Cleaning up docs.

docs/Quadratic.ipynb

@@ -43,10 +43,19 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Write a straightforward program with variable names.\n",
+    "## Write a straightforward program with variable names.\n",
+    "\n",
     "    b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2\n",
     "\n",
+    "We use `cleave` to compute the sum and difference and then `app2` to finish computing both roots using a quoted program `[2a truediv]` built with `cons`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "### Check it.\n",
+    "Evaluating by hand:\n",
     "\n",
     "     b neg b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2\n",
     "    -b     b sqr 4 a c * * - sqrt [+] [-] cleave a 2 * [truediv] cons app2\n",
@@ -59,7 +68,15 @@
     "    -b -b+sqrt(b^2-4ac)    -b-sqrt(b^2-4ac)    2a    [truediv] cons app2\n",
     "    -b -b+sqrt(b^2-4ac)    -b-sqrt(b^2-4ac)    [2a truediv]         app2\n",
     "    -b -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a\n",
-    "### Codicil\n",
+    "\n",
+    "(Eventually we’ll be able to use e.g. Sympy versions of the Joy commands to do this sort of thing symbolically. This is part of what is meant by a “categorical” language.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Cleanup\n",
     "    -b -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a                          roll< pop\n",
     "       -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a -b                             pop\n",
     "       -b+sqrt(b^2-4ac)/2a -b-sqrt(b^2-4ac)/2a"
@@ -69,7 +86,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Derive a definition.\n",
+    "## Derive a definition.\n",
     "\n",
     "    b neg b           sqr 4 a c        * * - sqrt [+] [-] cleave a       2 * [truediv] cons app2 roll< pop\n",
     "    b    [neg] dupdip sqr 4 a c        * * - sqrt [+] [-] cleave a       2 * [truediv] cons app2 roll< pop\n",
@@ -108,17 +125,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Simplify\n",
+    "## Simplify\n",
     "We can define a `pm` plus-or-minus function:"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": 4,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "define('pm == [+] [-] cleave popdd')"
+    "    pm == [+] [-] cleave popdd"
    ]
   },
   {
@@ -130,7 +145,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -139,7 +154,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -159,27 +174,19 @@
    "metadata": {},
    "source": [
     "### Define a \"native\" `pm` function.\n",
-    "The definition of `pm` above is pretty elegant, but the implementation takes a lot of steps relative to what it's accomplishing.  Since we are likely to use `pm` more than once in the future, let's write a primitive in Python and add it to the dictionary."
+    "The definition of `pm` above is pretty elegant, but the implementation takes a lot of steps relative to what it's accomplishing.  Since we are likely to use `pm` more than once in the future, let's write a primitive in Python and add it to the dictionary.  (This has been done already.)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
-    "from joy.library import SimpleFunctionWrapper\n",
-    "from notebook_preamble import D\n",
-    "\n",
-    "\n",
-    "@SimpleFunctionWrapper\n",
     "def pm(stack):\n",
     "    a, (b, stack) = stack\n",
     "    p, m, = b + a, b - a\n",
-    "    return m, (p, stack)\n",
-    "\n",
-    "\n",
-    "D['pm'] = pm"
+    "    return m, (p, stack)"
    ]
   },
   {
@@ -191,7 +198,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {