diff --git a/docs/4. Replacing Functions in the Dictionary.ipynb b/docs/4. Replacing Functions in the Dictionary.ipynb
index 16cfeb7..c56d42b 100644
--- a/docs/4. Replacing Functions in the Dictionary.ipynb	
+++ b/docs/4. Replacing Functions in the Dictionary.ipynb	
@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Preamble"
+    "# Replacing Functions in the Dictionary"
    ]
   },
   {
@@ -20,13 +20,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### A long trace"
+    "## A long trace"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {},
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -85,63 +87,33 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Replacing `sum` and `size` with \"compiled\" versions.\n",
+    "## Replacing `size` with a Python version\n",
     "\n",
-    "Both `sum` and `size` are [catamorphisms](https://en.wikipedia.org/wiki/Catamorphism), they each convert a sequence to a single value."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Given a quoted sequence of numbers return the sum.\n",
-      "\n",
-      "sum == 0 swap [+] step\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "J('[sum] help')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0 swap [pop ++] step\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "J('[size] help')"
+    "Both `sum` and `size` each convert a sequence to a single value."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We can use \"compiled\" versions (they're not really compiled in this case, they're hand-written in Python) to speed up evaluation and make the trace more readable.  The `sum` function is already in the library.  It gets shadowed by the definition version above during `initialize()`."
+    "     sum == 0 swap [+] step\n",
+    "    size == 0 swap [pop ++] step"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "An efficient `sum` function is already in the library. But for `size` we can use a “compiled” version hand-written in Python to speed up evaluation and make the trace more readable."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
-    "from joy.library import SimpleFunctionWrapper, primitives\n",
+    "from joy.library import SimpleFunctionWrapper\n",
     "from joy.utils.stack import iter_stack\n",
     "\n",
     "\n",
@@ -152,39 +124,36 @@
     "    n = 0\n",
     "    for _ in iter_stack(sequence):\n",
     "        n += 1\n",
-    "    return n, stack\n",
-    "\n",
-    "\n",
-    "sum_ = next(p for p in primitives if p.name == 'sum')"
+    "    return n, stack"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Now we replace them old versions in the dictionary with the new versions and re-evaluate the expression."
+    "Now we replace the old version in the dictionary with the new version, and re-evaluate the expression."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
-    "old_sum, D['sum'] = D['sum'], sum_\n",
-    "old_size, D['size'] = D['size'], size"
+    "D['size'] = size"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "You can see that `size` and `sum` now execute in a single step."
+    "## A shorter trace\n",
+    "You can see that `size` now executes in a single step."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {