0,0 +1 @@
+**/.DS_STORE
--- a/godel/codemirror/codemirror.css
+++ b/godel/codemirror/codemirror.css
@ -0,0 +1,488 @@
+/* BASICS */
+
+.CodeMirror {
+  /* Set height, width, borders, and global font properties here */
+  font-family: monospace !important;
+  height: 300px;
+  color: black;
+  direction: ltr;
+}
+
+/* PADDING */
+
+.CodeMirror-lines {
+  padding: 4px 0; /* Vertical padding around content */
+}
+.CodeMirror pre.CodeMirror-line,
+.CodeMirror pre.CodeMirror-line-like {
+  padding: 0 4px; /* Horizontal padding of content */
+}
+
+.CodeMirror-scrollbar-filler,
+.CodeMirror-gutter-filler {
+  background-color: white; /* The little square between H and V scrollbars */
+}
+
+/* GUTTER */
+
+.CodeMirror-gutters {
+  border-right: 1px solid #ddd;
+  background-color: #f7f7f7;
+  white-space: nowrap;
+}
+.CodeMirror-linenumbers {
+}
+.CodeMirror-linenumber {
+  padding: 0 3px 0 5px;
+  min-width: 20px;
+  text-align: right;
+  color: #999;
+  white-space: nowrap;
+}
+
+.CodeMirror-guttermarker {
+  color: black;
+}
+.CodeMirror-guttermarker-subtle {
+  color: #999;
+}
+
+/* CURSOR */
+
+.CodeMirror-cursor {
+  border-left: 1px solid black;
+  border-right: none;
+  width: 0;
+}
+/* Shown when moving in bi-directional text */
+.CodeMirror div.CodeMirror-secondarycursor {
+  border-left: 1px solid silver;
+}
+.cm-fat-cursor .CodeMirror-cursor {
+  width: auto;
+  border: 0 !important;
+  background: #7e7;
+}
+.cm-fat-cursor div.CodeMirror-cursors {
+  z-index: 1;
+}
+.cm-fat-cursor .CodeMirror-line::selection,
+.cm-fat-cursor .CodeMirror-line > span::selection,
+.cm-fat-cursor .CodeMirror-line > span > span::selection {
+  background: transparent;
+}
+.cm-fat-cursor .CodeMirror-line::-moz-selection,
+.cm-fat-cursor .CodeMirror-line > span::-moz-selection,
+.cm-fat-cursor .CodeMirror-line > span > span::-moz-selection {
+  background: transparent;
+}
+.cm-fat-cursor {
+  caret-color: transparent;
+}
+@-moz-keyframes blink {
+  0% {
+  }
+  50% {
+    background-color: transparent;
+  }
+  100% {
+  }
+}
+@-webkit-keyframes blink {
+  0% {
+  }
+  50% {
+    background-color: transparent;
+  }
+  100% {
+  }
+}
+@keyframes blink {
+  0% {
+  }
+  50% {
+    background-color: transparent;
+  }
+  100% {
+  }
+}
+
+/* Can style cursor different in overwrite (non-insert) mode */
+.CodeMirror-overwrite .CodeMirror-cursor {
+}
+
+.cm-tab {
+  display: inline-block;
+  text-decoration: inherit;
+}
+
+.CodeMirror-rulers {
+  position: absolute;
+  left: 0;
+  right: 0;
+  top: -50px;
+  bottom: 0;
+  overflow: hidden;
+}
+.CodeMirror-ruler {
+  border-left: 1px solid #ccc;
+  top: 0;
+  bottom: 0;
+  position: absolute;
+}
+
+/* DEFAULT THEME */
+
+.cm-s-default .cm-header {
+  color: blue;
+}
+.cm-s-default .cm-quote {
+  color: #090;
+}
+.cm-negative {
+  color: #d44;
+}
+.cm-positive {
+  color: #292;
+}
+.cm-header,
+.cm-strong {
+  font-weight: bold;
+}
+.cm-em {
+  font-style: italic;
+}
+.cm-link {
+  text-decoration: underline;
+}
+.cm-strikethrough {
+  text-decoration: line-through;
+}
+
+.cm-s-default .cm-keyword {
+  color: #708;
+}
+.cm-s-default .cm-atom {
+  color: #219;
+}
+.cm-s-default .cm-number {
+  color: #164;
+}
+.cm-s-default .cm-def {
+  color: #00f;
+}
+.cm-s-default .cm-variable,
+.cm-s-default .cm-punctuation,
+.cm-s-default .cm-property,
+.cm-s-default .cm-operator {
+}
+.cm-s-default .cm-variable-2 {
+  color: #05a;
+}
+.cm-s-default .cm-variable-3,
+.cm-s-default .cm-type {
+  color: #085;
+}
+.cm-s-default .cm-comment {
+  color: #a50;
+}
+.cm-s-default .cm-string {
+  color: #a11;
+}
+.cm-s-default .cm-string-2 {
+  color: #f50;
+}
+.cm-s-default .cm-meta {
+  color: #555;
+}
+.cm-s-default .cm-qualifier {
+  color: #555;
+}
+.cm-s-default .cm-builtin {
+  color: #30a;
+}
+.cm-s-default .cm-bracket {
+  color: #997;
+}
+.cm-s-default .cm-tag {
+  color: #170;
+}
+.cm-s-default .cm-attribute {
+  color: #00c;
+}
+.cm-s-default .cm-hr {
+  color: #999;
+}
+.cm-s-default .cm-link {
+  color: #00c;
+}
+
+.cm-s-default .cm-error {
+  color: #f00;
+}
+.cm-invalidchar {
+  color: #f00;
+}
+
+.CodeMirror-composing {
+  border-bottom: 2px solid;
+}
+
+/* Default styles for common addons */
+
+div.CodeMirror span.CodeMirror-matchingbracket {
+  color: #0b0;
+}
+div.CodeMirror span.CodeMirror-nonmatchingbracket {
+  color: #a22;
+}
+.CodeMirror-matchingtag {
+  background: rgba(255, 150, 0, 0.3);
+}
+.CodeMirror-activeline-background {
+  background: #e8f2ff;
+}
+
+/* STOP */
+
+/* The rest of this file contains styles related to the mechanics of
+   the editor. You probably shouldn't touch them. */
+
+.CodeMirror {
+  position: relative;
+  overflow: hidden;
+  background: white;
+}
+
+.CodeMirror-scroll {
+  overflow: scroll !important; /* Things will break if this is overridden */
+  /* 50px is the magic margin used to hide the element's real scrollbars */
+  /* See overflow: hidden in .CodeMirror */
+  margin-bottom: -50px;
+  margin-right: -50px;
+  padding-bottom: 50px;
+  height: 100%;
+  outline: none; /* Prevent dragging from highlighting the element */
+  position: relative;
+  z-index: 0;
+}
+.CodeMirror-sizer {
+  position: relative;
+  border-right: 50px solid transparent;
+}
+
+/* The fake, visible scrollbars. Used to force redraw during scrolling
+   before actual scrolling happens, thus preventing shaking and
+   flickering artifacts. */
+.CodeMirror-vscrollbar,
+.CodeMirror-hscrollbar,
+.CodeMirror-scrollbar-filler,
+.CodeMirror-gutter-filler {
+  position: absolute;
+  z-index: 6;
+  display: none;
+  outline: none;
+}
+.CodeMirror-vscrollbar {
+  right: 0;
+  top: 0;
+  overflow-x: hidden;
+  overflow-y: scroll;
+}
+.CodeMirror-hscrollbar {
+  bottom: 0;
+  left: 0;
+  overflow-y: hidden;
+  overflow-x: scroll;
+}
+.CodeMirror-scrollbar-filler {
+  right: 0;
+  bottom: 0;
+}
+.CodeMirror-gutter-filler {
+  left: 0;
+  bottom: 0;
+}
+
+.CodeMirror-gutters {
+  position: absolute;
+  left: 0;
+  top: 0;
+  min-height: 100%;
+  z-index: 3;
+}
+.CodeMirror-gutter {
+  white-space: normal;
+  height: 100%;
+  display: inline-block;
+  vertical-align: top;
+  margin-bottom: -50px;
+}
+.CodeMirror-gutter-wrapper {
+  position: absolute;
+  z-index: 4;
+  background: none !important;
+  border: none !important;
+}
+.CodeMirror-gutter-background {
+  position: absolute;
+  top: 0;
+  bottom: 0;
+  z-index: 4;
+}
+.CodeMirror-gutter-elt {
+  position: absolute;
+  cursor: default;
+  z-index: 4;
+}
+.CodeMirror-gutter-wrapper ::selection {
+  background-color: transparent;
+}
+.CodeMirror-gutter-wrapper ::-moz-selection {
+  background-color: transparent;
+}
+
+.CodeMirror-lines {
+  cursor: text;
+  min-height: 1px; /* prevents collapsing before first draw */
+}
+.CodeMirror pre.CodeMirror-line,
+.CodeMirror pre.CodeMirror-line-like {
+  /* Reset some styles that the rest of the page might have set */
+  -moz-border-radius: 0;
+  -webkit-border-radius: 0;
+  border-radius: 0;
+  border-width: 0;
+  background: transparent;
+  font-family: inherit;
+  font-size: inherit;
+  margin: 0;
+  white-space: pre;
+  word-wrap: normal;
+  line-height: inherit;
+  color: inherit;
+  z-index: 2;
+  position: relative;
+  overflow: visible;
+  -webkit-tap-highlight-color: transparent;
+  -webkit-font-variant-ligatures: contextual;
+  font-variant-ligatures: contextual;
+}
+.CodeMirror-wrap pre.CodeMirror-line,
+.CodeMirror-wrap pre.CodeMirror-line-like {
+  word-wrap: break-word;
+  white-space: pre-wrap;
+  word-break: normal;
+}
+
+.CodeMirror-linebackground {
+  position: absolute;
+  left: 0;
+  right: 0;
+  top: 0;
+  bottom: 0;
+  z-index: 0;
+}
+
+.CodeMirror-linewidget {
+  position: relative;
+  z-index: 2;
+  padding: 0.1px; /* Force widget margins to stay inside of the container */
+}
+
+.CodeMirror-widget {
+}
+
+.CodeMirror-rtl pre {
+  direction: rtl;
+}
+
+.CodeMirror-code {
+  outline: none;
+}
+
+/* Force content-box sizing for the elements where we expect it */
+.CodeMirror-scroll,
+.CodeMirror-sizer,
+.CodeMirror-gutter,
+.CodeMirror-gutters,
+.CodeMirror-linenumber {
+  -moz-box-sizing: content-box;
+  box-sizing: content-box;
+}
+
+.CodeMirror-measure {
+  position: absolute;
+  width: 100%;
+  height: 0;
+  overflow: hidden;
+  visibility: hidden;
+}
+
+.CodeMirror-cursor {
+  position: absolute;
+  pointer-events: none;
+}
+.CodeMirror-measure pre {
+  position: static;
+}
+
+div.CodeMirror-cursors {
+  visibility: hidden;
+  position: relative;
+  z-index: 3;
+}
+div.CodeMirror-dragcursors {
+  visibility: visible;
+}
+
+.CodeMirror-focused div.CodeMirror-cursors {
+  visibility: visible;
+}
+
+.CodeMirror-selected {
+  background: #d9d9d9;
+}
+.CodeMirror-focused .CodeMirror-selected {
+  background: #d7d4f0;
+}
+.CodeMirror-crosshair {
+  cursor: crosshair;
+}
+.CodeMirror-line::selection,
+.CodeMirror-line > span::selection,
+.CodeMirror-line > span > span::selection {
+  background: #d7d4f0;
+}
+.CodeMirror-line::-moz-selection,
+.CodeMirror-line > span::-moz-selection,
+.CodeMirror-line > span > span::-moz-selection {
+  background: #d7d4f0;
+}
+
+.cm-searching {
+  background-color: #ffa;
+  background-color: rgba(255, 255, 0, 0.4);
+}
+
+/* Used to force a border model for a node */
+.cm-force-border {
+  padding-right: 0.1px;
+}
+
+@media print {
+  /* Hide the cursor when printing */
+  .CodeMirror div.CodeMirror-cursors {
+    visibility: hidden;
+  }
+}
+
+/* See issue #2901 */
+.cm-tab-wrap-hack:after {
+  content: "";
+}
+
+/* Help users use markselection to safely style text background */
+span.CodeMirror-selectedtext {
+  background: none;
+}
--- a/godel/codemirror/codemirror.js
+++ b/godel/codemirror/codemirror.js
--- a/godel/css/styles.css
+++ b/godel/css/styles.css
@ -0,0 +1,82 @@
+* {
+  margin: 0;
+}
+
+button {
+  background: #bbbbbb;
+  border: 1px solid white;
+  border-radius: 0.2rem;
+  padding: 0.3rem;
+  display: inline-block;
+  cursor: pointer;
+}
+
+button:hover {
+  background: #cccccc;
+}
+
+body {
+  font-family: "Trebuchet MS", sans-serif;
+  background-color: #aaaaaa;
+}
+
+.container {
+  display: flex;
+  width: 90%;
+  margin-left: auto;
+  margin-right: auto;
+  flex-direction: column;
+  gap: 1rem;
+
+  padding: 2rem;
+}
+
+.textarea-container {
+  display: flex;
+  flex-direction: column;
+  gap: 1rem;
+  box-shadow: 5px 5px 5px #666666;
+  border: 2px solid white;
+  border-radius: 0.25rem;
+  padding: 1rem;
+  flex: 1;
+}
+
+.source-container {
+  display: flex;
+  flex-direction: row;
+  gap: 1rem;
+  height: 100%;
+}
+
+textarea {
+  border-radius: 0.25rem;
+}
+
+.CodeMirror {
+  height: 50vh;
+}
+
+.error {
+  color: red;
+}
+
+.success {
+  color: green;
+}
+
+hr {
+  border-top: 2px solid black;
+  border-bottom: none;
+}
+
+pre {
+  white-space: pre-wrap;
+  word-wrap: break-word;
+}
+
+@media only screen and (max-width: 1000px) {
+  .source-container {
+    flex-direction: column;
+  }
+}
--- a/godel/grammar.peg
+++ b/godel/grammar.peg
@ -0,0 +1,77 @@
+Program = lines: (ProgramInstruction / (_/[\n]))* {
+  return { instructions: lines.filter((line) => typeof line !== "string" || line.trim() != "") };
+}
+
+ProgramInstruction = _? instruction: (LabeledInstruction / Instruction) _? [\n]? {
+  let x = 0;
+  let y = 0;
+  if (instruction.label) {
+    x = instruction.label.godel;
+    y = instruction.instruction.godel;
+  } else {
+    y = instruction.godel;
+  }
+  return { instruction, godel: ((2 ** x) * ((2 * y) + 1) - 1) };
+}
+
+LabeledInstruction = label:Label _ instruction:Instruction {
+  return { label, instruction };
+}
+
+Label = "[" _? label:LABEL_V _? "]" {
+  return label;
+}
+  
+Instruction = conditional: Conditional { return { conditional, godel: conditional.godel }; } 
+  / assignment: Assignment { return { assignment, godel: assignment.godel }; }
+  / goto: Goto { return { goto, godel: goto.godel }; }
+
+Goto = GOTO _ label: LABEL_V {
+  return { label, godel: label.godel + 2 };
+}
+
+Conditional = "IF" _ variable: VAR  _? "!=" _? "0" _ goto: Goto {
+  const y = variable.godel - 1;
+  const x = goto.godel;
+  return { variable, goto, godel: ((2 ** x) * ((2 * y) + 1) - 1) };
+}
+
+Assignment = variable: VAR _ "<-" _ expr: Expression {
+  if (expr.left.symbol != variable.symbol) {
+    error("left hand variable must match right hand");
+  }
+  const x = expr.instructionNumber;
+  const y = variable.godel - 1;
+  return { variable, expr, godel: ((2 ** x) * ((2 * y) + 1) - 1) };
+}
+
+Expression = left: VAR _ opr: OPERATION _ "1" {
+  const instructionNumber = { "+" : 1, "-" : 2 }[opr];
+  return { left, opr, instructionNumber };
+} / left: VAR  {
+  return { left, instructionNumber: 0 };
+}
+
+VAR = symbol:"Y" { return { symbol, godel: 1 }; } / symbol:("X" / "Z") ind:Integer+ {
+  const index = parseInt(ind);
+  const order = ["X", "Z"];
+  const godel = index * order.length + order.indexOf(symbol);
+  return { symbol: symbol + ind, godel };
+}
+
+GOTO = "GOTO"
+
+OPERATION = "+" / "-"
+
+LABEL_V = symbol:END_LABEL { return symbol } / symbol:[A-E] ind:Integer+ {
+  const index = parseInt(ind);
+  const godel = (symbol.charCodeAt(0) - "A".charCodeAt(0) + 1) + 5*(index-1);
+  return { symbol: symbol + ind, godel };
+}
+
+END_LABEL = "E1"
+
+Integer "integer"
+  = [0-9]+ { return parseInt(text(), 10); }
+
+_ "whitespace" = [ \t]+ {  }
--- a/godel/index.html
+++ b/godel/index.html
@ -0,0 +1,96 @@
+<!DOCTYPE html>
+<html>
+<head>
+  <title>Liz's L-Program Compiler</title>
+  <link rel="stylesheet" type="text/css" href=
+  "codemirror/codemirror.css">
+  <link rel="stylesheet" type="text/css" href="css/styles.css">
+</head>
+<body>
+  <div class="container">
+    <h1>Liz's L-Program Compiler</h1>
+    <p><i>Developed for Kulyukin's CS5000</i></p>
+    <hr>
+    <div class="source-container">
+      <div class="textarea-container">
+        <h3>L Source</h3>
+        <textarea id=
+        "instructions">// 0. primitive instructions only
+// 1. labels match the regex [A-E](:digit:)+.
+// 2. variables are initialized to zero and match 
+//    (Y | (X|Z)(:digit:)+).
