{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples (and some documentation) for the Words in the Library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from notebook_preamble import J, V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stack Chatter\n",
    "This is what I like to call the functions that just rearrange things on the stack.  (One thing I want to mention is that during a hypothetical compilation phase these \"stack chatter\" words effectively disappear, because we can map the logical stack locations to registers that remain static for the duration of the computation.  This remains to be done but it's \"off the shelf\" technology.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `clear`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 clear')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `dup` `dupd`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 3\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 dup')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 2 3\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 dupd')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `enstacken` `disenstacken` `stack` `unstack`\n",
    "\n",
    "Replace the stack with a quote of itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 2 1]\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 enstacken')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unpack a list onto the stack."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 5 6 3 2 1\n"
     ]
    }
   ],
   "source": [
    "J('4 5 6 [3 2 1] unstack')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the stack on the stack."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 [3 2 1]\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 stack')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Replace the stack with the list on top.\n",
    "The items appear reversed but they are not,\n",
    "is on the top of both the list and the stack."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 5 4\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 [4 5 6] disenstacken')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `pop` `popd` `popop`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 pop')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 3\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 popd')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 popop')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `roll<` `rolldown` `roll>` `rollup`\n",
    "The \"down\" and \"up\" refer to the movement of two of the top three items (displacing the third.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 3 1\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 roll<')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 1 2\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 roll>')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `swap`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 3 2\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 swap')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `tuck` `over`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 3 2 3\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 tuck')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 2\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 over')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `unit` `quoted` `unquoted`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 [3]\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 unit')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 [2] 3\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 quoted')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3\n"
     ]
    }
   ],
   "source": [
    "J('1 [2] 3 unquoted')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              • 1 [dup] 3 unquoted\n",
      "            1 • [dup] 3 unquoted\n",
      "      1 [dup] • 3 unquoted\n",
      "    1 [dup] 3 • unquoted\n",
      "    1 [dup] 3 • [i] dip\n",
      "1 [dup] 3 [i] • dip\n",
      "      1 [dup] • i 3\n",
      "            1 • dup 3\n",
      "          1 1 • 3\n",
      "        1 1 3 • \n"
     ]
    }
   ],
   "source": [
    "V('1 [dup] 3 unquoted')  # Unquoting evaluates.  Be aware."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# List words"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `concat` `swoncat` `shunt`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5 6]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3] [4 5 6] concat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 5 6 1 2 3]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3] [4 5 6] swoncat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[6 5 4 1 2 3]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3] [4 5 6] shunt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `cons` `swons` `uncons`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n"
     ]
    }
   ],
   "source": [
    "J('1 [2 3] cons')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n"
     ]
    }
   ],
   "source": [
    "J('[2 3] 1 swons')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 [2 3]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3] uncons')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `first` `second` `third` `rest`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 4] first')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 4] second')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 4] third')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 4]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 4] rest')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `flatten`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 [3] 4 5 6]\n"
     ]
    }
   ],
   "source": [
    "J('[[1] [2 [3] 4] [5 6]] flatten')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `getitem` `at` `of` `drop` `take`\n",
    "\n",
    "`at` and `getitem` are the same function. `of == swap at`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    }
   ],
   "source": [
    "J('[10 11 12 13 14] 2 getitem')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 4] 0 at')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "J('2 [1 2 3 4] of')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 4] 2 drop')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 1]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 4] 2 take')  # reverses the order"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`reverse` could be defines as `reverse == dup size take`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `remove`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 1 4]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 1 4] 1 remove')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `reverse`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 3 2 1]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 4] reverse')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `size`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    }
   ],
   "source": [
    "J('[1 1 1 1] size')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `swaack`\n",
    "\"Swap stack\" swap the list on the top of the stack for the stack, and put the old stack on top of the new one.  Think of it as a context switch.  Niether of the lists/stacks change their order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 5 4 [3 2 1]\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 [4 5 6] swaack')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `choice` `select`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    }
   ],
   "source": [
    "J('23 9 1 choice')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23\n"
     ]
    }
   ],
   "source": [
    "J('23 9 0 choice')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    }
   ],
   "source": [
    "J('[23 9 7] 1 select')  # select is basically getitem, should retire it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23\n"
     ]
    }
   ],
   "source": [
    "J('[23 9 7] 0 select')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `zip`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6 1] [5 2] [4 3]]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3] [6 5 4] zip')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7 7 7]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3] [6 5 4] zip [sum] map')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math words"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `+` `add`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32\n"
     ]
    }
   ],
   "source": [
    "J('23 9 +')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `-` `sub`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14\n"
     ]
    }
   ],
   "source": [
    "J('23 9 -')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `*` `mul`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "207\n"
     ]
    }
   ],
   "source": [
    "J('23 9 *')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `/` `div` `floordiv` `truediv`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5555555555555554\n"
     ]
    }
   ],
   "source": [
    "J('23 9 /')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.5555555555555554\n"
     ]
    }
   ],
   "source": [
    "J('23 -9 truediv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5555555555555554\n"
     ]
    }
   ],
   "source": [
    "J('23 9 div')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "J('23 9 floordiv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.5555555555555554\n"
     ]
    }
   ],
   "source": [
    "J('23 -9 div')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3\n"
     ]
    }
   ],
   "source": [
    "J('23 -9 floordiv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `%` `mod` `modulus` `rem` `remainder`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "J('23 9 %')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `neg`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-23 5\n"
     ]
    }
   ],
   "source": [
    "J('23 neg -5 neg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### pow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1024\n"
     ]
    }
   ],
   "source": [
    "J('2 10 pow')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `sqr` `sqrt`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "529\n"
     ]
    }
   ],
   "source": [
    "J('23 sqr')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.795831523312719\n"
     ]
    }
   ],
   "source": [
    "J('23 sqrt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `++` `succ` `--` `pred`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "J('1 ++')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "J('1 --')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `<<` `lshift` `>>` `rshift`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16\n"
     ]
    }
   ],
   "source": [
    "J('8 1 <<')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    }
   ],
   "source": [
    "J('8 1 >>')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `average`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.75\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 5] average')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `range` `range_to_zero` `down_to_zero`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 3 2 1 0]\n"
     ]
    }
   ],
   "source": [
    "J('5 range')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5]\n"
     ]
    }
   ],
   "source": [
    "J('5 range_to_zero')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 4 3 2 1 0\n"
     ]
    }
   ],
   "source": [
    "J('5 down_to_zero')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `product`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 5] product')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `sum`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 5] sum')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `min`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 3 5] min')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `gcd`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15\n"
     ]
    }
   ],
   "source": [
    "J('45 30 gcd')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `least_fraction`\n",
    "If we represent fractions as a quoted pair of integers [q d] this word reduces them to their ... least common factors or whatever."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.0 2.0]\n"
     ]
    }
   ],
   "source": [
    "J('[45 30] least_fraction')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[23.0 12.0]\n"
     ]
    }
   ],
   "source": [
    "J('[23 12] least_fraction')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logic and Comparison"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `?` `truthy`\n",
    "Get the Boolean value of the item on the top of the stack."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "J('23 truthy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "J('[] truthy')  # Python semantics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "J('0 truthy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    ? == dup truthy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        • 23 ?\n",
      "     23 • ?\n",
      "     23 • dup truthy\n",
      "  23 23 • truthy\n",
      "23 True • \n"
     ]
    }
   ],
   "source": [
    "V('23 ?')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[] False\n"
     ]
    }
   ],
   "source": [
    "J('[] ?')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 False\n"
     ]
    }
   ],
   "source": [
    "J('0 ?')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `&` `and` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "J('23 9 &')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `!=` `<>` `ne`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "J('23 9 !=')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The usual suspects:\n",
    "- `<` `lt`\n",
    "- `<=` `le`  \n",
    "- `=` `eq`\n",
    "- `>` `gt`\n",
    "- `>=` `ge`\n",
    "- `not`\n",
    "- `or`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `^` `xor`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "J('1 1 ^')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "J('1 0 ^')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Miscellaneous"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `help`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on help ====\n",
      "\n",
      "Accepts a quoted symbol on the top of the stack and prints its docs.\n",
      "\n",
      "---- end (help)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "J('[help] help')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `parse`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on parse ====\n",
      "\n",
      "Parse the string on the stack to a Joy expression.\n",
      "\n",
      "---- end (parse)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "J('[parse] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 [2 [3] dup]\n"
     ]
    }
   ],
   "source": [
    "J('1 \"2 [3] dup\" parse')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `run`\n",
    "Evaluate a quoted Joy sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5]\n"
     ]
    }
   ],
   "source": [
    "J('[1 2 dup + +] run')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Combinators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `app1` `app2` `app3`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on app1 ====\n",
      "\n",
      "Given a quoted program on TOS and anything as the second stack item run\n",
      "the program and replace the two args with the first result of the\n",
      "program.\n",
      "::\n",
      "\n",
      "                 ... x [Q] . app1\n",
      "        -----------------------------------\n",
      "           ... [x ...] [Q] . infra first\n",
      "\n",
      "---- end (app1)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "J('[app1] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 160\n"
     ]
    }
   ],
   "source": [
    "J('10 4 [sqr *] app1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 90 160\n"
     ]
    }
   ],
   "source": [
    "J('10 3 4 [sqr *] app2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on app2 ====\n",
      "\n",
      "Like app1 with two items.\n",
      "::\n",
      "\n",
      "               ... y x [Q] . app2\n",
      "        -----------------------------------\n",
      "           ... [y ...] [Q] . infra first\n",
      "               [x ...] [Q]   infra first\n",
      "\n",
      "---- end (app2)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "J('[app2] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 40 90 160\n"
     ]
    }
   ],
   "source": [
    "J('10 2 3 4 [sqr *] app3')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `anamorphism`\n",
    "Given an initial value, a predicate function `[P]`, and a generator function `[G]`, the `anamorphism` combinator creates a sequence.\n",
    "\n",
    "       n [P] [G] anamorphism\n",
    "    ---------------------------\n",
    "              [...]\n",
    "\n",
    "Example, `range`:\n",
    "\n",
    "    range == [0 <=] [1 - dup] anamorphism"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 1 0]\n"
     ]
    }
   ],
   "source": [
    "J('3 [0 <=] [1 - dup] anamorphism')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `branch`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    }
   ],
   "source": [
    "J('3 4 1 [+] [*] branch')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    }
   ],
   "source": [
    "J('3 4 0 [+] [*] branch')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `cleave`\n",
    "    ... x [P] [Q] cleave\n",
    "\n",
    "From the original Joy docs: \"The cleave combinator expects two quotations, and below that an item `x`\n",
    "It first executes `[P]`, with `x` on top, and saves the top result element.\n",
    "Then it executes `[Q]`, again with `x`, and saves the top result.\n",
    "Finally it restores the stack to what it was below `x` and pushes the two\n",
    "results P(X) and Q(X).\"\n",
    "\n",
    "Note that `P` and `Q` can use items from the stack freely, since the stack (below `x`) is restored.  `cleave` is a kind of *parallel* primitive, and it would make sense to create a version that uses, e.g. Python threads or something, to actually run `P` and `Q` concurrently.  The current implementation of `cleave` is a definition in terms of `app2`:\n",
    "\n",
    "    cleave == [i] app2 [popd] dip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 12 8\n"
     ]
    }
   ],
   "source": [
    "J('10 2 [+] [-] cleave')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `dip` `dipd` `dipdd`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 7 5\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 4 5 [+] dip')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 5 4 5\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 4 5 [+] dipd')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 3 4 5\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 4 5 [+] dipdd')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `dupdip`\n",
    "Expects a quoted program `[Q]` on the stack and some item under it, `dup` the item and `dip` the quoted program under it.\n",
    "\n",
    "    n [Q] dupdip == n Q n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        • 23 [++] dupdip *\n",
      "     23 • [++] dupdip *\n",
      "23 [++] • dupdip *\n",
      "     23 • ++ 23 *\n",
      "     24 • 23 *\n",
      "  24 23 • *\n",
      "    552 • \n"
     ]
    }
   ],
   "source": [
    "V('23 [++] dupdip *')  # N(N + 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `genrec` `primrec`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on genrec ====\n",
      "\n",
      "General Recursion Combinator.\n",
      "::\n",
      "\n",
      "                          [if] [then] [rec1] [rec2] genrec\n",
      "    ---------------------------------------------------------------------\n",
      "       [if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte\n",
      "\n",
      "From \"Recursion Theory and Joy\" (j05cmp.html) by Manfred von Thun:\n",
      "\"The genrec combinator takes four program parameters in addition to\n",
      "whatever data parameters it needs. Fourth from the top is an if-part,\n",
      "followed by a then-part. If the if-part yields true, then the then-part\n",
      "is executed and the combinator terminates. The other two parameters are\n",
      "the rec1-part and the rec2-part. If the if-part yields false, the\n",
      "rec1-part is executed. Following that the four program parameters and\n",
      "the combinator are again pushed onto the stack bundled up in a quoted\n",
      "form. Then the rec2-part is executed, where it will find the bundled\n",
      "form. Typically it will then execute the bundled form, either with i or\n",
      "with app2, or some other combinator.\"\n",
      "\n",
      "The way to design one of these is to fix your base case [then] and the\n",
      "test [if], and then treat rec1 and rec2 as an else-part \"sandwiching\"\n",
      "a quotation of the whole function.\n",
      "\n",
      "For example, given a (general recursive) function 'F':\n",
      "::\n",
      "\n",
      "        F == [I] [T] [R1] [R2] genrec\n",
      "\n",
      "If the [I] if-part fails you must derive R1 and R2 from:\n",
      "::\n",
      "\n",
      "        ... R1 [F] R2\n",
      "\n",
      "Just set the stack arguments in front, and figure out what R1 and R2\n",
      "have to do to apply the quoted [F] in the proper way.  In effect, the\n",
      "genrec combinator turns into an ifte combinator with a quoted copy of\n",
      "the original definition in the else-part:\n",
      "::\n",
      "\n",
      "        F == [I] [T] [R1]   [R2] genrec\n",
      "          == [I] [T] [R1 [F] R2] ifte\n",
      "\n",
      "Primitive recursive functions are those where R2 == i.\n",
      "::\n",
      "\n",
      "        P == [I] [T] [R] tailrec\n",
      "          == [I] [T] [R [P] i] ifte\n",
      "          == [I] [T] [R P] ifte\n",
      "\n",
      "---- end (genrec)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "J('[genrec] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    }
   ],
   "source": [
    "J('3 [1 <=] [] [dup --] [i *] genrec')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `i`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            • 1 2 3 [+ +] i\n",
      "          1 • 2 3 [+ +] i\n",
      "        1 2 • 3 [+ +] i\n",
      "      1 2 3 • [+ +] i\n",
      "1 2 3 [+ +] • i\n",
      "      1 2 3 • + +\n",
      "        1 5 • +\n",
      "          6 • \n"
     ]
    }
   ],
   "source": [
    "V('1 2 3 [+ +] i')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `ifte`\n",
    "    [predicate] [then] [else] ifte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "J('1 2 [1] [+] [*] ifte')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "J('1 2 [0] [+] [*] ifte')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `infra`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    • 1 2 3 [4 5 6] [* +] infra\n",
      "                  1 • 2 3 [4 5 6] [* +] infra\n",
      "                1 2 • 3 [4 5 6] [* +] infra\n",
      "              1 2 3 • [4 5 6] [* +] infra\n",
      "      1 2 3 [4 5 6] • [* +] infra\n",
      "1 2 3 [4 5 6] [* +] • infra\n",
      "              6 5 4 • * + [3 2 1] swaack\n",
      "               6 20 • + [3 2 1] swaack\n",
      "                 26 • [3 2 1] swaack\n",
      "         26 [3 2 1] • swaack\n",
      "         1 2 3 [26] • \n"
     ]
    }
   ],
   "source": [
    "V('1 2 3 [4 5 6] [* +] infra')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `loop`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on loop ====\n",
      "\n",
      "Basic loop combinator.\n",
      "::\n",
      "\n",
      "           ... True [Q] loop\n",
      "        -----------------------\n",
      "              ... Q [Q] loop\n",
      "\n",
      "           ... False [Q] loop\n",
      "        ------------------------\n",
      "                  ...\n",
      "\n",
      "---- end (loop)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "J('[loop] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              • 3 dup [1 - dup] loop\n",
      "            3 • dup [1 - dup] loop\n",
      "          3 3 • [1 - dup] loop\n",
      "3 3 [1 - dup] • loop\n",
      "            3 • 1 - dup [1 - dup] loop\n",
      "          3 1 • - dup [1 - dup] loop\n",
      "            2 • dup [1 - dup] loop\n",
      "          2 2 • [1 - dup] loop\n",
      "2 2 [1 - dup] • loop\n",
      "            2 • 1 - dup [1 - dup] loop\n",
      "          2 1 • - dup [1 - dup] loop\n",
      "            1 • dup [1 - dup] loop\n",
