fluidb/docs/tutorial/tutorial.ipynb

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   "cell_type": "markdown",
   "id": "3df9ce6e-3722-4334-abf9-703d62c27eab",
   "metadata": {},
   "source": [
    "# The Cozo database tutorial"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63c695dc-6e85-42bb-b39b-1f0fd14ed5eb",
   "metadata": {},
   "source": [
    "This tutorial will teach you the basics of using the Cozo database with the query language CozoScript.\n",
    "There are no database-specific prerequisites, \n",
    "though it would be helpful if you already know some other databases, \n",
    "especially SQL databases."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2bfcfe4-c06c-4b02-a040-6fd840b77820",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb1fefcf-81b5-4ccf-8179-631fdb011bae",
   "metadata": {},
   "source": [
    "The best way to learn from this tutorial is to run the queries as they are introduced.\n",
    "For this, you need to install the Cozo database on your local machine."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f26f0f5-a3ff-4145-a9d5-84c65e368afa",
   "metadata": {},
   "source": [
    "Cozo is distributed as a single gzipped/zipped binary. \n",
    "Go to https://github.com/cozodb/cozo/releases and download the latest release binary for your operating system to a local directory.\n",
    "\n",
    "If your operating system is Linux/Mac, \n",
    "open a terminal command prompt, \n",
    "`cd` into the directory of your download,\n",
    "and run"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "341d8539-d6e1-4610-bd1e-6c29568573a8",
   "metadata": {},
   "source": [
    "```bash\n",
    "gunzip cozoserver-*.gz\n",
    "mv cozoserver-* cozoserver\n",
    "chmod +x cozoserver\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "536fb265-e25f-469d-843e-935b272c7298",
   "metadata": {},
   "source": [
    "If you are on Windows instead, open a PowerShell and run"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9809d37e-b1b3-4419-8c19-5fe7bc8994a6",
   "metadata": {},
   "source": [
    "```powershell\n",
    "Expand-Archive -Path .\\cozoserver-*.zip -DestinationPath .\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12da9726-3c18-4011-98ea-e2aae105ee08",
   "metadata": {},
   "source": [
    "To run the server, you need to specify a directory to store persistent data on your file system. \n",
    "In the following, we will use a directory called `tutorial-data` in the same directory as the binary executable.\n",
    "In the terminal, run"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59c6fdfc-1a3c-4da3-8138-6c653592995f",
   "metadata": {},
   "source": [
    "```bash\n",
    "./cozoserver ./tutorial-data\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41820cf5-a800-4c81-8a17-227e9692aae2",
   "metadata": {},
   "source": [
    "The same command should work in PowerShell as well.\n",
    "\n",
    "If you see something like `Database web API running at ...` displayed in your terminal, \n",
    "then the server is successfully started. \n",
    "Keep the server running when you are following the tutorial.\n",
    "When you are done, `CTRL-C` in the terminal will stop the server.\n",
    "You can restart the server again by running the command again.\n",
    "\n",
    "More options when starting the server are available. Run"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e975d0a6-0851-4eed-9a24-d6b3d55fa09f",
   "metadata": {},
   "source": [
    "```bash\n",
    "./cozoserver -h\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f192cf0b-a30d-46ad-85a1-d81f7590b78b",
   "metadata": {},
   "source": [
    "for more details."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ec06d2e-1187-48c8-8777-f84b4c71c741",
   "metadata": {},
   "source": [
    "## A place to run queries\n",
    "\n",
    "Cozo exposes an HTTP API, so theoretically you can follow along using tools like `curl`. \n",
    "If you are interested, consult the [manual](https://cozodb.github.io/current/manual/setup.html#the-query-api) for the request format the API expects.\n",
    "For a better user experience, we suggest following one of the following two subsections instead."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4e8b790-7c0f-4538-b20e-2c3fb4065dc8",
   "metadata": {},
   "source": [
    "### Option 1: the JupyterLab notebook\n",
    "\n",
    "This option provides the best user experience but also requires you to install quite a lot of things, \n",
    "though you may already have them installed on your computer if you use the python data science stack.\n",
    "First, you will need python installed. \n",
    "Then install JupyterLab by following the instruction at https://jupyter.org/install.\n",
    "Next, run the following to install a Jupyter extension to help query Cozo:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37b47a25-3708-490d-ba08-975771dc469d",
   "metadata": {},
   "source": [
    "```bash\n",
    "pip install pycozo pandas\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c07f306-9abc-4dd2-b78c-5b46a823982e",
   "metadata": {},
   "source": [
    "While you are at it, right-click on https://raw.githubusercontent.com/cozodb/cozo/main/docs/tutorial/tutorial.ipynb \n",
    "and save the notebook of this tutorial to your disk.\n",
    "\n",
    "Then run Jupyter Lab, open the saved tutorial document, and follow along."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5154e084-d997-4f22-97fb-ce5808fb1da3",
   "metadata": {},
   "source": [
    "We need to enable the extension in the notebook. Run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2e0d11d7-64d7-4577-a28d-7541ee8875fa",
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   "source": [
    "%load_ext pycozo.ipyext_direct"
   ]
  },
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   "source": [
    "Then the \"hello world\" query:"
   ]
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       "      <td id=\"T_38e67_row0_col0\" class=\"data row0 col0\" >hello</td>\n",
       "      <td id=\"T_38e67_row0_col1\" class=\"data row0 col1\" >world</td>\n",
       "      <td id=\"T_38e67_row0_col2\" class=\"data row0 col2\" >Cozo!</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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    "?[] <- [['hello', 'world', 'Cozo!']]"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "If you get the same words back formatted in a table, congratulations! \n",
    "You can skip to the next section where we start learning CozoScript proper.\n",
    "If you want to know more about what the `pycozo` extension did and more tricks that you can do with the extension, read the [manual](https://cozodb.github.io/current/manual/setup.html#jupyterlab)."
   ]
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   "cell_type": "markdown",
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   "source": [
    "### Option 2: the JavaScript console in your browser"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ddc55d2-604b-4218-af45-8c62d79db201",
   "metadata": {},
   "source": [
    "If you have never used Python before, the first option may be overwhelming. \n",
    "Or you just want to try Cozo out first to decide quickly if it has anything interesting for you.\n",
    "Whatever your reason for not wanting to install the whole python toolchain, we have you covered."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1147466d-d925-4c32-8b6c-28bdabc656fb",
   "metadata": {},
   "source": [
    "Your local machine at least has a modern web browser, like a recent version of Firefox, Chrome, or Edge, right?\n",
    "Good. \n",
    "\n",
    "Use your browser to navigate to http://127.0.0.1:9070 (the address shown in your terminal when you run `cozoserver`).\n",
    "You should be greeted by a page saying that the server is running.\n",
    "Now open the developer tools of your browser by right-clicking the page and selecting \"Inspect\" from the menu \n",
    "(if you cannot find it, you may need to fiddle with your browser settings to enable the developer tools).\n",
    "Switch to the \"Console\" tab of the developer tools if it is not already open. \n",
    "\n",
    "If you see some messages where \n",
    "the \"Cozo Makeshift Javascript Console\" welcomes you, you are ready. Run the \"hello world\" query by typing the following into the console and pressing enter:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97547c5d-e2b4-4205-ac10-b2aeb5855782",
   "metadata": {},
   "source": [
    "```javascript\n",
    "await run(`?[] <- [['hello', 'world', 'Cozo!']]`)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81fe58e2-3c52-4859-828d-533b25a62468",
   "metadata": {},
   "source": [
    "If you see the three words echoed back in a table, you are successful. When following the tutorial, you have to wrap all queries within the backticks `` in the above command to run them in the JavaScript console."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "545ed77c-eeb9-4008-972e-0bdc1d6b7478",
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   "source": [
    "## Your first relations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61d8ce38-d2e0-4b5f-a9f7-64e9a65e0fe0",
   "metadata": {},
   "source": [
    "Cozo is a relational database. The \"hello world\" query"
   ]
  },
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       "      <td id=\"T_a5997_row0_col0\" class=\"data row0 col0\" >hello</td>\n",
       "      <td id=\"T_a5997_row0_col1\" class=\"data row0 col1\" >world</td>\n",
       "      <td id=\"T_a5997_row0_col2\" class=\"data row0 col2\" >Cozo!</td>\n",
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    "?[] <- [['hello', 'world', 'Cozo!']]"
   ]
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  {
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   "source": [
    "as you might have guessed, simply passes an ad hoc relation, here represented by a list of lists, and ask the database to return the relation to you.\n",
    "\n",
    "You can pass more rows, or a different number of columns, to corroborate further your guess:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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       "    </tr>\n",
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       "      <th id=\"T_d9c76_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_d9c76_row1_col0\" class=\"data row1 col0\" >a</td>\n",
       "      <td id=\"T_d9c76_row1_col1\" class=\"data row1 col1\" >b</td>\n",
       "      <td id=\"T_d9c76_row1_col2\" class=\"data row1 col2\" >c</td>\n",
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    "?[] <- [[1, 2, 3], ['a', 'b', 'c']]"
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  {
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   "source": [
    "This example shows how to enter literals for numbers, strings, booleans and `null`:"
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  {
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       "      <th id=\"T_250c4_level0_col4\" class=\"col_heading level0 col4\" >4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_250c4_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_250c4_row0_col0\" class=\"data row0 col0\" >True</td>\n",
       "      <td id=\"T_250c4_row0_col1\" class=\"data row0 col1\" >False</td>\n",
       "      <td id=\"T_250c4_row0_col2\" class=\"data row0 col2\" >None</td>\n",
       "      <td id=\"T_250c4_row0_col3\" class=\"data row0 col3\" >-0.014000</td>\n",
       "      <td id=\"T_250c4_row0_col4\" class=\"data row0 col4\" >A string with double quotes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_250c4_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_250c4_row1_col0\" class=\"data row1 col0\" >1.500000</td>\n",
       "      <td id=\"T_250c4_row1_col1\" class=\"data row1 col1\" >2.500000</td>\n",
       "      <td id=\"T_250c4_row1_col2\" class=\"data row1 col2\" >3</td>\n",
       "      <td id=\"T_250c4_row1_col3\" class=\"data row1 col3\" >4</td>\n",
       "      <td id=\"T_250c4_row1_col4\" class=\"data row1 col4\" >5.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_250c4_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_250c4_row2_col0\" class=\"data row2 col0\" >aA</td>\n",
       "      <td id=\"T_250c4_row2_col1\" class=\"data row2 col1\" >bB</td>\n",
       "      <td id=\"T_250c4_row2_col2\" class=\"data row2 col2\" >cC</td>\n",
       "      <td id=\"T_250c4_row2_col3\" class=\"data row2 col3\" >dD</td>\n",
       "      <td id=\"T_250c4_row2_col4\" class=\"data row2 col4\" >eE</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
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     "execution_count": 5,
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   "source": [
    "?[] <- [[1.5, 2.5, 3, 4, 5.5], \n",
    "        ['aA', 'bB', 'cC', 'dD', 'eE'], \n",
    "        [true, false, null, -1.4e-2, \"A string with double quotes\"]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "615e35d7-f5c0-4d71-ac62-6934c658a715",
   "metadata": {},
   "source": [
    "The literal representations are similar to those in JavaScript. \n",
    "In particular, strings in double quotes are guaranteed to be interpreted in the same way as in JSON."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d76ab84-36a3-4d1d-9da2-a891de52b011",
   "metadata": {},
   "source": [
    "You may be surprised by the order of the returned rows in the last example: the returned order is not the same as the input order.\n",
    "This is because in Cozo relations are stored (either in memory or on disk) as trees, and trees are always sorted.\n",
    "\n",
    "Another consequence of trees is that you can have no duplicate rows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "28ab3f6e-0e32-486d-83fb-4fd5581e20dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "<style type=\"text/css\">\n",
       "#T_908e7_row0_col0, #T_908e7_row1_col0 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_908e7\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_908e7_level0_col0\" class=\"col_heading level0 col0\" >0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_908e7_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_908e7_row0_col0\" class=\"data row0 col0\" >1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_908e7_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_908e7_row1_col0\" class=\"data row1 col0\" >2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f1582b0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[] <- [[1], [2], [1], [2], [1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a5d9022-c9b2-48c9-b447-ae69a2fc3a21",
   "metadata": {},
   "source": [
    "We say that relations in Cozo follow _set semantics_ where de-duplication is automatic. \n",
    "By contrast, SQL usually follows _bag semantics_ (some databases do this by secretly having a unique internal key for every row, in Cozo you must do this explicitly if you need to simulate duplicate rows).\n",
    "\n",
    "Why does Cozo break tradition and go with set semantics?\n",
    "Set semantics is much more convenient when you have recursions between relations involved,\n",
    "and Cozo is designed to deal with very complicated recursions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcdfc9e4-1bc4-4473-8dd5-44097a164fbe",
   "metadata": {},
   "source": [
    "## Expressions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09dd8c4c-fb0e-4f53-9dec-b3fbcb6dce5b",
   "metadata": {},
   "source": [
    "The next example shows the use of various expressions and comments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dff14dab-2cc1-4917-aaa5-8feb1f075cf9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_386a7_row0_col0, #T_386a7_row0_col1, #T_386a7_row0_col2, #T_386a7_row0_col3, #T_386a7_row0_col4, #T_386a7_row0_col5, #T_386a7_row0_col7 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "#T_386a7_row0_col6 {\n",
       "  color: black;\n",
       "}\n",
       "#T_386a7_row0_col8 {\n",
       "  color: #bf5b3d;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_386a7\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_386a7_level0_col0\" class=\"col_heading level0 col0\" >0</th>\n",
       "      <th id=\"T_386a7_level0_col1\" class=\"col_heading level0 col1\" >1</th>\n",
       "      <th id=\"T_386a7_level0_col2\" class=\"col_heading level0 col2\" >2</th>\n",
       "      <th id=\"T_386a7_level0_col3\" class=\"col_heading level0 col3\" >3</th>\n",
       "      <th id=\"T_386a7_level0_col4\" class=\"col_heading level0 col4\" >4</th>\n",
       "      <th id=\"T_386a7_level0_col5\" class=\"col_heading level0 col5\" >5</th>\n",
       "      <th id=\"T_386a7_level0_col6\" class=\"col_heading level0 col6\" >6</th>\n",
       "      <th id=\"T_386a7_level0_col7\" class=\"col_heading level0 col7\" >7</th>\n",
       "      <th id=\"T_386a7_level0_col8\" class=\"col_heading level0 col8\" >8</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_386a7_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_386a7_row0_col0\" class=\"data row0 col0\" >3</td>\n",
       "      <td id=\"T_386a7_row0_col1\" class=\"data row0 col1\" >0.750000</td>\n",
       "      <td id=\"T_386a7_row0_col2\" class=\"data row0 col2\" >False</td>\n",
       "      <td id=\"T_386a7_row0_col3\" class=\"data row0 col3\" >False</td>\n",
       "      <td id=\"T_386a7_row0_col4\" class=\"data row0 col4\" >True</td>\n",
       "      <td id=\"T_386a7_row0_col5\" class=\"data row0 col5\" >False</td>\n",
       "      <td id=\"T_386a7_row0_col6\" class=\"data row0 col6\" >hello</td>\n",
       "      <td id=\"T_386a7_row0_col7\" class=\"data row0 col7\" >0.911531</td>\n",
       "      <td id=\"T_386a7_row0_col8\" class=\"data row0 col8\" >[1, 2, 3, 4, 5, 6, 7]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x106b9c6d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[] <- [[\n",
    "            1 + 2, # addition\n",
    "            3 / 4, # division\n",
    "            5 == 6, # equality\n",
    "            7 > 8, # greater\n",
    "            true || false, # or\n",
    "            false && true, # and\n",
    "            lowercase('HELLO'), # function\n",
    "            rand_float(), # function taking no argument\n",
    "            union([1, 2, 3], [3, 4, 5], [5, 6, 7]), # variadic function\n",
    "        ]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c5ee182-2ca8-49b3-8937-19da63124143",
   "metadata": {},
   "source": [
    "Notice in the last column the use of list literals within expressions. \n",
    "See [here](https://cozodb.github.io/current/manual/functions.html) the full list of functions.\n",
    "The syntax is deliberately made almost identical to C-like languages."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bcc26ff-9901-4d6e-a895-cb77dbfafe3a",
   "metadata": {},
   "source": [
    "## Rules and relations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eefa79d-a14e-4179-81b0-04da2b47c498",
   "metadata": {},
   "source": [
    "Previous examples all start with `?[] <-`, which denotes a _rule_ named `?`, which is a _constant rule_, which when evaluated just echoes the list of lists back as a relation.\n",
    "\n",
    "Rules can have other names, but the rule named `?` is special in that its evaluation determines the return relation of the query.\n",
    "\n",
    "Before we go beyond constant rules, note that we can give _bindings_ in the _head_ of rules:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2a35a414-7037-4a2a-a07b-086463a4d4ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_43c5e_row0_col0, #T_43c5e_row0_col1, #T_43c5e_row0_col2 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "#T_43c5e_row1_col0, #T_43c5e_row1_col1, #T_43c5e_row1_col2 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_43c5e\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_43c5e_level0_col0\" class=\"col_heading level0 col0\" >first</th>\n",
       "      <th id=\"T_43c5e_level0_col1\" class=\"col_heading level0 col1\" >second</th>\n",
       "      <th id=\"T_43c5e_level0_col2\" class=\"col_heading level0 col2\" >third</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_43c5e_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_43c5e_row0_col0\" class=\"data row0 col0\" >1</td>\n",
       "      <td id=\"T_43c5e_row0_col1\" class=\"data row0 col1\" >2</td>\n",
       "      <td id=\"T_43c5e_row0_col2\" class=\"data row0 col2\" >3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_43c5e_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_43c5e_row1_col0\" class=\"data row1 col0\" >a</td>\n",
       "      <td id=\"T_43c5e_row1_col1\" class=\"data row1 col1\" >b</td>\n",
       "      <td id=\"T_43c5e_row1_col2\" class=\"data row1 col2\" >c</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x106b9fca0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[first, second, third] <- [[1, 2, 3], ['a', 'b', 'c']]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba32d27c-0787-48d3-94fb-79e77a8cce0c",
   "metadata": {},
   "source": [
    "If you give bindings, the number of bindings must match the actual data, otherwise, you will get an error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b25901e4-fc6a-4cb0-9ca2-b9aeac80cc83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[31mparser::fixed_rule_head_arity_mismatch\u001b[0m\n",
       "\n",
       "  \u001b[31m×\u001b[0m Fixed rule head arity mismatch\n",
       "   ╭────\n",
       " \u001b[2m1\u001b[0m │ ?[first, second] <- [[1, 2, 3], ['a', 'b', 'c']]\n",
       "   · \u001b[35;1m─────────────────────────────────────────────────\u001b[0m\n",
       "   ╰────\n",
       "\u001b[36m  help: \u001b[0mExpected arity: 3, number of arguments given: 2\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[first, second] <- [[1, 2, 3], ['a', 'b', 'c']]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c71fb449-6a9c-4a7e-bed9-44230a41d5dd",
   "metadata": {},
   "source": [
    "Now let's define rules that use other rules:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bc63b0b2-fa28-4d02-be90-23690f6021aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_3d5c7_row0_col0, #T_3d5c7_row0_col1, #T_3d5c7_row0_col2 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "#T_3d5c7_row1_col0, #T_3d5c7_row1_col1, #T_3d5c7_row1_col2 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_3d5c7\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_3d5c7_level0_col0\" class=\"col_heading level0 col0\" >a</th>\n",
       "      <th id=\"T_3d5c7_level0_col1\" class=\"col_heading level0 col1\" >b</th>\n",
       "      <th id=\"T_3d5c7_level0_col2\" class=\"col_heading level0 col2\" >c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_3d5c7_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_3d5c7_row0_col0\" class=\"data row0 col0\" >1</td>\n",
       "      <td id=\"T_3d5c7_row0_col1\" class=\"data row0 col1\" >2</td>\n",
       "      <td id=\"T_3d5c7_row0_col2\" class=\"data row0 col2\" >3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3d5c7_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_3d5c7_row1_col0\" class=\"data row1 col0\" >a</td>\n",
       "      <td id=\"T_3d5c7_row1_col1\" class=\"data row1 col1\" >b</td>\n",
       "      <td id=\"T_3d5c7_row1_col2\" class=\"data row1 col2\" >c</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d1b70>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule[first, second, third] <- [[1, 2, 3], ['a', 'b', 'c']]\n",
    "?[a, b, c] := rule[a, b, c]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d86d57af-fadb-441a-926f-142c613ca1f7",
   "metadata": {},
   "source": [
    "This first defines a constant rule named `rule`. The `?` rule is now an _inline rule_, denoted by the connecting symbol `:=`. In its body it _applies_ the fixed rule, by giving the name of the rule followed by three _fresh bindings_, which are the _variables_ `a`, `b` and `c`.\n",
    "\n",
    "With inline rules, you can manipulate the order of the columns, or what columns are returned:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d5d52704-e2ed-430c-b9da-939964f7b8e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_89208_row0_col0, #T_89208_row0_col1 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "#T_89208_row1_col0, #T_89208_row1_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_89208\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_89208_level0_col0\" class=\"col_heading level0 col0\" >c</th>\n",
       "      <th id=\"T_89208_level0_col1\" class=\"col_heading level0 col1\" >b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_89208_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_89208_row0_col0\" class=\"data row0 col0\" >3</td>\n",
       "      <td id=\"T_89208_row0_col1\" class=\"data row0 col1\" >2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_89208_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_89208_row1_col0\" class=\"data row1 col0\" >c</td>\n",
       "      <td id=\"T_89208_row1_col1\" class=\"data row1 col1\" >b</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d0220>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule[first, second, third] <- [[1, 2, 3], ['a', 'b', 'c']]\n",
    "?[c, b] := rule[a, b, c]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb8a68dc-ab27-494b-86cd-b38502ea1a7c",
   "metadata": {},
   "source": [
    "The body of an inline rule, which are the things to the right of the connecting symbol `:=`, consists of _atoms_. \n",
    "The previous example has a single rule application atom as the body. Multiple atoms are connected by commas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "657050ce-5c99-494b-b2e7-283ae73de8fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_1a0cd_row0_col0, #T_1a0cd_row0_col1 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_1a0cd\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_1a0cd_level0_col0\" class=\"col_heading level0 col0\" >c</th>\n",
       "      <th id=\"T_1a0cd_level0_col1\" class=\"col_heading level0 col1\" >b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_1a0cd_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_1a0cd_row0_col0\" class=\"data row0 col0\" >3</td>\n",
       "      <td id=\"T_1a0cd_row0_col1\" class=\"data row0 col1\" >2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d3a60>"
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     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[c, b] := rule[a, b, c], is_num(a)\n",
    "rule[first, second, third] <- [[1, 2, 3], ['a', 'b', 'c']]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15c68fce-5318-453d-9e59-aee862ed5036",
   "metadata": {},
   "source": [
    "Here the second atom is an _expression_ `is_num(a)`. \n",
    "Only rows for which the expression evaluates to `true` are returned, so expression atoms act as filters. \n",
    "By the way, we see that the order in which the rules are given is immaterial."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7793c44a-302c-4ed1-985e-4951c0a78b20",
   "metadata": {},
   "source": [
    "You can also bind constants to rule applications directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "44745ced-563b-41ce-aace-ce43f7ada7f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
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     "output_type": "display_data"
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       "<style type=\"text/css\">\n",
       "#T_cc714_row0_col0, #T_cc714_row0_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_cc714\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_cc714_level0_col0\" class=\"col_heading level0 col0\" >c</th>\n",
       "      <th id=\"T_cc714_level0_col1\" class=\"col_heading level0 col1\" >b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_cc714_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_cc714_row0_col0\" class=\"data row0 col0\" >c</td>\n",
       "      <td id=\"T_cc714_row0_col1\" class=\"data row0 col1\" >b</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d2650>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rule[first, second, third] <- [[1, 2, 3], ['a', 'b', 'c']]\n",
    "?[c, b] := rule['a', b, c]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40b1fc69-c118-4876-a2d5-5fd2d8931811",
   "metadata": {},
   "source": [
    "You introduce additional bindings with the _unification operator_ `=`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cf32547a-7def-4dec-8d05-77c7c910be2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_fc5e3_row0_col0, #T_fc5e3_row0_col1, #T_fc5e3_row0_col2 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_fc5e3\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_fc5e3_level0_col0\" class=\"col_heading level0 col0\" >c</th>\n",
       "      <th id=\"T_fc5e3_level0_col1\" class=\"col_heading level0 col1\" >b</th>\n",
       "      <th id=\"T_fc5e3_level0_col2\" class=\"col_heading level0 col2\" >d</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_fc5e3_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_fc5e3_row0_col0\" class=\"data row0 col0\" >3</td>\n",
       "      <td id=\"T_fc5e3_row0_col1\" class=\"data row0 col1\" >2</td>\n",
       "      <td id=\"T_fc5e3_row0_col2\" class=\"data row0 col2\" >9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
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       "<pandas.io.formats.style.Styler at 0x11f2d2710>"
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     },
     "execution_count": 14,
     "metadata": {},
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    }
   ],
   "source": [
    "rule[first, second, third] <- [[1, 2, 3], ['a', 'b', 'c']]\n",
    "?[c, b, d] := rule[a, b, c], is_num(a), d = a + b + 2*c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5384db7-8cab-4262-94f5-a2b7298417e8",
   "metadata": {},
   "source": [
    "Having multiple rule applications in the body generates every combination of the bindings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "59d2a912-50d6-474a-ae9b-74f024a58bdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_1c432_row0_col0, #T_1c432_row0_col1, #T_1c432_row1_col0, #T_1c432_row1_col1, #T_1c432_row2_col0, #T_1c432_row2_col1, #T_1c432_row3_col0, #T_1c432_row3_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_1c432\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_1c432_level0_col0\" class=\"col_heading level0 col0\" >l1</th>\n",
       "      <th id=\"T_1c432_level0_col1\" class=\"col_heading level0 col1\" >l2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_1c432_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_1c432_row0_col0\" class=\"data row0 col0\" >a</td>\n",
       "      <td id=\"T_1c432_row0_col1\" class=\"data row0 col1\" >B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_1c432_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_1c432_row1_col0\" class=\"data row1 col0\" >a</td>\n",
       "      <td id=\"T_1c432_row1_col1\" class=\"data row1 col1\" >C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_1c432_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_1c432_row2_col0\" class=\"data row2 col0\" >b</td>\n",
       "      <td id=\"T_1c432_row2_col1\" class=\"data row2 col1\" >B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_1c432_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_1c432_row3_col0\" class=\"data row3 col0\" >b</td>\n",
       "      <td id=\"T_1c432_row3_col1\" class=\"data row3 col1\" >C</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d1e10>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1[] <- [[1, 'a'], [2, 'b']]\n",
    "r2[] <- [[2, 'B'], [3, 'C']]\n",
    "\n",
    "?[l1, l2] := r1[a, l1], \n",
    "             r2[b, l2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b26be73d-dc5c-400b-9af4-d3aa9af0c430",
   "metadata": {},
   "source": [
    "This corresponds to a Cartesian join in relational algebra. \n",
    "Notice the bindings in the rule applications are all distinct.\n",
    "If bindings are reused, then we get the effect of _unification_,\n",
    "which corresponds to joins in relational algebra:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "20256fd6-b5c0-4947-a860-021846bef5fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_5c969_row0_col0, #T_5c969_row0_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_5c969\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_5c969_level0_col0\" class=\"col_heading level0 col0\" >l1</th>\n",
       "      <th id=\"T_5c969_level0_col1\" class=\"col_heading level0 col1\" >l2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_5c969_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_5c969_row0_col0\" class=\"data row0 col0\" >b</td>\n",
       "      <td id=\"T_5c969_row0_col1\" class=\"data row0 col1\" >B</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
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       "<pandas.io.formats.style.Styler at 0x11f2d0850>"
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     "execution_count": 16,
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   ],
   "source": [
    "r1[] <- [[1, 'a'], [2, 'b']]\n",
    "r2[] <- [[2, 'B'], [3, 'C']]\n",
    "\n",
    "?[l1, l2] := r1[a, l1], \n",
    "             r2[a, l2] # reused `a`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf4be53c-118f-46b8-9c42-cb259aed6e87",
   "metadata": {},
   "source": [
    "The explicit unification `=` unifies with a single value. There is another kind of unification that unifies values within a list. Observe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5c7d2b90-8494-4521-aac6-2445473e50d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_e4e89_row0_col0, #T_e4e89_row1_col0, #T_e4e89_row2_col0, #T_e4e89_row3_col0, #T_e4e89_row4_col0, #T_e4e89_row5_col0 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "#T_e4e89_row0_col1, #T_e4e89_row1_col1, #T_e4e89_row2_col1, #T_e4e89_row3_col1, #T_e4e89_row4_col1, #T_e4e89_row5_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_e4e89\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_e4e89_level0_col0\" class=\"col_heading level0 col0\" >x</th>\n",
       "      <th id=\"T_e4e89_level0_col1\" class=\"col_heading level0 col1\" >y</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_e4e89_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_e4e89_row0_col0\" class=\"data row0 col0\" >1</td>\n",
       "      <td id=\"T_e4e89_row0_col1\" class=\"data row0 col1\" >x</td>\n",
       "    </tr>\n",
       "    <tr>\n",
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       "      <td id=\"T_e4e89_row1_col0\" class=\"data row1 col0\" >1</td>\n",
       "      <td id=\"T_e4e89_row1_col1\" class=\"data row1 col1\" >y</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_e4e89_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_e4e89_row2_col0\" class=\"data row2 col0\" >2</td>\n",
       "      <td id=\"T_e4e89_row2_col1\" class=\"data row2 col1\" >x</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_e4e89_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_e4e89_row3_col0\" class=\"data row3 col0\" >2</td>\n",
       "      <td id=\"T_e4e89_row3_col1\" class=\"data row3 col1\" >y</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_e4e89_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_e4e89_row4_col0\" class=\"data row4 col0\" >3</td>\n",
       "      <td id=\"T_e4e89_row4_col1\" class=\"data row4 col1\" >x</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_e4e89_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_e4e89_row5_col0\" class=\"data row5 col0\" >3</td>\n",
       "      <td id=\"T_e4e89_row5_col1\" class=\"data row5 col1\" >y</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
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       "<pandas.io.formats.style.Styler at 0x11f2d1870>"
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     },
     "execution_count": 17,
     "metadata": {},
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    }
   ],
   "source": [
    "?[x, y] := x in [1, 2, 3], y in ['x', 'y']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af092ab5-2692-4b12-a6a7-eae8def60cac",
   "metadata": {},
   "source": [
    "For the head of inline rules, you do not need to use all variables that appear in the body. But whatever you use must appear in the body, this is called the _safety rule_:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5a13303d-4f61-4bc5-85d1-391773a9bc7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[31meval::unbound_symb_in_head\u001b[0m\n",
       "\n",
       "  \u001b[31m×\u001b[0m Symbol 'x' in rule head is unbound\n",
       "   ╭─[3:1]\n",
       " \u001b[2m3\u001b[0m │ \n",
       " \u001b[2m4\u001b[0m │ ?[l1, l2, x] := r1[a, l1], \n",
       "   · \u001b[35;1m          ─\u001b[0m\n",
       " \u001b[2m5\u001b[0m │                 r2[a, l2]\n",
       "   ╰────\n",
       "\u001b[36m  help: \u001b[0mNote that symbols occurring only in negated positions are not considered bound\n"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1[] <- [[1, 'a'], [2, 'b']]\n",
    "r2[] <- [[2, 'B'], [3, 'C']]\n",
    "\n",
    "?[l1, l2, x] := r1[a, l1], \n",
    "                r2[a, l2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0c1b973-4ecf-459d-99d9-bab9665a7d23",
   "metadata": {},
   "source": [
    "## Stored relations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb7e8795-7b95-4653-958c-c9682f25e137",
   "metadata": {},
   "source": [
    "The constructs that we have introduced already cover most of what relational algebra can do. That's some economy of syntax! \n",
    "However, as a database, we need to know how to store data persistently. In Cozo, persistent relations are called _stored relations_."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79357544-8eeb-4b33-b49c-bd6cb4de57cb",
   "metadata": {},
   "source": [
    "There is no ceremony required at all when you want to store data in Cozo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2944f226-c865-4fd6-b412-cb34e2e50705",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
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     },
     "metadata": {},
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    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_6769b_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_6769b\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_6769b_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_6769b_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_6769b_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d3550>"
      ]
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     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1[] <- [[1, 'a'], [2, 'b']]\n",
    "r2[] <- [[2, 'B'], [3, 'C']]\n",
    "\n",
    "?[l1, l2] := r1[a, l1], \n",
    "             r2[a, l2]\n",
    "    \n",
    ":create stored {l1, l2}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e911e87-a80e-4b1b-a878-613b61e339bc",
   "metadata": {},
   "source": [
    "The query itself is identical to the one which we have run before, except we have added the `:create` query option, instructing the system to store the result in a stored relation named `stored`, containing the columns `l1` and `l2`.\n",
    "\n",
    "By the way, if you just want to create the relation without adding any data, you can omit the queries. No need to have an empty `?` query."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60c8509a-0aea-4d0b-9ca3-e8d0b00e73ad",
   "metadata": {},
   "source": [
    "You can verify that you now have the required stored relation in your system by running a _system op_:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e151e2e6-f185-4659-89c6-a274c643a03a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_edaba_row0_col0, #T_edaba_row0_col2 {\n",
       "  color: black;\n",
       "}\n",
       "#T_edaba_row0_col1, #T_edaba_row0_col3, #T_edaba_row0_col4, #T_edaba_row0_col5, #T_edaba_row0_col6, #T_edaba_row0_col7 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_edaba\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_edaba_level0_col0\" class=\"col_heading level0 col0\" >name</th>\n",
       "      <th id=\"T_edaba_level0_col1\" class=\"col_heading level0 col1\" >arity</th>\n",
       "      <th id=\"T_edaba_level0_col2\" class=\"col_heading level0 col2\" >access_level</th>\n",
       "      <th id=\"T_edaba_level0_col3\" class=\"col_heading level0 col3\" >n_keys</th>\n",
       "      <th id=\"T_edaba_level0_col4\" class=\"col_heading level0 col4\" >n_non_keys</th>\n",
       "      <th id=\"T_edaba_level0_col5\" class=\"col_heading level0 col5\" >n_put_triggers</th>\n",
       "      <th id=\"T_edaba_level0_col6\" class=\"col_heading level0 col6\" >n_rm_triggers</th>\n",
       "      <th id=\"T_edaba_level0_col7\" class=\"col_heading level0 col7\" >n_replace_triggers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_edaba_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_edaba_row0_col0\" class=\"data row0 col0\" >stored</td>\n",
       "      <td id=\"T_edaba_row0_col1\" class=\"data row0 col1\" >2</td>\n",
       "      <td id=\"T_edaba_row0_col2\" class=\"data row0 col2\" >normal</td>\n",
       "      <td id=\"T_edaba_row0_col3\" class=\"data row0 col3\" >2</td>\n",
       "      <td id=\"T_edaba_row0_col4\" class=\"data row0 col4\" >0</td>\n",
       "      <td id=\"T_edaba_row0_col5\" class=\"data row0 col5\" >0</td>\n",
       "      <td id=\"T_edaba_row0_col6\" class=\"data row0 col6\" >0</td>\n",
       "      <td id=\"T_edaba_row0_col7\" class=\"data row0 col7\" >0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d1f60>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "::relations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30d7999f-6939-497d-98d6-e5edc6af44a1",
   "metadata": {},
   "source": [
    "You can also investigate the columns of the stored relation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "fd8c4f13-96c8-4f3c-b295-ea493d3875f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_0e398_row0_col0, #T_0e398_row0_col3, #T_0e398_row1_col0, #T_0e398_row1_col3 {\n",
       "  color: black;\n",
       "}\n",
       "#T_0e398_row0_col1, #T_0e398_row0_col2, #T_0e398_row0_col4, #T_0e398_row1_col1, #T_0e398_row1_col2, #T_0e398_row1_col4 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_0e398\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_0e398_level0_col0\" class=\"col_heading level0 col0\" >column</th>\n",
       "      <th id=\"T_0e398_level0_col1\" class=\"col_heading level0 col1\" >is_key</th>\n",
       "      <th id=\"T_0e398_level0_col2\" class=\"col_heading level0 col2\" >index</th>\n",
       "      <th id=\"T_0e398_level0_col3\" class=\"col_heading level0 col3\" >type</th>\n",
       "      <th id=\"T_0e398_level0_col4\" class=\"col_heading level0 col4\" >has_default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_0e398_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_0e398_row0_col0\" class=\"data row0 col0\" >l1</td>\n",
       "      <td id=\"T_0e398_row0_col1\" class=\"data row0 col1\" >True</td>\n",
       "      <td id=\"T_0e398_row0_col2\" class=\"data row0 col2\" >0</td>\n",
       "      <td id=\"T_0e398_row0_col3\" class=\"data row0 col3\" >Any?</td>\n",
       "      <td id=\"T_0e398_row0_col4\" class=\"data row0 col4\" >False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_0e398_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_0e398_row1_col0\" class=\"data row1 col0\" >l2</td>\n",
       "      <td id=\"T_0e398_row1_col1\" class=\"data row1 col1\" >True</td>\n",
       "      <td id=\"T_0e398_row1_col2\" class=\"data row1 col2\" >1</td>\n",
       "      <td id=\"T_0e398_row1_col3\" class=\"data row1 col3\" >Any?</td>\n",
       "      <td id=\"T_0e398_row1_col4\" class=\"data row1 col4\" >False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d3c10>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "::columns stored "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79d320aa-bf41-4676-a778-7ff00b704ced",
   "metadata": {},
   "source": [
    "Stored relations can be used in a similar way to relations defined via inline rules or fixed rules. The only difference is that you prefix the relation name with a colon:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3d4a2c70-7ed3-403b-9528-a696fe7b08a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_aa019_row0_col0, #T_aa019_row0_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_aa019\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_aa019_level0_col0\" class=\"col_heading level0 col0\" >a</th>\n",
       "      <th id=\"T_aa019_level0_col1\" class=\"col_heading level0 col1\" >b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_aa019_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_aa019_row0_col0\" class=\"data row0 col0\" >b</td>\n",
       "      <td id=\"T_aa019_row0_col1\" class=\"data row0 col1\" >B</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d25f0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[a, b] := @stored[a, b]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "821c1a1f-ef11-4429-ba99-c2599bc18857",
   "metadata": {},
   "source": [
    "Unlike relations defined inline, the columns of stored relations have fixed names. You can use this to your advantage by selectively referring to columns by name.\n",
    "This is especially useful if you have a lot of columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "dba56d3f-8162-4519-8934-12d5c6935239",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_3d251_row0_col0, #T_3d251_row0_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_3d251\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_3d251_level0_col0\" class=\"col_heading level0 col0\" >a</th>\n",
       "      <th id=\"T_3d251_level0_col1\" class=\"col_heading level0 col1\" >b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_3d251_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_3d251_row0_col0\" class=\"data row0 col0\" >b</td>\n",
       "      <td id=\"T_3d251_row0_col1\" class=\"data row0 col1\" >B</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d3640>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[a, b] := @stored{l2: b, l1: a}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "135b9fb5-96fd-444b-aa44-ad8dd754318d",
   "metadata": {},
   "source": [
    "If you are fine with using the name of the column as the binding, a shorthand is available:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a5a29a9c-5320-4c9f-a153-a96c662cf5d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_1bf22_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_1bf22\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_1bf22_level0_col0\" class=\"col_heading level0 col0\" >l2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_1bf22_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_1bf22_row0_col0\" class=\"data row0 col0\" >B</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c2d10>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[l2] := @stored{l2}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2424a684-89fb-449e-a5e6-931353bb482f",
   "metadata": {},
   "source": [
    "Inserting more data into stored relation is easy by using the `:put` query option:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "eb8b4f2c-a2e7-45e3-8c18-6b6b8329344c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_58bf6_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_58bf6\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_58bf6_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_58bf6_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_58bf6_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c1960>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[l1, l2] <- [['e', 'E']]\n",
    "    \n",
    ":put stored {l1, l2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ef21c6f3-ce5c-434c-a580-3d1442ebe7c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_399e6_row0_col0, #T_399e6_row0_col1, #T_399e6_row1_col0, #T_399e6_row1_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_399e6\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_399e6_level0_col0\" class=\"col_heading level0 col0\" >l1</th>\n",
       "      <th id=\"T_399e6_level0_col1\" class=\"col_heading level0 col1\" >l2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_399e6_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_399e6_row0_col0\" class=\"data row0 col0\" >b</td>\n",
       "      <td id=\"T_399e6_row0_col1\" class=\"data row0 col1\" >B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_399e6_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_399e6_row1_col0\" class=\"data row1 col0\" >e</td>\n",
       "      <td id=\"T_399e6_row1_col1\" class=\"data row1 col1\" >E</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d1bd0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[l1, l2] := @stored[l1, l2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a58b487a-6a44-43c7-9351-b78a49770a46",
   "metadata": {},
   "source": [
    "To remove rows, use the `:rm` query option:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2c1d522b-286f-41be-9796-da165999e1df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_cf159_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_cf159\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_cf159_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_cf159_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_cf159_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c1d80>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[l1, l2] <- [['e', 'E']]\n",
    "    \n",
    ":rm stored {l1, l2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "d9ce93f8-dc37-4c37-9f47-904066c1341a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_69994_row0_col0, #T_69994_row0_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_69994\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_69994_level0_col0\" class=\"col_heading level0 col0\" >l1</th>\n",
       "      <th id=\"T_69994_level0_col1\" class=\"col_heading level0 col1\" >l2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_69994_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_69994_row0_col0\" class=\"data row0 col0\" >b</td>\n",
       "      <td id=\"T_69994_row0_col1\" class=\"data row0 col1\" >B</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c2a10>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[l1, l2] := @stored[l1, l2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f70e3b5-0b96-42ce-8a34-9d45beaf1772",
   "metadata": {},
   "source": [
    "You can get rid of a stored relation with the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "f27e0eb3-711f-4d68-bd02-1e4cfddfd9ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_6ad54_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_6ad54\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_6ad54_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_6ad54_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_6ad54_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c2260>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "::remove stored"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c938ecd5-8166-4f78-8fa1-234c75691d5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "</style>\n",
       "<table id=\"T_13798\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_13798_level0_col0\" class=\"col_heading level0 col0\" >name</th>\n",
       "      <th id=\"T_13798_level0_col1\" class=\"col_heading level0 col1\" >arity</th>\n",
       "      <th id=\"T_13798_level0_col2\" class=\"col_heading level0 col2\" >access_level</th>\n",
       "      <th id=\"T_13798_level0_col3\" class=\"col_heading level0 col3\" >n_keys</th>\n",
       "      <th id=\"T_13798_level0_col4\" class=\"col_heading level0 col4\" >n_non_keys</th>\n",
       "      <th id=\"T_13798_level0_col5\" class=\"col_heading level0 col5\" >n_put_triggers</th>\n",
       "      <th id=\"T_13798_level0_col6\" class=\"col_heading level0 col6\" >n_rm_triggers</th>\n",
       "      <th id=\"T_13798_level0_col7\" class=\"col_heading level0 col7\" >n_replace_triggers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c3010>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "::relations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df2bff7d-3164-409a-a7fd-4e074be7ecbc",
   "metadata": {},
   "source": [
    "As we have mentioned, every relation in Cozo is a tree. Stored relation is no exception.\n",
    "So far, our trees store all the data in their keys.\n",
    "You can instruct Cozo to only treat some of the data as keys, thereby indicating a _functional dependency_:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "3a133dc0-5334-4acb-972a-305b5927941a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_5edba_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_5edba\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_5edba_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_5edba_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_5edba_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c2bf0>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[a, b, c] <- [[1, 'a', 'A'],\n",
    "               [2, 'b', 'B'],\n",
    "               [3, 'c', 'C'],\n",
    "               [4, 'd', 'D']]\n",
    "\n",
    ":create fd {a, b => c}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "3ff9ac04-531d-4726-aeb2-d8feab7bc149",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_3d350_row0_col0, #T_3d350_row1_col0, #T_3d350_row2_col0, #T_3d350_row3_col0 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "#T_3d350_row0_col1, #T_3d350_row0_col2, #T_3d350_row1_col1, #T_3d350_row1_col2, #T_3d350_row2_col1, #T_3d350_row2_col2, #T_3d350_row3_col1, #T_3d350_row3_col2 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_3d350\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_3d350_level0_col0\" class=\"col_heading level0 col0\" >a</th>\n",
       "      <th id=\"T_3d350_level0_col1\" class=\"col_heading level0 col1\" >b</th>\n",
       "      <th id=\"T_3d350_level0_col2\" class=\"col_heading level0 col2\" >c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_3d350_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_3d350_row0_col0\" class=\"data row0 col0\" >1</td>\n",
       "      <td id=\"T_3d350_row0_col1\" class=\"data row0 col1\" >a</td>\n",
       "      <td id=\"T_3d350_row0_col2\" class=\"data row0 col2\" >A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3d350_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_3d350_row1_col0\" class=\"data row1 col0\" >2</td>\n",
       "      <td id=\"T_3d350_row1_col1\" class=\"data row1 col1\" >b</td>\n",
       "      <td id=\"T_3d350_row1_col2\" class=\"data row1 col2\" >B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3d350_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_3d350_row2_col0\" class=\"data row2 col0\" >3</td>\n",
       "      <td id=\"T_3d350_row2_col1\" class=\"data row2 col1\" >c</td>\n",
       "      <td id=\"T_3d350_row2_col2\" class=\"data row2 col2\" >C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_3d350_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_3d350_row3_col0\" class=\"data row3 col0\" >4</td>\n",
       "      <td id=\"T_3d350_row3_col1\" class=\"data row3 col1\" >d</td>\n",
       "      <td id=\"T_3d350_row3_col2\" class=\"data row3 col2\" >D</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c3a90>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[a, b, c] := @fd[a, b, c]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53128ced-3edb-4f8a-bbff-506e7139711f",
   "metadata": {},
   "source": [
    "Now if you insert another row with an existing key, that row will be updated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "fd442640-4664-4f1c-a0a7-0a265d19ca74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_8efb5_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_8efb5\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_8efb5_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_8efb5_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_8efb5_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2fafb0>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[a, b, c] <- [[3, 'c', 'CCCCCCC']]\n",
    "\n",
    ":put fd {a, b => c}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "980e4530-baec-40c5-9d68-e60d3dd8fb73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_6d6a0_row0_col0, #T_6d6a0_row1_col0, #T_6d6a0_row2_col0, #T_6d6a0_row3_col0 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "#T_6d6a0_row0_col1, #T_6d6a0_row0_col2, #T_6d6a0_row1_col1, #T_6d6a0_row1_col2, #T_6d6a0_row2_col1, #T_6d6a0_row2_col2, #T_6d6a0_row3_col1, #T_6d6a0_row3_col2 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_6d6a0\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_6d6a0_level0_col0\" class=\"col_heading level0 col0\" >a</th>\n",
       "      <th id=\"T_6d6a0_level0_col1\" class=\"col_heading level0 col1\" >b</th>\n",
       "      <th id=\"T_6d6a0_level0_col2\" class=\"col_heading level0 col2\" >c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_6d6a0_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_6d6a0_row0_col0\" class=\"data row0 col0\" >1</td>\n",
       "      <td id=\"T_6d6a0_row0_col1\" class=\"data row0 col1\" >a</td>\n",
       "      <td id=\"T_6d6a0_row0_col2\" class=\"data row0 col2\" >A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6d6a0_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_6d6a0_row1_col0\" class=\"data row1 col0\" >2</td>\n",
       "      <td id=\"T_6d6a0_row1_col1\" class=\"data row1 col1\" >b</td>\n",
       "      <td id=\"T_6d6a0_row1_col2\" class=\"data row1 col2\" >B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6d6a0_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_6d6a0_row2_col0\" class=\"data row2 col0\" >3</td>\n",
       "      <td id=\"T_6d6a0_row2_col1\" class=\"data row2 col1\" >c</td>\n",
       "      <td id=\"T_6d6a0_row2_col2\" class=\"data row2 col2\" >CCCCCCC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6d6a0_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_6d6a0_row3_col0\" class=\"data row3 col0\" >4</td>\n",
       "      <td id=\"T_6d6a0_row3_col1\" class=\"data row3 col1\" >d</td>\n",
       "      <td id=\"T_6d6a0_row3_col2\" class=\"data row3 col2\" >D</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d2860>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[a, b, c] := @fd[a, b, c]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f84ee9b-46b2-448a-b399-914cf5d4d810",
   "metadata": {},
   "source": [
    "You can easily check whether a column is in a key position by looking at the `is_key` column in the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "07bdf041-6b4f-4686-9aa5-3d95f323a397",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_afd6c_row0_col0, #T_afd6c_row0_col3, #T_afd6c_row1_col0, #T_afd6c_row1_col3, #T_afd6c_row2_col0, #T_afd6c_row2_col3 {\n",
       "  color: black;\n",
       "}\n",
       "#T_afd6c_row0_col1, #T_afd6c_row0_col2, #T_afd6c_row0_col4, #T_afd6c_row1_col1, #T_afd6c_row1_col2, #T_afd6c_row1_col4, #T_afd6c_row2_col1, #T_afd6c_row2_col2, #T_afd6c_row2_col4 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_afd6c\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_afd6c_level0_col0\" class=\"col_heading level0 col0\" >column</th>\n",
       "      <th id=\"T_afd6c_level0_col1\" class=\"col_heading level0 col1\" >is_key</th>\n",
       "      <th id=\"T_afd6c_level0_col2\" class=\"col_heading level0 col2\" >index</th>\n",
       "      <th id=\"T_afd6c_level0_col3\" class=\"col_heading level0 col3\" >type</th>\n",
       "      <th id=\"T_afd6c_level0_col4\" class=\"col_heading level0 col4\" >has_default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_afd6c_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_afd6c_row0_col0\" class=\"data row0 col0\" >a</td>\n",
       "      <td id=\"T_afd6c_row0_col1\" class=\"data row0 col1\" >True</td>\n",
       "      <td id=\"T_afd6c_row0_col2\" class=\"data row0 col2\" >0</td>\n",
       "      <td id=\"T_afd6c_row0_col3\" class=\"data row0 col3\" >Any?</td>\n",
       "      <td id=\"T_afd6c_row0_col4\" class=\"data row0 col4\" >False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_afd6c_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_afd6c_row1_col0\" class=\"data row1 col0\" >b</td>\n",
       "      <td id=\"T_afd6c_row1_col1\" class=\"data row1 col1\" >True</td>\n",
       "      <td id=\"T_afd6c_row1_col2\" class=\"data row1 col2\" >1</td>\n",
       "      <td id=\"T_afd6c_row1_col3\" class=\"data row1 col3\" >Any?</td>\n",
       "      <td id=\"T_afd6c_row1_col4\" class=\"data row1 col4\" >False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_afd6c_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_afd6c_row2_col0\" class=\"data row2 col0\" >c</td>\n",
       "      <td id=\"T_afd6c_row2_col1\" class=\"data row2 col1\" >False</td>\n",
       "      <td id=\"T_afd6c_row2_col2\" class=\"data row2 col2\" >2</td>\n",
       "      <td id=\"T_afd6c_row2_col3\" class=\"data row2 col3\" >Any?</td>\n",
       "      <td id=\"T_afd6c_row2_col4\" class=\"data row2 col4\" >False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2d0ee0>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "::columns fd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "183002b2-1041-4843-a3a8-d1496ec6a4b6",
   "metadata": {},
   "source": [
    "You may have noticed that columns also have types and default values associated with them, and stored relations can have triggers. These are discussed in the [manual](https://cozodb.github.io/current/manual/stored.html).\n",
    "We won't overload you with all the complexities in this tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "726ae4cf-d643-4c27-abe2-56c04050e02e",
   "metadata": {},
   "source": [
    "The stored relations API are designed to be easy to use. However, sometimes being too easy can be bad, for example, it is possible to wipe an important stored relation full of data by a `:replace` erroneously introduced in a rarely used piece of code somewhere. For valuable stored relations, therefore, we recommend that you set the appropriate _access level_, as explained [here](https://cozodb.github.io/current/manual/stored.html#stored-relations)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30504cd6-7fb6-4ae3-ba2c-79eefa288095",
   "metadata": {},
   "source": [
    "Before continuing, let's remove the stored relation we introduced:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "8e70a093-600c-48c5-90f5-ff3f340287d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_b477d_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_b477d\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_b477d_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_b477d_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_b477d_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2f9900>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "::remove fd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b702c08-b59a-451c-826c-919a533b9094",
   "metadata": {},
   "source": [
    "## Graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f22421f2-6492-4e0a-a66b-672ff7a3d3b5",
   "metadata": {},
   "source": [
    "Now let's consider a graph, stored as a relation. Let's first make it a stored relation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "fba82f6e-124b-478d-893d-b69bc79680cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
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       "<style type=\"text/css\">\n",
       "#T_97b6d_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_97b6d\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_97b6d_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_97b6d_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_97b6d_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c28c0>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[loving, loved] <- [['alice', 'eve'],\n",
    "                     ['bob', 'alice'],\n",
    "                     ['eve', 'alice'],\n",
    "                     ['eve', 'bob'],\n",
    "                     ['eve', 'charlie'],\n",
    "                     ['charlie', 'eve'],\n",
    "                     ['david', 'george'],\n",
    "                     ['george', 'george']]\n",
    "\n",
    ":replace love {loving, loved}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b1cf760-0989-48b3-aaed-3270c2d188bf",
   "metadata": {},
   "source": [
    "The graph we have created reads like \"Alice loves Eve, Bob loves Alice\", \"nobody loves David, David loves George, but George only loves himself\", and so on. \n",
    "Here we used `:replace` instead of `:create`. The difference is that if `love` already exists, it will be wiped and replaced with the new data given."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59d559f0-3325-4bee-b209-3dbe26c3b90c",
   "metadata": {},
   "source": [
    "With the graph available, we can investigate competing interests:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "64fb79e4-381e-4190-ac19-05b53e76cf6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_71831_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_71831\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_71831_level0_col0\" class=\"col_heading level0 col0\" >loved_by_b_e</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_71831_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_71831_row0_col0\" class=\"data row0 col0\" >alice</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2fb4f0>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[loved_by_b_e] := @love['eve', loved_by_b_e], @love['bob', loved_by_b_e]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48fa9636-5727-4984-af6e-f318c3e98b85",
   "metadata": {},
   "source": [
    "So far we have only seen bodies consisting of _conjunction_ of atoms. Disjunction is also available, by using the `or` keyword:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "132c8855-cca2-4cb3-ae53-53d2ff92f4a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_0accb_row0_col0, #T_0accb_row1_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_0accb\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_0accb_level0_col0\" class=\"col_heading level0 col0\" >loved_by_b_e</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_0accb_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_0accb_row0_col0\" class=\"data row0 col0\" >alice</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_0accb_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_0accb_row1_col0\" class=\"data row1 col0\" >charlie</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2c1a20>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[loved_by_b_e] := @love['eve', loved_by_b_e] or @love['bob', loved_by_b_e], \n",
    "                   loved_by_b_e != 'bob', \n",
    "                   loved_by_b_e != 'eve'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8ebc9a1-356e-4ba1-952c-c66920551381",
   "metadata": {},
   "source": [
    "Another way to write the same query is to have multiple definitions of the same rule, with different bodies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "4e7ba20f-2a10-41f0-9062-cc269b36554d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_97b66_row0_col0, #T_97b66_row1_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_97b66\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_97b66_level0_col0\" class=\"col_heading level0 col0\" >loved_by_b_e</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_97b66_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_97b66_row0_col0\" class=\"data row0 col0\" >alice</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_97b66_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_97b66_row1_col0\" class=\"data row1 col0\" >charlie</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2f9ba0>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[loved_by_b_e] := @love['eve', loved_by_b_e], \n",
    "                   loved_by_b_e != 'bob', \n",
    "                   loved_by_b_e != 'eve'\n",
    "?[loved_by_b_e] := @love['bob', loved_by_b_e], \n",
    "                   loved_by_b_e != 'bob', \n",
    "                   loved_by_b_e != 'eve'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b859b50-a748-4e20-9900-7ee053078a7f",
   "metadata": {},
   "source": [
    "The first way of writing the query (using `or`) is just syntax sugar for the second way. When you have multiple definitions of the same inline rule, the rule heads must be compatible. Fixed rules cannot have multiple definitions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f357511-fb25-441f-bf9f-d1e583368928",
   "metadata": {},
   "source": [
    "## Negation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78242c93-bf6e-4e72-84e1-e7706f84e633",
   "metadata": {},
   "source": [
    "The next example demonstrates filters using negated expressions, which should already be familiar now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "ff02b41d-d3aa-4267-b7e9-b56874f37bf9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_ef280_row0_col0, #T_ef280_row1_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_ef280\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_ef280_level0_col0\" class=\"col_heading level0 col0\" >loved</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_ef280_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_ef280_row0_col0\" class=\"data row0 col0\" >alice</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ef280_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_ef280_row1_col0\" class=\"data row1 col0\" >george</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2face0>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[loved] := @love[person, loved], !ends_with(person, 'e')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "433386de-59b5-4169-b0fb-20ad28df401b",
   "metadata": {},
   "source": [
    "Rule applications can also be negated. Not with the `!` operator, but with the `not` keyword instead:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "5eda38db-ddba-45e1-8bd5-4b39116fd81f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_ebcd2_row0_col0, #T_ebcd2_row1_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_ebcd2\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_ebcd2_level0_col0\" class=\"col_heading level0 col0\" >loved_by_e_not_b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_ebcd2_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_ebcd2_row0_col0\" class=\"data row0 col0\" >bob</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ebcd2_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_ebcd2_row1_col0\" class=\"data row1 col0\" >charlie</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2f9690>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[loved_by_e_not_b] := @love['eve', loved_by_e_not_b], not @love['bob', loved_by_e_not_b]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b2c4fa2-1f07-440a-a7fa-1f9a3cbfdc3c",
   "metadata": {},
   "source": [
    "You can say that there are two sets of logical operations in Cozo, one set that acts on the level of expressions, and another set that acts on the level of atoms:\n",
    "\n",
    "* For atoms: `,` or `and` (conjunction), `or` (disjunction), `not` (negation)\n",
    "* For expressions: `&&` (conjunction), `||` (disjunction), `!` (negation)\n",
    "\n",
    "The difference between `,` and `and` is operator precedence: `and` has higher precedence than `or`, whereas `,` has lower precedence than `or`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d382525-25a5-49d1-9d8e-4a057de933a0",
   "metadata": {},
   "source": [
    "Negation of atoms has to abide by the _safety rule_. Let's violate it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "7db09fb7-25a5-424a-a66a-0bc24d6d4fc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[31meval::unbound_symb_in_head\u001b[0m\n",
       "\n",
       "  \u001b[31m×\u001b[0m Symbol 'not_loved_by_b' in rule head is unbound\n",
       "   ╭────\n",
       " \u001b[2m1\u001b[0m │ ?[not_loved_by_b] := not @love['bob', not_loved_by_b]\n",
       "   · \u001b[35;1m  ──────────────\u001b[0m\n",
       "   ╰────\n",
       "\u001b[36m  help: \u001b[0mNote that symbols occurring only in negated positions are not considered bound\n"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[not_loved_by_b] := not @love['bob', not_loved_by_b]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44d83981-21eb-406c-9287-0e50aff5c423",
   "metadata": {},
   "source": [
    "Why is this query not allowed? Well, what can it possibly return?\n",
    "For example, should the query return 'gold', since according to the facts at hand, \n",
    "Bob has no interest in 'gold'? \n",
    "So should our query return every possible string except a select few? \n",
    "That's not reasonable."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "204fbb34-293e-4c63-a1c4-14e5a48491d7",
   "metadata": {},
   "source": [
    "To make our query reasonable, we have to explicitly give our query a _closed world_ in which to operate the negation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "225a4625-b99a-41a8-a2ef-fa553065e8aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_042db_row0_col0, #T_042db_row1_col0, #T_042db_row2_col0, #T_042db_row3_col0, #T_042db_row4_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_042db\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_042db_level0_col0\" class=\"col_heading level0 col0\" >not_loved_by_b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_042db_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_042db_row0_col0\" class=\"data row0 col0\" >bob</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_042db_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_042db_row1_col0\" class=\"data row1 col0\" >charlie</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_042db_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_042db_row2_col0\" class=\"data row2 col0\" >david</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_042db_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_042db_row3_col0\" class=\"data row3 col0\" >eve</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_042db_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_042db_row4_col0\" class=\"data row4 col0\" >george</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2fad40>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "the_population[p] := @love[p, _a]\n",
    "the_population[p] := @love[_a, p]\n",
    "\n",
    "?[not_loved_by_b] := the_population[not_loved_by_b], not @love['bob', not_loved_by_b]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ac5f2cd-5a05-4b84-898d-f5a08c15907a",
   "metadata": {},
   "source": [
    "## Recursion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a61abee-f5ae-4447-ae7b-d857bfe5b870",
   "metadata": {},
   "source": [
    "Inline rules can refer to other rules by applying them. Inline rules can have multiple definitions. If you combine these two, you get recursions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "7a63d36e-a03d-4b4a-a825-cdc3ed036f1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_ee26c_row0_col0, #T_ee26c_row1_col0, #T_ee26c_row2_col0, #T_ee26c_row3_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_ee26c\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_ee26c_level0_col0\" class=\"col_heading level0 col0\" >chained</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_ee26c_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_ee26c_row0_col0\" class=\"data row0 col0\" >alice</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ee26c_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_ee26c_row1_col0\" class=\"data row1 col0\" >bob</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ee26c_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_ee26c_row2_col0\" class=\"data row2 col0\" >charlie</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ee26c_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_ee26c_row3_col0\" class=\"data row3 col0\" >eve</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2f9f90>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alice_love_chain[person] := @love['alice', person]\n",
    "alice_love_chain[person] := alice_love_chain[in_person], @love[in_person, person]\n",
    "\n",
    "?[chained] := alice_love_chain[chained]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00db7e33-13e8-4b5f-9438-b14ec8b37bf5",
   "metadata": {},
   "source": [
    "Someone \"chained\" is either loved by Alice directly or loved by someone already in the chain. The query as written reads very naturally."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1666bf8f-4e41-4428-bdc8-c1d05f6783df",
   "metadata": {},
   "source": [
    "You may object that you only need to be able to refer to other rules by applying them to have recursion, and multiple definitions are not required. Technically, true, but the resulting queries are not useful. Observe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "cbf96780-d71b-471e-8add-dbd2d0f13f24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "</style>\n",
       "<table id=\"T_e8eff\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_e8eff_level0_col0\" class=\"col_heading level0 col0\" >chained</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2f9990>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alice_love_chain[person] := alice_love_chain[in_person], @love[in_person, person]\n",
    "\n",
    "?[chained] := alice_love_chain[chained]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac4a9d13-3360-487d-81c8-8da33f781bae",
   "metadata": {},
   "source": [
    "This is the _closed-world assumption_. If there is no way to _deduce_ a fact from the given facts, _then_ the fact itself is false. You need multiple definitions to \"bootstrap\" the query."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18f93e8f-d0d7-4238-b057-682a2e4daa70",
   "metadata": {},
   "source": [
    "You can do crazy things with recursion and negation. Fortunately, Cozo will try to stop you when you want to run something unreasonable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "21d2a0da-9c12-454f-b3d7-43a13496cdef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[31meval::unstratifiable\u001b[0m\n",
       "\n",
       "  \u001b[31m×\u001b[0m Query is unstratifiable\n",
       "\u001b[36m  help: \u001b[0mThe rule 'q' is in the strongly connected component [\"p\", \"q\"],\n",
       "        and is involved in at least one forbidden dependency\n",
       "        (negation, non-meet aggregation, or algorithm-application).\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "world[a] := a in [1, 2]\n",
    "\n",
    "p[a] := world[a], not q[a]\n",
    "q[a] := world[a], not p[a]\n",
    "\n",
    "?[a] := p[a]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51c7dd9e-51f2-4bb0-9e9b-c912b3f87036",
   "metadata": {},
   "source": [
    "Never mind the error message. If you consider the query as an equation to be solved, then `p[a] <- [[1]]` and `q[a] <- [[2]]` is a solution. But there is no way to _deduce_ this solution constructively. Furthermore, `q[a] <- [[1]]` and `p[a] <- [[2]]` is also a solution which is incompatible with the first."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72cfad4e-20de-4700-a191-03647fd6cdf8",
   "metadata": {},
   "source": [
    "## Aggregation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62149092-fb2f-47b2-bb0d-404fc17c28c1",
   "metadata": {},
   "source": [
    "For computing statistics, _aggregations_ are useful. In Cozo, aggregations are applied in the head of inline rules:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "70705529-80be-4990-9ea5-9f7842ba1543",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_a5da9_row0_col0, #T_a5da9_row1_col0, #T_a5da9_row2_col0, #T_a5da9_row3_col0, #T_a5da9_row4_col0 {\n",
       "  color: black;\n",
       "}\n",
       "#T_a5da9_row0_col1, #T_a5da9_row1_col1, #T_a5da9_row2_col1, #T_a5da9_row3_col1, #T_a5da9_row4_col1 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_a5da9\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_a5da9_level0_col0\" class=\"col_heading level0 col0\" >person</th>\n",
       "      <th id=\"T_a5da9_level0_col1\" class=\"col_heading level0 col1\" >count(loved_by)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_a5da9_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_a5da9_row0_col0\" class=\"data row0 col0\" >alice</td>\n",
       "      <td id=\"T_a5da9_row0_col1\" class=\"data row0 col1\" >2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a5da9_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_a5da9_row1_col0\" class=\"data row1 col0\" >bob</td>\n",
       "      <td id=\"T_a5da9_row1_col1\" class=\"data row1 col1\" >1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a5da9_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_a5da9_row2_col0\" class=\"data row2 col0\" >charlie</td>\n",
       "      <td id=\"T_a5da9_row2_col1\" class=\"data row2 col1\" >1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a5da9_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_a5da9_row3_col0\" class=\"data row3 col0\" >eve</td>\n",
       "      <td id=\"T_a5da9_row3_col1\" class=\"data row3 col1\" >2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a5da9_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_a5da9_row4_col0\" class=\"data row4 col0\" >george</td>\n",
       "      <td id=\"T_a5da9_row4_col1\" class=\"data row4 col1\" >2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f322a40>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[person, count(loved_by)] := @love[loved_by, person]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19f47c1e-ffb6-4531-b181-0995bfeb63df",
   "metadata": {},
   "source": [
    "The usual `sum`, `mean`, etc. are all available. Having aggregations apply in the head of the rule instead of in the body is powerful, as we will see later in the extended examples.\n",
    "\n",
    "Here is the [full list](https://cozodb.github.io/current/manual/aggregations.html) of aggregations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e39b8d9-0d52-433e-bec4-d856afd83606",
   "metadata": {},
   "source": [
    "## Query options"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "921d1c1a-3396-41d2-9010-1f3b9318cce8",
   "metadata": {},
   "source": [
    "We already know how to use query options to manipulate stored relations. There are also query options for controlling what is returned. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "542e2947-95b3-41d1-8f91-007aa353d09d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_8492e_row0_col0, #T_8492e_row0_col1, #T_8492e_row1_col0, #T_8492e_row1_col1, #T_8492e_row2_col0, #T_8492e_row2_col1, #T_8492e_row3_col0, #T_8492e_row3_col1, #T_8492e_row4_col0, #T_8492e_row4_col1, #T_8492e_row5_col0, #T_8492e_row5_col1, #T_8492e_row6_col0, #T_8492e_row6_col1, #T_8492e_row7_col0, #T_8492e_row7_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_8492e\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_8492e_level0_col0\" class=\"col_heading level0 col0\" >loving</th>\n",
       "      <th id=\"T_8492e_level0_col1\" class=\"col_heading level0 col1\" >loved</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_8492e_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_8492e_row0_col0\" class=\"data row0 col0\" >alice</td>\n",
       "      <td id=\"T_8492e_row0_col1\" class=\"data row0 col1\" >eve</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_8492e_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_8492e_row1_col0\" class=\"data row1 col0\" >bob</td>\n",
       "      <td id=\"T_8492e_row1_col1\" class=\"data row1 col1\" >alice</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_8492e_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_8492e_row2_col0\" class=\"data row2 col0\" >charlie</td>\n",
       "      <td id=\"T_8492e_row2_col1\" class=\"data row2 col1\" >eve</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_8492e_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_8492e_row3_col0\" class=\"data row3 col0\" >david</td>\n",
       "      <td id=\"T_8492e_row3_col1\" class=\"data row3 col1\" >george</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_8492e_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_8492e_row4_col0\" class=\"data row4 col0\" >eve</td>\n",
       "      <td id=\"T_8492e_row4_col1\" class=\"data row4 col1\" >alice</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_8492e_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_8492e_row5_col0\" class=\"data row5 col0\" >eve</td>\n",
       "      <td id=\"T_8492e_row5_col1\" class=\"data row5 col1\" >bob</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_8492e_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_8492e_row6_col0\" class=\"data row6 col0\" >eve</td>\n",
       "      <td id=\"T_8492e_row6_col1\" class=\"data row6 col1\" >charlie</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_8492e_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_8492e_row7_col0\" class=\"data row7 col0\" >george</td>\n",
       "      <td id=\"T_8492e_row7_col1\" class=\"data row7 col1\" >george</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f320e50>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[loving, loved] := @love{ loving, loved }"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ef5dc9c-1c58-49de-8cd6-4f725b001551",
   "metadata": {},
   "source": [
    "returns all rows. If we only want one row:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "58f1d43f-3f50-42df-8e27-8f6e549cbc6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_30c22_row0_col0, #T_30c22_row0_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_30c22\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_30c22_level0_col0\" class=\"col_heading level0 col0\" >loving</th>\n",
       "      <th id=\"T_30c22_level0_col1\" class=\"col_heading level0 col1\" >loved</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_30c22_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_30c22_row0_col0\" class=\"data row0 col0\" >alice</td>\n",
       "      <td id=\"T_30c22_row0_col1\" class=\"data row0 col1\" >eve</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
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       "<pandas.io.formats.style.Styler at 0x11f3226b0>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[loving, loved] := @love{ loving, loved }\n",
    "\n",
    ":limit 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe622726-e0b0-4ea3-878a-75e7de93a669",
   "metadata": {},
   "source": [
    "sorted by `loved` in descending order, then `loving` in ascending order, and skip the first row:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "60f3673b-3273-49a3-b893-1236faf64490",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_cac58_row0_col0, #T_cac58_row0_col1, #T_cac58_row1_col0, #T_cac58_row1_col1, #T_cac58_row2_col0, #T_cac58_row2_col1, #T_cac58_row3_col0, #T_cac58_row3_col1, #T_cac58_row4_col0, #T_cac58_row4_col1, #T_cac58_row5_col0, #T_cac58_row5_col1, #T_cac58_row6_col0, #T_cac58_row6_col1 {\n",
       "  color: black;\n",
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       "</style>\n",
       "<table id=\"T_cac58\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_cac58_level0_col0\" class=\"col_heading level0 col0\" >loving</th>\n",
       "      <th id=\"T_cac58_level0_col1\" class=\"col_heading level0 col1\" >loved</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_cac58_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_cac58_row0_col0\" class=\"data row0 col0\" >george</td>\n",
       "      <td id=\"T_cac58_row0_col1\" class=\"data row0 col1\" >george</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cac58_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_cac58_row1_col0\" class=\"data row1 col0\" >alice</td>\n",
       "      <td id=\"T_cac58_row1_col1\" class=\"data row1 col1\" >eve</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cac58_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_cac58_row2_col0\" class=\"data row2 col0\" >charlie</td>\n",
       "      <td id=\"T_cac58_row2_col1\" class=\"data row2 col1\" >eve</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cac58_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_cac58_row3_col0\" class=\"data row3 col0\" >eve</td>\n",
       "      <td id=\"T_cac58_row3_col1\" class=\"data row3 col1\" >charlie</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cac58_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_cac58_row4_col0\" class=\"data row4 col0\" >eve</td>\n",
       "      <td id=\"T_cac58_row4_col1\" class=\"data row4 col1\" >bob</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cac58_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_cac58_row5_col0\" class=\"data row5 col0\" >bob</td>\n",
       "      <td id=\"T_cac58_row5_col1\" class=\"data row5 col1\" >alice</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cac58_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_cac58_row6_col0\" class=\"data row6 col0\" >eve</td>\n",
       "      <td id=\"T_cac58_row6_col1\" class=\"data row6 col1\" >alice</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f2f8df0>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[loving, loved] := @love{ loving, loved }\n",
    "\n",
    ":order -loved, loving\n",
    ":offset 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c481e69-9640-4246-8ab8-e66549653c0d",
   "metadata": {},
   "source": [
    "Putting `-` in front of variables in `:order` clause denotes reverse order. Nothing or `+` denotes the normal order."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40e456b1-2030-4013-894d-a45e81e6b74e",
   "metadata": {},
   "source": [
    "There are many more query options, as explained [here](https://cozodb.github.io/current/manual/queries.html#query-options)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6aebc44-2523-4bc6-8c65-3554e985aef1",
   "metadata": {},
   "source": [
    "## Fixed rules"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf08e8f6-ce6a-4212-a456-98fa57d457b4",
   "metadata": {},
   "source": [
    "You may be wondering why we are calling rules defined `:=` _inline_ rules. \n",
    "Well, the logic that defines how the output relation is computed is given _inline_, as a series of atoms.\n",
    "\n",
    "By contrast, rules defined using `<-` are called _constant_ rules, which are special cases of _fixed rules_:\n",
    "rules whose logic is defined in fixed implementations hidden from the user.\n",
    "\n",
    "The `<-` syntax is syntax sugar. The full syntax is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "91414374-23cb-4310-ac36-a372e151ef6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_ae1b6_row0_col0, #T_ae1b6_row0_col1, #T_ae1b6_row0_col2 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_ae1b6\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_ae1b6_level0_col0\" class=\"col_heading level0 col0\" >0</th>\n",
       "      <th id=\"T_ae1b6_level0_col1\" class=\"col_heading level0 col1\" >1</th>\n",