+// 3. instructions must be delimited by a newline.
+// 4. anything following the comment token "//" up to a
+//    newline are ignored.
+// 5. by default, a computation that takes more than 500_000
+//    "procedures", it will be halted.
+// 6. the implicit exit label "E1" exists; thus to exit
+//    prematurely, "GOTO E1".
+// 7. input your initial snapshot in the "variables" map
+//    on the Program in the compiled JS output
+// 8. for a more detailed view on the grammar, it's at
+//    /godel/grammar.peg
+
+// THIS PROGRAM COMPUTES X1 + X2
+
+// Y &lt;- X1
+[ A1 ] IF X1 != 0 GOTO A2
+       GOTO B1
+[ A2 ] X1 &lt;- X1 - 1
+       Y &lt;- Y + 1
+       GOTO A1
+
+// Z1 &lt;- X2
+[ B1 ] IF X2 != 0 GOTO B2
+       GOTO C1
+[ B2 ] X2 &lt;- X2 - 1
+       Z1 &lt;- Z1 + 1
+       GOTO B1
+
+// Y &lt;- Y + Z1
+[ C1 ] IF Z1 != 0 GOTO C2
+       GOTO E1
+[ C2 ] Z1 &lt;- Z1 - 1
+       Y &lt;- Y + 1
+       GOTO C1</textarea>
+        <div>
+          <button id="compile">Compile</button> <button id=
+          "copy">Copy</button>
+        </div>
+        <div>
+          <span style="margin-left: 0.5rem" id=
+          "compile_status"></span>
+        </div>
+      </div>
+      <div class="textarea-container">
+        <h3>Compiled JS</h3>
+        <textarea id="compiled"></textarea>
+        <div>
+          <button id="eval">Eval</button>
+        </div>
+        <div>
+          <span style="margin-left: 0.5rem" id=
+          "eval_status"></span>
+        </div>
+      </div>
+    </div>
+    <div class="textarea-container">
+      <h3>Godel</h3>
+      <p>Sequence:</p>
+      <pre id="godel_sequence"></pre>
+      <div>
+        <p>Number: <button id="godel_number_comp" style=
+        "display: none">Compute (this might take a
+        while)</button></p>
+      </div>
+      <pre id="godel_number"></pre>
+    </div>
+  </div>
+  <script src="codemirror/codemirror.js"></script> 
+  <script src="js-beautify/js-beautify.js"></script> 
+  <script src="js/observable.js"></script> 
+  <script src="js/parser.js"></script> 
+  <script src="js/compiler.js"></script> 
+  <script src="js/main.js"></script>
+</body>
+</html>
--- a/godel/js-beautify/js-beautify.js
+++ b/godel/js-beautify/js-beautify.js
--- a/godel/js/compiler.js
+++ b/godel/js/compiler.js
@ -0,0 +1,182 @@
+class StringBuilder {
+  constructor() {
+    this.stringPieces = [];
+  }
+  add(s) {
+    this.stringPieces.push(s);
+  }
+  build() {
+    return this.stringPieces.join("");
+  }
+}
+
+const compileGoto = (gotoNode, stringBuilder) => {
+  stringBuilder.add(`this.followGoto("${gotoNode.label.symbol}");\nreturn;\n`);
+};
+
+const compileConditional = (conditionalNode, stringBuilder) => {
+  const {
+    variable: { symbol: variable },
+    goto: gotoNode,
+  } = conditionalNode;
+
+  stringBuilder.add(`if (this.get("${variable}") != 0) {\n`);
+  compileGoto(gotoNode, stringBuilder);
+  stringBuilder.add(`}\n`);
+};
+
+const compileAssignment = (assignmentNode, stringBuilder) => {
+  const {
+    variable: { symbol: variable },
+    expr,
+  } = assignmentNode;
+  if (expr.opr) {
+    if (expr.opr == "+") stringBuilder.add(`this.addOne("${variable}");\n`);
+    else if (expr.opr == "-")
+      stringBuilder.add(`this.subtractOne("${variable}");\n`);
+  } else {
+    stringBuilder.add("// noop \n");
+  }
+};
+
+const compileInstruction = (instruction, stringBuilder) => {
+  if (instruction.goto) {
+    compileGoto(instruction.goto, stringBuilder);
+    return; // ignore unreachable addition to instructionPointer
+  }
+
+  if (instruction.conditional) {
+    compileConditional(instruction.conditional, stringBuilder);
+  } else if (instruction.assignment) {
+    compileAssignment(instruction.assignment, stringBuilder);
+  }
+
+  stringBuilder.add("this.instructionPointer++;\n");
+};
+
+const compile = (ast) => {
+  const godelSequence = [];
+
+  const stringBuilder = new StringBuilder();
+  stringBuilder.add(`
+    class Program {
+      constructor() {
+        this.variables = new Map(); // variable -> natural number val
+        this.labelInstructions = new Map(); // labels to instruction indices
+        this.instructions = new Map(); // instruction indices to procedures
+
+        this.instructions.set(0, () => this.main());
+        this.instructionPointer = 0;
+        this.variables.set("Y", 0);
+
+        // -- program-specific state init --
+        this.finalInstruction = ${
+          ast.instructions.length + 1
+        }; // instruction of the implied "exit" label
+        // "E1" is the exit label
+        this.labelInstructions.set("E1", this.finalInstruction); 
+      }
+
+      get(variable) {
+        if (!this.variables.has(variable)) {
+          this.variables.set(variable, 0);
+        }
+        return this.variables.get(variable);
+      }
+
+      addOne(variable) {
+        const val = this.get(variable);
+        this.variables.set(variable, val + 1);
+      }
+
+      subtractOne(variable) {
+        const val = this.get(variable);
+        this.variables.set(variable, val - 1);
+      }
+
+      followGoto(label) {
+        this.instructionPointer = this.labelInstructions.get(label);
+      }
+
+      step() {
+        if (!this.isCompleted()) {
+          const procedure = this.instructions.get(this.instructionPointer);
+          procedure();
+ 
+        }
+        return this.instructionPointer;
+      }
+
+      isCompleted() {
+        return this.instructionPointer == this.finalInstruction;
+      }
+
+      getResult() {
+        return this.variables.get("Y");
+      }
+
+      run(maxIter=500_000) {
+        let iter = 0;
+        while (!this.isCompleted() && (++iter) < maxIter) this.step();
+        if (iter < maxIter) {
+          return this.getResult();
+        }
+        throw new Error("Too many iterations. To resolve, please ask"
+           + " Turing how we can find if a program will halt during compilation.");
+      }
+
+      main() {
+`);
+
+  stringBuilder.add("// -- build label -> instruction map --\n");
+  for (let i = 0; i < ast.instructions.length; i++) {
+    const instruction = ast.instructions[i];
+    godelSequence.push(instruction.godel);
+
+    const line = instruction.instruction;
+    const instructionIdx = i + 1;
+    if (line.label) {
+      const symbol = line.label.symbol;
+      stringBuilder.add(
+        `this.instructions.set(${instructionIdx}, () => this.${symbol}());\n`
+      );
+      stringBuilder.add(
+        `this.labelInstructions.set("${symbol}", ${instructionIdx});\n`
+      );
+    }
+  }
+
+  stringBuilder.add("// -- compiled instructions --\n");
+  for (let i = 0; i < ast.instructions.length; i++) {
+    let instruction = ast.instructions[i].instruction;
+    const instructionIdx = i + 1;
+    if (instruction.label) {
+      const symbol = instruction.label.symbol;
+
+      stringBuilder.add(
+        `  this.followGoto("${symbol}");\n}\n\n${symbol}() {\n`
+      );
+      stringBuilder.add(`this.instructionPointer = ${instructionIdx};\n`);
+      instruction = instruction.instruction;
+    }
+
+    compileInstruction(instruction, stringBuilder);
+  }
+
+  stringBuilder.add(`  }\n}\n`);
+  stringBuilder.add("// -- \n");
+  stringBuilder.add("const program = new Program();\n\n");
+  stringBuilder.add("// !! set the initial Snapshot here !!\n");
+  stringBuilder.add('// program.variables.set("X1", 2);\n\n');
+  stringBuilder.add("program.run();\n");
+  stringBuilder.add("console.log(program.variables);\n");
+  stringBuilder.add("program.getResult();\n");
+
+  return {
+    js: js_beautify(stringBuilder.build(), {
+      indent_size: 2,
+      wrap_line_length: 100,
+    }),
+    godelSequence,
+  };
+};
--- a/godel/js/godelWorker.js
+++ b/godel/js/godelWorker.js
@ -0,0 +1,27 @@
+const isPrime = (n) =>
+  !Array(Math.ceil(Math.sqrt(n)))
+    .fill(0)
+    .map((_, i) => i + 2) // first prime is 2
+    .some((i) => n !== i && n % i === 0);
+
+const primesCache = [2];
+const p = (i) => {
+  if (primesCache.length <= i) {
+    let x = primesCache.at(-1);
+    while (primesCache.length <= i) {
+      if (isPrime(++x)) primesCache.push(x);
+    }
+  }
+  return primesCache.at(i - 1);
+};
+
+const computeGodelNumber = (godelSequence) =>
+  godelSequence.reduce((acc, num, i) => {
+    const prime = p(i + 1);
+    return BigInt(acc) * BigInt(prime) ** BigInt(num);
+  }, 1) - BigInt(1);
+
+self.addEventListener("message", (e) => {
+  const godelNumber = computeGodelNumber(e.data);
+  postMessage(godelNumber);
+});
--- a/godel/js/main.js
+++ b/godel/js/main.js
@ -0,0 +1,175 @@
+const MESSAGES = {
+  COMPILE: "COMPILE",
+  COMPILE_RESULT: "COMPILE_RESULT",
+  EVAL: "EVAL",
+  EVAL_STATUS: "EVAL_RESULT",
+};
+
+// -- the "real" code --
+
+const state = new Observable();
+
+const prepareSource = (text) => text.replaceAll(/\/\/.*/g, "").trim();
+
+const main = () => {
+  let program;
+
+  state.subscribe((msg) => {
+    if (msg.type == MESSAGES.COMPILE) {
+      const { value } = msg;
+      const source = prepareSource(value);
+
+      try {
+        const ast = parser.parse(source);
+        const { js, godelSequence } = compile(ast);
+
+        state.notify({
+          type: MESSAGES.COMPILE_RESULT,
+          success: true,
+          js,
+          godelSequence,
+        });
+      } catch (e) {
+        console.error(e);
+        state.notify({
+          type: MESSAGES.COMPILE_RESULT,
+          error: e.toString(),
+        });
+      }
+    }
+    if (msg.type == MESSAGES.EVAL) {
+      const source = compiledEditorEl.getValue();
+      try {
+        const result = eval(source);
+        state.notify({
+          type: MESSAGES.EVAL_RESULT,
+          success: true,
+          value: result,
+        });
+      } catch (e) {
+        state.notify({
+          type: MESSAGES.EVAL_RESULT,
+          error: e.toString(),
+        });
+      }
+    }
+  });
+};
+main();
+
+// -- a bit of some hacky ui code --
+
+const codeMirrorConfig = {
+  lineNumbers: true,
+};
+const instructionsEl = document.getElementById("instructions");
+const instructionsEditorEl = CodeMirror.fromTextArea(
+  instructionsEl,
+  codeMirrorConfig
+);
+
+const compileButton = document.getElementById("compile");
+const evalButton = document.getElementById("eval");
+const evalStatusEl = document.getElementById("eval_status");
+const compileStatusEl = document.getElementById("compile_status");
+const compiledEl = document.getElementById("compiled");
+const compiledEditorEl = CodeMirror.fromTextArea(compiledEl, codeMirrorConfig);
+const godelSequenceEl = document.getElementById("godel_sequence");
+const godelNumberEl = document.getElementById("godel_number");
+const godelNumberComputeBtn = document.getElementById("godel_number_comp");
+const copyStateButton = document.getElementById("copy");
+
+// hackily copy the program state and put it in the clipboard
+copyStateButton.addEventListener("click", () => {
+  const instructions = btoa(instructionsEditorEl.getValue());
+
+  navigator.clipboard
+    .writeText(
+      window.location.href.split("?")[0] + `?instructions=${instructions}`
+    )
+    .then(() => alert("copied to clipboard"));
+});
+
+state.subscribe((msg) => {
+  if (msg.type == MESSAGES.COMPILE_RESULT) {
+    evalStatusEl.classList.remove("error");
+    evalStatusEl.classList.remove("success");
+    evalStatusEl.innerHTML = "";
+
+    if (msg.success) {
+      const { js, godelSequence } = msg;
+      compiledEditorEl.setValue(js);
+
+      godelSequenceEl.innerHTML = `[${godelSequence.join(", ")}]`;
+      godelNumberComputeBtn.style.display = "inline";
+
+      compileStatusEl.classList.add("success");
+      compileStatusEl.classList.remove("error");
+      compileStatusEl.innerHTML = `Successful compile at ${new Date().toLocaleString()}!`;
+    } else if (msg.error) {
+      compiledEditorEl.setValue("");
+      godelSequenceEl.innerHTML = "";
+      godelNumberEl.innerHTML = "";
+      godelNumberComputeBtn.style.display = "none";
+
+      compileStatusEl.classList.remove("success");
+      compileStatusEl.classList.add("error");
+      compileStatusEl.innerHTML = msg.error;
+    }
+  }
+});
+
+state.subscribe((msg) => {
+  if (msg.type == MESSAGES.COMPILE_RESULT) {
