{
 "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",
    "(I may have these paired up wrong.  I.e. `disenstacken` should be `unstack` and vice versa.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 2 1]\n"
     ]
    }
   ],
   "source": [
    "J('1 2 3 enstacken') # Replace the stack with a quote of itself."
   ]
  },
  {
   "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] disenstacken')  # Unpack a list onto 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')  # Get the stack on 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] unstack')  # Replace the stack with the list on top.\n",
    "                            # The items appear reversed but they are not,\n",
    "                            # 4 is on the top of both the list and the stack."
   ]
  },
  {
   "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": [
    {
     "ename": "KeyError",
     "evalue": "swoncat",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-22-15579491b615>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mJ\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'[1 2 3] [4 5 6] swoncat'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/home/sforman/Desktop/ArchLayer/System/source/Thun/docs/notebook_preamble.py\u001b[0m in \u001b[0;36mJ\u001b[0;34m(text, stack, dictionary)\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mJ\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstack\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mS\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdictionary\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mD\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 32\u001b[0;31m     \u001b[0;32mprint\u001b[0m \u001b[0mstack_to_string\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstack\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdictionary\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     33\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/sforman/Desktop/ArchLayer/System/source/Thun/venv/local/lib/python2.7/site-packages/joy/joy.pyc\u001b[0m in \u001b[0;36mrun\u001b[0;34m(text, stack, dictionary, viewer)\u001b[0m\n\u001b[1;32m     77\u001b[0m \t'''\n\u001b[1;32m     78\u001b[0m         \u001b[0mexpression\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtext_to_expression\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtext\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 79\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mjoy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstack\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdictionary\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mviewer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     80\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     81\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/sforman/Desktop/ArchLayer/System/source/Thun/venv/local/lib/python2.7/site-packages/joy/joy.pyc\u001b[0m in \u001b[0;36mjoy\u001b[0;34m(stack, expression, dictionary, viewer)\u001b[0m\n\u001b[1;32m     56\u001b[0m                 \u001b[0mterm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexpression\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mexpression\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     57\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mterm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSymbol\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 58\u001b[0;31m                         \u001b[0mterm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdictionary\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mterm\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     59\u001b[0m                         \u001b[0mstack\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdictionary\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mterm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstack\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexpression\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdictionary\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     60\u001b[0m                 \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: swoncat"
     ]
    }
   ],
   "source": [
    "J('[1 2 3] [4 5 6] swoncat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('[1 2 3] [4 5 6] shunt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `cons` `swons` `uncons`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 [2 3] cons')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[2 3] 1 swons')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3] uncons')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `first` `second` `third` `rest`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 4] first')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 4] second')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 4] third')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('[1 2 3 4] rest')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `flatten`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('[10 11 12 13 14] 2 getitem')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 4] 0 at')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('2 [1 2 3 4] of')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 4] 2 drop')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 1 4] 1 remove')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `reverse`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('[1 2 3 4] reverse')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `size`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "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": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('1 2 3 [4 5 6] swaack')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `choice` `select`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('23 9 1 choice')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 9 0 choice')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('[23 9 7] 1 select')  # select is basically getitem, should retire it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[23 9 7] 0 select')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `zip`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3] [6 5 4] zip')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 9 +')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `-` `sub`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 9 -')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `*` `mul`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 9 *')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `/` `div` `floordiv` `truediv`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('23 9 /')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "J('23 -9 truediv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "J('23 9 div')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "J('23 9 floordiv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "J('23 -9 div')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "J('23 -9 floordiv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `%` `mod` `modulus` `rem` `remainder`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 9 %')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `neg`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 neg -5 neg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### pow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('2 10 pow')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `sqr` `sqrt`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 sqr')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 sqrt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `++` `succ` `--` `pred`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 ++')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('1 --')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `<<` `lshift` `>>` `rshift`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('8 1 <<')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('8 1 >>')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `average`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 5] average')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `range` `range_to_zero` `down_to_zero`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('5 range')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('5 range_to_zero')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('5 down_to_zero')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `product`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 5] product')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `sum`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 5] sum')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `min`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[1 2 3 5] min')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `gcd`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[45 30] least_fraction')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 truthy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[] truthy')  # Python semantics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('0 truthy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    ? == dup truthy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('23 ?')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[] ?')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('0 ?')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `&` `and` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('23 9 &')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `!=` `<>` `ne`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 1 ^')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 0 ^')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Miscellaneous"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `help`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('[help] help')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `parse`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "J('[parse] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 \"2 [3] dup\" parse')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `run`\n",
    "Evaluate a quoted Joy sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[app1] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('10 4 [sqr *] app1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('10 3 4 [sqr *] app2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[app2] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('3 [0 <=] [1 - dup] anamorphism')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `branch`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('3 4 1 [+] [*] branch')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('10 2 [+] [-] cleave')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `dip` `dipd` `dipdd`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] dip')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] dipd')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('23 [++] dupdip *')  # N(N + 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `genrec` `primrec`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[genrec] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('3 [1 <=] [] [dup --] [i *] genrec')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `i`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "V('1 2 3 [+ +] i')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `ifte`\n",
    "    [predicate] [then] [else] ifte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 [1] [+] [*] ifte')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 [0] [+] [*] ifte')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `infra`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('1 2 3 [4 5 6] [* +] infra')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `loop`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[loop] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('3 dup [1 - dup] loop')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `map` `pam`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('10 [1 2 3] [*] map')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] nullary')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] unary')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] binary')  # + has arity 2 so this is technically pointless..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('1 2 3 4 5 [+] ternary')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `step`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[step] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "V('0 [1 2 3] [+] step')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `times`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('3 2 1 2 [+] times')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `b`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[b] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V('1 2 [3] [4] b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `while`\n",
    "    [predicate] [body] while"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('3 [0 >] [dup --] while')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `x`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[x] help')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[] void')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[[]] void')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[[][[]]] void')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J('[[[]][[][]]] void')"
   ]
  }
 ],
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