Add Tree library (#373)

* add tree.js, update index.js

* remove TREE case from loadLib

Author: lywjoel

public/externalLibs/index.js

@@ -32,6 +32,8 @@ function loadAllLibs() {
     // list visualizer
     '/externalLibs/visualizer/KineticJS.js',
     '/externalLibs/visualizer/visualizer.js',
+    // binary tree library
+    '/externalLibs/tree.js',
   ];
 
   for (var i = 0; i < files.length; i++) {

public/externalLibs/tree.js

@@ -0,0 +1,49 @@
+// tree.js: Binary Tree abstraction for M5
+// requires list.js
+
+// Author: Joel Lee
+
+// make_empty_binary_tree returns an empty list
+function make_empty_binary_tree() {
+    return [];
+}
+
+// checks if a given list is a valid binary tree, according to the abstraction
+function is_binary_tree(t) {
+    return (is_empty_binary_tree(t) || 
+        ((length(t) === 3) 
+            && is_binary_tree(left_subtree_of(t)) 
+            && is_binary_tree(right_subtree_of(t))));
+}
+
+// make_binary_tree_node returns a binary tree node composed of the 
+// three elements passed in
+function make_binary_tree_node(left, value, right) {
+    if (!is_binary_tree(left)) {
+        throw new Error("Left subtree is not a valid binary tree");
+    } else if (!is_binary_tree(right)) {
+        throw new Error("Right subtree is not a valid binary tree");
+    }
+    return list(left, value, right);
+}
+
+// is_empty_binary_tree checks if given binary tree node is an empty list
+function is_empty_binary_tree(t) {
+    return is_empty_list(t);
+}
+
+// left_subtree_of returns the left subtree of a given binary tree node
+function left_subtree_of(t) {
+    return list_ref(t, 0);
+}
+
+// value_of returns the value of a given binary tree node
+function value_of(t) {
+    return list_ref(t, 1);
+}
+
+// right_subtree_of returns the right subtree of a given binary tree node
+function right_subtree_of(t) {
+    return list_ref(t, 2);
+}
+