      "          1 1 • [1 - dup] loop\n",
      "1 1 [1 - dup] • loop\n",
      "            1 • 1 - dup [1 - dup] loop\n",
      "          1 1 • - dup [1 - dup] loop\n",
      "            0 • dup [1 - dup] loop\n",
      "          0 0 • [1 - dup] loop\n",
      "0 0 [1 - dup] • loop\n",
      "            0 • \n"
     ]
    }
   ],
   "source": [
    "V('3 dup [1 - dup] loop')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `map` `pam`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 [10 20 30]\n"
     ]
    }
   ],
   "source": [
    "J('10 [1 2 3] [*] map')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 5 [50 2.0 15 5]\n"
     ]
    }
   ],
   "source": [
    "J('10 5 [[*][/][+][-]] pam')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `nullary` `unary` `binary` `ternary`\n",
    "Run a quoted program enforcing [arity](https://en.wikipedia.org/wiki/Arity)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 4 5 9\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 4 5 [+] nullary')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 4 9\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 4 5 [+] unary')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 9\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 4 5 [+] binary')  # + has arity 2 so this is technically pointless..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 9\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 4 5 [+] ternary')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `step`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on step ====\n",
      "\n",
      "Run a quoted program on each item in a sequence.\n",
      "::\n",
      "\n",
      "           ... [] [Q] . step\n",
      "        -----------------------\n",
      "                  ... .\n",
      "\n",
      "\n",
      "           ... [a] [Q] . step\n",
      "        ------------------------\n",
      "                 ... a . Q\n",
      "\n",
      "\n",
      "           ... [a b c] [Q] . step\n",
      "        ----------------------------------------\n",
      "                     ... a . Q [b c] [Q] step\n",
      "\n",
      "The step combinator executes the quotation on each member of the list\n",
      "on top of the stack.\n",
      "\n",
      "---- end (step)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "J('[step] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              • 0 [1 2 3] [+] step\n",
      "            0 • [1 2 3] [+] step\n",
      "    0 [1 2 3] • [+] step\n",
      "0 [1 2 3] [+] • step\n",
      "      0 1 [+] • i [2 3] [+] step\n",
      "          0 1 • + [2 3] [+] step\n",
      "            1 • [2 3] [+] step\n",
      "      1 [2 3] • [+] step\n",
      "  1 [2 3] [+] • step\n",
      "      1 2 [+] • i [3] [+] step\n",
      "          1 2 • + [3] [+] step\n",
      "            3 • [3] [+] step\n",
      "        3 [3] • [+] step\n",
      "    3 [3] [+] • step\n",
      "      3 3 [+] • i\n",
      "          3 3 • +\n",
      "            6 • \n"
     ]
    }
   ],
   "source": [
    "V('0 [1 2 3] [+] step')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `times`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            • 3 2 1 2 [+] times\n",
      "          3 • 2 1 2 [+] times\n",
      "        3 2 • 1 2 [+] times\n",
      "      3 2 1 • 2 [+] times\n",
      "    3 2 1 2 • [+] times\n",
      "3 2 1 2 [+] • times\n",
      "      3 2 1 • + 1 [+] times\n",
      "        3 3 • 1 [+] times\n",
      "      3 3 1 • [+] times\n",
      "  3 3 1 [+] • times\n",
      "        3 3 • +\n",
      "          6 • \n"
     ]
    }
   ],
   "source": [
    "V('3 2 1 2 [+] times')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `b`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on b ====\n",
      "\n",
      "::\n",
      "\n",
      "        b == [i] dip i\n",
      "\n",
      "        ... [P] [Q] b == ... [P] i [Q] i\n",
      "        ... [P] [Q] b == ... P Q\n",
      "\n",
      "---- end (b)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "J('[b] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            • 1 2 [3] [4] b\n",
      "          1 • 2 [3] [4] b\n",
      "        1 2 • [3] [4] b\n",
      "    1 2 [3] • [4] b\n",
      "1 2 [3] [4] • b\n",
      "        1 2 • 3 4\n",
      "      1 2 3 • 4\n",
      "    1 2 3 4 • \n"
     ]
    }
   ],
   "source": [
    "V('1 2 [3] [4] b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `while`\n",
    "    [predicate] [body] while"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 2 1 0\n"
     ]
    }
   ],
   "source": [
    "J('3 [0 >] [dup --] while')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `x`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==== Help on x ====\n",
      "\n",
      "::\n",
      "\n",
      "        x == dup i\n",
      "\n",
      "        ... [Q] x = ... [Q] dup i\n",
      "        ... [Q] x = ... [Q] [Q] i\n",
      "        ... [Q] x = ... [Q]  Q\n",
      "\n",
      "---- end (x)\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "J('[x] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            • 1 [2] [i 3] x\n",
      "          1 • [2] [i 3] x\n",
      "      1 [2] • [i 3] x\n",
      "1 [2] [i 3] • x\n",
      "1 [2] [i 3] • i 3\n",
      "      1 [2] • i 3 3\n",
      "          1 • 2 3 3\n",
      "        1 2 • 3 3\n",
      "      1 2 3 • 3\n",
      "    1 2 3 3 • \n"
     ]
    }
   ],
   "source": [
    "V('1 [2] [i 3] x')  # Kind of a pointless example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# `void`\n",
    "Implements [**Laws of Form** *arithmetic*](https://en.wikipedia.org/wiki/Laws_of_Form#The_primary_arithmetic_.28Chapter_4.29) over quote-only datastructures (that is, datastructures that consist soley of containers, without strings or numbers or anything else.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "J('[] void')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "J('[[]] void')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "J('[[][[]]] void')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "J('[[[]][[][]]] void')"
   ]
  }
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