       "      <th id=\"T_ae1b6_level0_col2\" class=\"col_heading level0 col2\" >2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_ae1b6_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_ae1b6_row0_col0\" class=\"data row0 col0\" >hello</td>\n",
       "      <td id=\"T_ae1b6_row0_col1\" class=\"data row0 col1\" >world</td>\n",
       "      <td id=\"T_ae1b6_row0_col2\" class=\"data row0 col2\" >Cozo!</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f321540>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[] <~ Constant(data: [['hello', 'world', 'Cozo!']])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b836e0b-1b38-485a-ade2-69742b29d09f",
   "metadata": {},
   "source": [
    "Here we are using the fixed rule `Constant`, which takes one _option_ named `data`. Note the curly tail of the arrow.\n",
    "\n",
    "Fixed rules take in some input relations, and by applying custom logic, produce their output relation. The `Constant` fixed rule take in zero input relations.\n",
    "\n",
    "As an example of a less trivial fixed rule, let's say we want to find out who is most popular in the `love` graph. How do we define popularity? \n",
    "One way is to say that the higher [PageRank](https://en.wikipedia.org/wiki/PageRank) a person has, the more popular. Calculating PageRank using inline rules\n",
    "is very awkward (but doable). Fortunately, one of the fixed rules is an optimized PageRank implementation, so let's just use it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "f596d73d-1879-49e7-834a-5c489752a152",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_80b19_row0_col0, #T_80b19_row1_col0, #T_80b19_row2_col0, #T_80b19_row3_col0, #T_80b19_row4_col0, #T_80b19_row5_col0 {\n",
       "  color: black;\n",
       "}\n",
       "#T_80b19_row0_col1, #T_80b19_row1_col1, #T_80b19_row2_col1, #T_80b19_row3_col1, #T_80b19_row4_col1, #T_80b19_row5_col1 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_80b19\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_80b19_level0_col0\" class=\"col_heading level0 col0\" >person</th>\n",
       "      <th id=\"T_80b19_level0_col1\" class=\"col_heading level0 col1\" >page_rank</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_80b19_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_80b19_row0_col0\" class=\"data row0 col0\" >alice</td>\n",
       "      <td id=\"T_80b19_row0_col1\" class=\"data row0 col1\" >1.191497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_80b19_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_80b19_row1_col0\" class=\"data row1 col0\" >eve</td>\n",
       "      <td id=\"T_80b19_row1_col1\" class=\"data row1 col1\" >1.191497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_80b19_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_80b19_row2_col0\" class=\"data row2 col0\" >george</td>\n",
       "      <td id=\"T_80b19_row2_col1\" class=\"data row2 col1\" >1.064742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_80b19_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_80b19_row3_col0\" class=\"data row3 col0\" >bob</td>\n",
       "      <td id=\"T_80b19_row3_col1\" class=\"data row3 col1\" >0.921087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_80b19_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_80b19_row4_col0\" class=\"data row4 col0\" >charlie</td>\n",
       "      <td id=\"T_80b19_row4_col1\" class=\"data row4 col1\" >0.921087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_80b19_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_80b19_row5_col0\" class=\"data row5 col0\" >david</td>\n",
       "      <td id=\"T_80b19_row5_col1\" class=\"data row5 col1\" >0.574623</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f321600>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[person, page_rank] <~ PageRank(@love[])\n",
    "\n",
    ":order -page_rank"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "394a62e3-ad1c-49a0-944f-f0de0150d2e0",
   "metadata": {},
   "source": [
    "Here the input relation is a stored relation. Input relations are distinguished from options by not having any names preceding them.\n",
    "\n",
    "Each fixed rule is different, and you must read their [documentation](https://cozodb.github.io/current/manual/algorithms.html) to learn how to correctly use them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "db73e2f7-61a1-4824-9c47-c6da461b632b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_adf71_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_adf71\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_adf71_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_adf71_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_adf71_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f320a00>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "::remove love"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a16bee55-9802-4089-a0c2-c6f85213cf13",
   "metadata": {},
   "source": [
    "## Extended example: the air routes dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72e46708-93cd-45de-8d9e-79adb8cc1da0",
   "metadata": {},
   "source": [
    "Now you have a basic understanding of using the various constructs of Cozo, let's deal with a less trivial dataset.\n",
    "\n",
    "The data we are going to use, and many examples that we will present, are adapted from the book [Practical Gremlin](https://kelvinlawrence.net/book/Gremlin-Graph-Guide.html), which teaches the Gremlin graph query language, a very different, imperative take on graphs (Datalog, by contrast, is declarative)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54e3ec1d-c139-48ab-8205-49b71aba4c67",
   "metadata": {},
   "source": [
    "First, let's import the data into our database. We will use fixed rules to do that. First, we define the `airport` relation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "dd70c091-063d-4f0e-995d-06b7f428a4b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 46ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_51be4_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_51be4\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_51be4_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_51be4_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_51be4_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f320790>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res[idx, label, typ, code, icao, desc, region, runways, longest, elev, country, city, lat, lon] <~\n",
    "    CsvReader(types: ['Int', 'Any', 'Any', 'Any', 'Any', 'Any', 'Any', 'Int?', 'Float?', 'Float?', 'Any', 'Any', 'Float?', 'Float?'],\n",
    "              url: 'https://github.com/cozodb/cozo/raw/main/tests/air-routes-latest-nodes.csv', \n",
    "              # url: 'file://./tests/air-routes-latest-nodes.csv', \n",
    "              has_headers: true)\n",
    "\n",
    "?[code, icao, desc, region, runways, longest, elev, country, city, lat, lon] :=\n",
    "    res[idx, label, typ, code, icao, desc, region, runways, longest, elev, country, city, lat, lon],\n",
    "    label == 'airport'\n",
    "\n",
    ":replace airport {\n",
    "    code: String \n",
    "    => \n",
    "    icao: String, \n",
    "    desc: String, \n",
    "    region: String, \n",
    "    runways: Int, \n",
    "    longest: Float, \n",
    "    elev: Float, \n",
    "    country: String, \n",
    "    city: String, \n",
    "    lat: Float, \n",
    "    lon: Float\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "708cd3df-4da7-42e2-a1a3-f36e37fed7f4",
   "metadata": {},
   "source": [
    "The `CsvReader` utility downloads a CSV file from the internet and attempts to parse its content into a relation.\n",
    "When we store the relation, we specified types for the columns. The `code` column acts as a primary key for the `airport` stored relation.\n",
    "\n",
    "If your Internet connection is slow, it might help if you download the CSV file manually to your disk and load the local file. \n",
    "The line commented out shows how to do it. The relative path is relative to the directory in which you run the `cozoserver` executable.\n",
    "As the same file will be downloaded multiple times below, you may also want to download it just once to the local disk if your connection is metered."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79d41137-1936-4023-a870-91158693c6bb",
   "metadata": {},
   "source": [
    "Next is `country`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "51e71275-3911-42c0-b993-8916ba953fdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 12ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_a814d_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_a814d\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_a814d_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_a814d_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_a814d_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f321000>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res[idx, label, typ, code, icao, desc] <~\n",
    "    CsvReader(types: ['Int', 'Any', 'Any', 'Any', 'Any', 'Any'],\n",
    "              url: 'https://github.com/cozodb/cozo/raw/main/tests/air-routes-latest-nodes.csv', \n",
    "              # url: 'file://./tests/air-routes-latest-nodes.csv', \n",
    "              has_headers: true)\n",
    "?[code, desc] :=\n",
    "    res[idx, label, typ, code, icao, desc],\n",
    "    label == 'country'\n",
    "\n",
    ":replace country {\n",
    "    code: String\n",
    "    =>\n",
    "    desc: String\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72901087-cebd-472e-ba31-adee8dc72abc",
   "metadata": {},
   "source": [
    "`continent`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "d5660e58-0fec-4929-941d-0debb9234e50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 10ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_548d0_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_548d0\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_548d0_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_548d0_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_548d0_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f322cb0>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res[idx, label, typ, code, icao, desc] <~\n",
    "    CsvReader(types: ['Int', 'Any', 'Any', 'Any', 'Any', 'Any'],\n",
    "              url: 'https://github.com/cozodb/cozo/raw/main/tests/air-routes-latest-nodes.csv', \n",
    "              # url: 'file://./tests/air-routes-latest-nodes.csv', \n",
    "              has_headers: true)\n",
    "?[idx, code, desc] :=\n",
    "    res[idx, label, typ, code, icao, desc],\n",
    "    label == 'continent'\n",
    "\n",
    ":replace continent {\n",
    "    code: String\n",
    "    =>\n",
    "    desc: String\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e2d30c1-90d3-4403-b816-a21d0baf0670",
   "metadata": {},
   "source": [
    "We need to make a translation table for the indices the original data use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "49433f68-afcd-4788-9e82-a8f57c24ee78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 33ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_f0f17_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_f0f17\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_f0f17_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_f0f17_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_f0f17_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3206a0>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res[idx, label, typ, code] <~\n",
    "    CsvReader(types: ['Int', 'Any', 'Any', 'Any'],\n",
    "              url: 'https://github.com/cozodb/cozo/raw/main/tests/air-routes-latest-nodes.csv', \n",
    "              # url: 'file://./tests/air-routes-latest-nodes.csv', \n",
    "              has_headers: true)\n",
    "?[idx, code] :=\n",
    "    res[idx, label, typ, code],\n",
    "\n",
    ":replace idx2code { idx => code }"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af261df6-ce89-47a0-b7d9-2efe794767fb",
   "metadata": {},
   "source": [
    "The `contain` relation contains information on the geographical inclusion of entities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "2ec122ba-a72b-4ee8-bd57-e6c9db7f6e15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 142ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_e8f19_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_e8f19\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_e8f19_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_e8f19_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_e8f19_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f320370>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res[] <~\n",
    "    CsvReader(types: ['Int', 'Int', 'Int', 'String'],\n",
    "              url: 'https://github.com/cozodb/cozo/raw/main/tests/air-routes-latest-edges.csv', \n",
    "              # url: 'file://./tests/air-routes-latest-edges.csv', \n",
    "              has_headers: true)\n",
    "?[entity, contained] :=\n",
    "    res[idx, fr_i, to_i, typ],\n",
    "    typ == 'contains',\n",
    "    @idx2code[fr_i, entity],\n",
    "    @idx2code[to_i, contained]\n",
    "\n",
    "\n",
    ":replace contain { entity: String, contained: String }"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddc41b91-021a-4ab4-b92f-63013dd655bf",
   "metadata": {},
   "source": [
    "Finally, the `route`s between the airports. This relation is much larger than the rest and contains about 60k rows, which may take a few seconds to download and process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "a916cb80-7463-44eb-8f15-c12cbe8091d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 656ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_d37e0_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_d37e0\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_d37e0_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_d37e0_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_d37e0_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f323220>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res[] <~\n",
    "    CsvReader(types: ['Int', 'Int', 'Int', 'String', 'Float?'],\n",
    "              url: 'https://github.com/cozodb/cozo/raw/main/tests/air-routes-latest-edges.csv', \n",
    "              # url: 'file://./tests/air-routes-latest-edges.csv', \n",
    "              has_headers: true)\n",
    "?[fr, to, dist] :=\n",
    "    res[idx, fr_i, to_i, typ, dist],\n",
    "    typ == 'route',\n",
    "    @idx2code[fr_i, fr],\n",
    "    @idx2code[to_i, to]\n",
    "\n",
    ":replace route { fr: String, to: String => dist: Float }"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1ce4c36-d196-414b-b7f4-295708849e19",
   "metadata": {},
   "source": [
    "We no longer need the `idx2code` relation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "5938a20c-56d7-41ec-b3b2-4ca2f5bd835b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_ca766_row0_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_ca766\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_ca766_level0_col0\" class=\"col_heading level0 col0\" >status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_ca766_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_ca766_row0_col0\" class=\"data row0 col0\" >OK</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b18d0>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "::remove idx2code"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65cb9b9d-79ce-4814-8f75-e6c22fe1d98d",
