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docs/Newton-Raphson.ipynb

@@ -87,17 +87,6 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "define('codireco == cons dip rest cons')\n",
-    "define('make_generator == [codireco] ccons')\n",
-    "define('ccons == cons cons')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
    "metadata": {
     "scrolled": true
    },
@@ -108,7 +97,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -132,7 +121,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -153,11 +142,11 @@
    "source": [
     "## Finding Consecutive Approximations within a Tolerance\n",
     "\n",
+    "From [\"Why Functional Programming Matters\" by John Hughes](https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf):\n",
+    "\n",
     "\n",
     "> The remainder of a square root finder is a function _within_, which takes a tolerance and a list of approximations and looks down the list for two successive approximations that differ by no more than the given tolerance.\n",
     "\n",
-    "From [\"Why Functional Programming Matters\" by John Hughes](https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf)\n",
-    "\n",
     "(And note that by “list” he means a lazily-evaluated list.)\n",
     "\n",
     "Using the _output_ `[a G]` of the above generator for square root approximations, and further assuming that the first term a has been generated already and epsilon ε is handy on the stack...\n",
@@ -189,7 +178,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -210,7 +199,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -226,8 +215,8 @@
     "    a [b G] ε R0 [within] R1\n",
     "\n",
     "1. Discard a.\n",
-    "2. Use x combinator to generate next term from G.\n",
-    "3. Run within with `i` (it is a `primrec` function.)\n",
+    "2. Use `x` combinator to generate next term from `G`.\n",
+    "3. Run `within` with `i` (it is a `primrec` function.)\n",
     "\n",
     "Pretty straightforward:\n",
     "\n",
@@ -243,7 +232,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -264,7 +253,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -272,6 +261,32 @@
     "define('sqrt == gsra within')"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Try it out..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "6.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "J('36 sqrt')"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 10,
@@ -291,6 +306,13 @@
     "J('23 sqrt')"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Check it."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 11,
@@ -312,6 +334,28 @@
    "source": [
     "4.795831523312719**2"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "4.795831523312719"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from math import sqrt\n",
+    "\n",
+    "sqrt(23)"
+   ]
   }
  ],
  "metadata": {