+    if (msg.success) {
+      const { godelSequence } = msg;
+
+      godelNumberComputeBtn.onclick = () => {
+        godelNumberEl.innerHTML = "working...";
+
+        const worker = new Worker("js/godelWorker.js");
+
+        worker.addEventListener("message", (e) => {
+          const godelNumber = e.data;
+          godelNumberEl.innerHTML = godelNumber.toString();
+        });
+
+        worker.postMessage(godelSequence);
+      };
+    } else if (msg.error) {
+      godelNumberComputeBtn.onclick = () => {};
+    }
+  }
+});
+
+state.subscribe((msg) => {
+  if (msg.type == MESSAGES.EVAL_RESULT) {
+    if (msg.success) {
+      evalStatusEl.classList.add("success");
+      evalStatusEl.classList.remove("error");
+      evalStatusEl.innerHTML = `Result: ${msg.value}`;
+    } else if (msg.error) {
+      evalStatusEl.classList.remove("success");
+      evalStatusEl.classList.add("error");
+      evalStatusEl.innerHTML = msg.error;
+    }
+  }
+});
+
+const urlParams = new URLSearchParams(window.location.search);
+if (urlParams.get("instructions")) {
+  instructionsEditorEl.setValue(atob(urlParams.get("instructions")));
+}
+
+compileButton.addEventListener("click", () => {
+  state.notify({
+    type: MESSAGES.COMPILE,
+    value: instructionsEditorEl.getValue(),
+  });
+});
+
+evalButton.addEventListener("click", () => {
+  state.notify({
+    type: MESSAGES.EVAL,
+  });
+});
--- a/godel/js/observable.js
+++ b/godel/js/observable.js
@ -0,0 +1,14 @@
+class Observable {
+  constructor() {
+    this.observers = [];
+  }
+  subscribe(f) {
+    this.observers.push(f);
+  }
+  unsubscribe(f) {
+    this.observers = this.observers.filter((subscriber) => subscriber !== f);
+  }
+  notify(data) {
+    this.observers.forEach((observer) => observer(data));
+  }
+}
--- a/godel/js/parser.js
+++ b/godel/js/parser.js
--- a/godel/js/turing_machine.js
+++ b/godel/js/turing_machine.js
@ -0,0 +1,72 @@
+class TuringMachine {
+  constructor(tape = [], rules = [], initialState = "q0", acceptState = "f") {
+    this.tape = tape;
+    this.rules = this.parseRules(rules);
+    this.state = initialState;
+    this.head = 0;
+    this.acceptState = acceptState;
+
+    this.iteration = 0;
+  }
+
+  getStateStatus() {
+    return `State: ${this.state}, Step: ${this.iteration}`;
+  }
+
+  getHead() {
+    return this.head;
+  }
+
+  getState() {
+    return this.state;
+  }
+
+  getTapeAtCell(idx) {
+    return this.tape[idx];
+  }
+
+  setTapeAtCell(idx, val) {
+    this.tape[idx] = val;
+  }
+
+  isAccepting() {
+    return this.state == this.acceptState;
+  }
+
+  parseRules(rules) {
+    const parsedRules = {};
+    for (const [currentState, readSymbol, action, newState] of rules) {
+      const key = `${currentState},${readSymbol}`;
+      const value = `${newState},${action}`;
+      parsedRules[key] = value;
+    }
+    return parsedRules;
+  }
+
+  step() {
+    const currentSymbol = this.tape[this.head];
+    const key = `${this.state},${currentSymbol}`;
+    if (!(key in this.rules)) {
+      return false;
+    }
+    const rule = this.rules[key];
+    const [newState, action] = rule.split(",");
+
+    this.state = newState;
+    this.iteration++;
+
+    if (action === "R") {
+      this.head += 1;
+    } else if (action === "L") {
+      this.head -= 1;
+    } else {
+      this.tape[this.head] = action;
+    }
+
+    if (this.isAccepting()) {
+      return false;
+    }
+
+    return this.head >= 0 && this.head < this.tape.length;
+  }
+}
--- a/index.html
+++ b/index.html
@ -44,6 +44,17 @@
          </div>
        </a>

+        <a class="project" href="/godel/">
+          <div class="project-logo-container">
+            <i class="fa-solid fa-microchip"></i>
+          </div>
+
+          <div class="project-body">
+            <h1>Godel Explorer</h1>
+            <p>Compile L-Programs into JavaScript and Godel numbers.</p>
+          </div>
+        </a>
+
        <a class="project" href="/turing-machine/">
          <div class="project-logo-container">
            <i class="fa-solid fa-tape"></i>