   "metadata": {},
   "source": [
    "Now let's verify all the relations we want are there:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "5c067dd0-7052-46c6-823b-ddf6cbb1b516",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_1fa08_row0_col0, #T_1fa08_row0_col2, #T_1fa08_row1_col0, #T_1fa08_row1_col2, #T_1fa08_row2_col0, #T_1fa08_row2_col2, #T_1fa08_row3_col0, #T_1fa08_row3_col2, #T_1fa08_row4_col0, #T_1fa08_row4_col2 {\n",
       "  color: black;\n",
       "}\n",
       "#T_1fa08_row0_col1, #T_1fa08_row0_col3, #T_1fa08_row0_col4, #T_1fa08_row0_col5, #T_1fa08_row0_col6, #T_1fa08_row0_col7, #T_1fa08_row1_col1, #T_1fa08_row1_col3, #T_1fa08_row1_col4, #T_1fa08_row1_col5, #T_1fa08_row1_col6, #T_1fa08_row1_col7, #T_1fa08_row2_col1, #T_1fa08_row2_col3, #T_1fa08_row2_col4, #T_1fa08_row2_col5, #T_1fa08_row2_col6, #T_1fa08_row2_col7, #T_1fa08_row3_col1, #T_1fa08_row3_col3, #T_1fa08_row3_col4, #T_1fa08_row3_col5, #T_1fa08_row3_col6, #T_1fa08_row3_col7, #T_1fa08_row4_col1, #T_1fa08_row4_col3, #T_1fa08_row4_col4, #T_1fa08_row4_col5, #T_1fa08_row4_col6, #T_1fa08_row4_col7 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_1fa08\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_1fa08_level0_col0\" class=\"col_heading level0 col0\" >name</th>\n",
       "      <th id=\"T_1fa08_level0_col1\" class=\"col_heading level0 col1\" >arity</th>\n",
       "      <th id=\"T_1fa08_level0_col2\" class=\"col_heading level0 col2\" >access_level</th>\n",
       "      <th id=\"T_1fa08_level0_col3\" class=\"col_heading level0 col3\" >n_keys</th>\n",
       "      <th id=\"T_1fa08_level0_col4\" class=\"col_heading level0 col4\" >n_non_keys</th>\n",
       "      <th id=\"T_1fa08_level0_col5\" class=\"col_heading level0 col5\" >n_put_triggers</th>\n",
       "      <th id=\"T_1fa08_level0_col6\" class=\"col_heading level0 col6\" >n_rm_triggers</th>\n",
       "      <th id=\"T_1fa08_level0_col7\" class=\"col_heading level0 col7\" >n_replace_triggers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_1fa08_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_1fa08_row0_col0\" class=\"data row0 col0\" >airport</td>\n",
       "      <td id=\"T_1fa08_row0_col1\" class=\"data row0 col1\" >11</td>\n",
       "      <td id=\"T_1fa08_row0_col2\" class=\"data row0 col2\" >normal</td>\n",
       "      <td id=\"T_1fa08_row0_col3\" class=\"data row0 col3\" >1</td>\n",
       "      <td id=\"T_1fa08_row0_col4\" class=\"data row0 col4\" >10</td>\n",
       "      <td id=\"T_1fa08_row0_col5\" class=\"data row0 col5\" >0</td>\n",
       "      <td id=\"T_1fa08_row0_col6\" class=\"data row0 col6\" >0</td>\n",
       "      <td id=\"T_1fa08_row0_col7\" class=\"data row0 col7\" >0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_1fa08_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_1fa08_row1_col0\" class=\"data row1 col0\" >contain</td>\n",
       "      <td id=\"T_1fa08_row1_col1\" class=\"data row1 col1\" >2</td>\n",
       "      <td id=\"T_1fa08_row1_col2\" class=\"data row1 col2\" >normal</td>\n",
       "      <td id=\"T_1fa08_row1_col3\" class=\"data row1 col3\" >2</td>\n",
       "      <td id=\"T_1fa08_row1_col4\" class=\"data row1 col4\" >0</td>\n",
       "      <td id=\"T_1fa08_row1_col5\" class=\"data row1 col5\" >0</td>\n",
       "      <td id=\"T_1fa08_row1_col6\" class=\"data row1 col6\" >0</td>\n",
       "      <td id=\"T_1fa08_row1_col7\" class=\"data row1 col7\" >0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_1fa08_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_1fa08_row2_col0\" class=\"data row2 col0\" >continent</td>\n",
       "      <td id=\"T_1fa08_row2_col1\" class=\"data row2 col1\" >2</td>\n",
       "      <td id=\"T_1fa08_row2_col2\" class=\"data row2 col2\" >normal</td>\n",
       "      <td id=\"T_1fa08_row2_col3\" class=\"data row2 col3\" >1</td>\n",
       "      <td id=\"T_1fa08_row2_col4\" class=\"data row2 col4\" >1</td>\n",
       "      <td id=\"T_1fa08_row2_col5\" class=\"data row2 col5\" >0</td>\n",
       "      <td id=\"T_1fa08_row2_col6\" class=\"data row2 col6\" >0</td>\n",
       "      <td id=\"T_1fa08_row2_col7\" class=\"data row2 col7\" >0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_1fa08_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_1fa08_row3_col0\" class=\"data row3 col0\" >country</td>\n",
       "      <td id=\"T_1fa08_row3_col1\" class=\"data row3 col1\" >2</td>\n",
       "      <td id=\"T_1fa08_row3_col2\" class=\"data row3 col2\" >normal</td>\n",
       "      <td id=\"T_1fa08_row3_col3\" class=\"data row3 col3\" >1</td>\n",
       "      <td id=\"T_1fa08_row3_col4\" class=\"data row3 col4\" >1</td>\n",
       "      <td id=\"T_1fa08_row3_col5\" class=\"data row3 col5\" >0</td>\n",
       "      <td id=\"T_1fa08_row3_col6\" class=\"data row3 col6\" >0</td>\n",
       "      <td id=\"T_1fa08_row3_col7\" class=\"data row3 col7\" >0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_1fa08_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_1fa08_row4_col0\" class=\"data row4 col0\" >route</td>\n",
       "      <td id=\"T_1fa08_row4_col1\" class=\"data row4 col1\" >3</td>\n",
       "      <td id=\"T_1fa08_row4_col2\" class=\"data row4 col2\" >normal</td>\n",
       "      <td id=\"T_1fa08_row4_col3\" class=\"data row4 col3\" >2</td>\n",
       "      <td id=\"T_1fa08_row4_col4\" class=\"data row4 col4\" >1</td>\n",
       "      <td id=\"T_1fa08_row4_col5\" class=\"data row4 col5\" >0</td>\n",
       "      <td id=\"T_1fa08_row4_col6\" class=\"data row4 col6\" >0</td>\n",
       "      <td id=\"T_1fa08_row4_col7\" class=\"data row4 col7\" >0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b0a90>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "::relations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d33e9f4-0876-46cd-bc6e-7ae42ce587dd",
   "metadata": {},
   "source": [
    "Now let's just look at some data. Start with airports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "fefbae3c-3b06-43ca-82b6-a10ee9174edf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_ab754_row0_col0, #T_ab754_row0_col1, #T_ab754_row0_col2, #T_ab754_row0_col3, #T_ab754_row1_col0, #T_ab754_row1_col1, #T_ab754_row1_col2, #T_ab754_row1_col3, #T_ab754_row2_col0, #T_ab754_row2_col1, #T_ab754_row2_col2, #T_ab754_row2_col3, #T_ab754_row3_col0, #T_ab754_row3_col1, #T_ab754_row3_col2, #T_ab754_row3_col3, #T_ab754_row4_col0, #T_ab754_row4_col1, #T_ab754_row4_col2, #T_ab754_row4_col3 {\n",
       "  color: black;\n",
       "}\n",
       "#T_ab754_row0_col4, #T_ab754_row0_col5, #T_ab754_row0_col6, #T_ab754_row1_col4, #T_ab754_row1_col5, #T_ab754_row1_col6, #T_ab754_row2_col4, #T_ab754_row2_col5, #T_ab754_row2_col6, #T_ab754_row3_col4, #T_ab754_row3_col5, #T_ab754_row3_col6, #T_ab754_row4_col4, #T_ab754_row4_col5, #T_ab754_row4_col6 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_ab754\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_ab754_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_ab754_level0_col1\" class=\"col_heading level0 col1\" >city</th>\n",
       "      <th id=\"T_ab754_level0_col2\" class=\"col_heading level0 col2\" >desc</th>\n",
       "      <th id=\"T_ab754_level0_col3\" class=\"col_heading level0 col3\" >region</th>\n",
       "      <th id=\"T_ab754_level0_col4\" class=\"col_heading level0 col4\" >runways</th>\n",
       "      <th id=\"T_ab754_level0_col5\" class=\"col_heading level0 col5\" >lat</th>\n",
       "      <th id=\"T_ab754_level0_col6\" class=\"col_heading level0 col6\" >lon</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_ab754_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_ab754_row0_col0\" class=\"data row0 col0\" >AAA</td>\n",
       "      <td id=\"T_ab754_row0_col1\" class=\"data row0 col1\" >Anaa</td>\n",
       "      <td id=\"T_ab754_row0_col2\" class=\"data row0 col2\" >Anaa Airport</td>\n",
       "      <td id=\"T_ab754_row0_col3\" class=\"data row0 col3\" >PF-U-A</td>\n",
       "      <td id=\"T_ab754_row0_col4\" class=\"data row0 col4\" >1</td>\n",
       "      <td id=\"T_ab754_row0_col5\" class=\"data row0 col5\" >-17.352600</td>\n",
       "      <td id=\"T_ab754_row0_col6\" class=\"data row0 col6\" >-145.509995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ab754_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_ab754_row1_col0\" class=\"data row1 col0\" >AAE</td>\n",
       "      <td id=\"T_ab754_row1_col1\" class=\"data row1 col1\" >Annabah</td>\n",
       "      <td id=\"T_ab754_row1_col2\" class=\"data row1 col2\" >Annaba Airport</td>\n",
       "      <td id=\"T_ab754_row1_col3\" class=\"data row1 col3\" >DZ-36</td>\n",
       "      <td id=\"T_ab754_row1_col4\" class=\"data row1 col4\" >2</td>\n",
       "      <td id=\"T_ab754_row1_col5\" class=\"data row1 col5\" >36.822201</td>\n",
       "      <td id=\"T_ab754_row1_col6\" class=\"data row1 col6\" >7.809170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ab754_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_ab754_row2_col0\" class=\"data row2 col0\" >AAL</td>\n",
       "      <td id=\"T_ab754_row2_col1\" class=\"data row2 col1\" >Aalborg</td>\n",
       "      <td id=\"T_ab754_row2_col2\" class=\"data row2 col2\" >Aalborg Airport</td>\n",
       "      <td id=\"T_ab754_row2_col3\" class=\"data row2 col3\" >DK-81</td>\n",
       "      <td id=\"T_ab754_row2_col4\" class=\"data row2 col4\" >2</td>\n",
       "      <td id=\"T_ab754_row2_col5\" class=\"data row2 col5\" >57.092759</td>\n",
       "      <td id=\"T_ab754_row2_col6\" class=\"data row2 col6\" >9.849243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ab754_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_ab754_row3_col0\" class=\"data row3 col0\" >AAN</td>\n",
       "      <td id=\"T_ab754_row3_col1\" class=\"data row3 col1\" >Al Ain</td>\n",
       "      <td id=\"T_ab754_row3_col2\" class=\"data row3 col2\" >Al Ain International Airport</td>\n",
       "      <td id=\"T_ab754_row3_col3\" class=\"data row3 col3\" >AE-AZ</td>\n",
       "      <td id=\"T_ab754_row3_col4\" class=\"data row3 col4\" >1</td>\n",
       "      <td id=\"T_ab754_row3_col5\" class=\"data row3 col5\" >24.261700</td>\n",
       "      <td id=\"T_ab754_row3_col6\" class=\"data row3 col6\" >55.609200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ab754_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_ab754_row4_col0\" class=\"data row4 col0\" >AAQ</td>\n",
       "      <td id=\"T_ab754_row4_col1\" class=\"data row4 col1\" >Anapa</td>\n",
       "      <td id=\"T_ab754_row4_col2\" class=\"data row4 col2\" >Anapa Airport</td>\n",
       "      <td id=\"T_ab754_row4_col3\" class=\"data row4 col3\" >RU-KDA</td>\n",
       "      <td id=\"T_ab754_row4_col4\" class=\"data row4 col4\" >1</td>\n",
       "      <td id=\"T_ab754_row4_col5\" class=\"data row4 col5\" >45.002102</td>\n",
       "      <td id=\"T_ab754_row4_col6\" class=\"data row4 col6\" >37.347301</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b3dc0>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[code, city, desc, region, runways, lat, lon] := @airport{code, city, desc, region, runways, lat, lon}\n",
    "    \n",
    ":limit 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b645ed53-c80a-4b50-8e4d-f5080c48de2d",
   "metadata": {},
   "source": [
    "Airports with the most runways:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "b733fffd-e292-4af9-9810-7010b87c2d09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 21ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
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       "#T_26677_row0_col0, #T_26677_row0_col1, #T_26677_row0_col2, #T_26677_row0_col3, #T_26677_row1_col0, #T_26677_row1_col1, #T_26677_row1_col2, #T_26677_row1_col3, #T_26677_row2_col0, #T_26677_row2_col1, #T_26677_row2_col2, #T_26677_row2_col3, #T_26677_row3_col0, #T_26677_row3_col1, #T_26677_row3_col2, #T_26677_row3_col3, #T_26677_row4_col0, #T_26677_row4_col1, #T_26677_row4_col2, #T_26677_row4_col3, #T_26677_row5_col0, #T_26677_row5_col1, #T_26677_row5_col2, #T_26677_row5_col3, #T_26677_row6_col0, #T_26677_row6_col1, #T_26677_row6_col2, #T_26677_row6_col3, #T_26677_row7_col0, #T_26677_row7_col1, #T_26677_row7_col2, #T_26677_row7_col3, #T_26677_row8_col0, #T_26677_row8_col1, #T_26677_row8_col2, #T_26677_row8_col3, #T_26677_row9_col0, #T_26677_row9_col1, #T_26677_row9_col2, #T_26677_row9_col3 {\n",
       "  color: black;\n",
       "}\n",
       "#T_26677_row0_col4, #T_26677_row0_col5, #T_26677_row0_col6, #T_26677_row1_col4, #T_26677_row1_col5, #T_26677_row1_col6, #T_26677_row2_col4, #T_26677_row2_col5, #T_26677_row2_col6, #T_26677_row3_col4, #T_26677_row3_col5, #T_26677_row3_col6, #T_26677_row4_col4, #T_26677_row4_col5, #T_26677_row4_col6, #T_26677_row5_col4, #T_26677_row5_col5, #T_26677_row5_col6, #T_26677_row6_col4, #T_26677_row6_col5, #T_26677_row6_col6, #T_26677_row7_col4, #T_26677_row7_col5, #T_26677_row7_col6, #T_26677_row8_col4, #T_26677_row8_col5, #T_26677_row8_col6, #T_26677_row9_col4, #T_26677_row9_col5, #T_26677_row9_col6 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_26677\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_26677_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_26677_level0_col1\" class=\"col_heading level0 col1\" >city</th>\n",
       "      <th id=\"T_26677_level0_col2\" class=\"col_heading level0 col2\" >desc</th>\n",
       "      <th id=\"T_26677_level0_col3\" class=\"col_heading level0 col3\" >region</th>\n",
       "      <th id=\"T_26677_level0_col4\" class=\"col_heading level0 col4\" >runways</th>\n",
       "      <th id=\"T_26677_level0_col5\" class=\"col_heading level0 col5\" >lat</th>\n",
       "      <th id=\"T_26677_level0_col6\" class=\"col_heading level0 col6\" >lon</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_26677_row0_col0\" class=\"data row0 col0\" >DFW</td>\n",
       "      <td id=\"T_26677_row0_col1\" class=\"data row0 col1\" >Dallas</td>\n",
       "      <td id=\"T_26677_row0_col2\" class=\"data row0 col2\" >Dallas/Fort Worth International Airport</td>\n",
       "      <td id=\"T_26677_row0_col3\" class=\"data row0 col3\" >US-TX</td>\n",
       "      <td id=\"T_26677_row0_col4\" class=\"data row0 col4\" >7</td>\n",
       "      <td id=\"T_26677_row0_col5\" class=\"data row0 col5\" >32.896801</td>\n",
       "      <td id=\"T_26677_row0_col6\" class=\"data row0 col6\" >-97.038002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_26677_row1_col0\" class=\"data row1 col0\" >ORD</td>\n",
       "      <td id=\"T_26677_row1_col1\" class=\"data row1 col1\" >Chicago</td>\n",
       "      <td id=\"T_26677_row1_col2\" class=\"data row1 col2\" >Chicago O'Hare International Airport</td>\n",
       "      <td id=\"T_26677_row1_col3\" class=\"data row1 col3\" >US-IL</td>\n",
       "      <td id=\"T_26677_row1_col4\" class=\"data row1 col4\" >7</td>\n",
       "      <td id=\"T_26677_row1_col5\" class=\"data row1 col5\" >41.978600</td>\n",
       "      <td id=\"T_26677_row1_col6\" class=\"data row1 col6\" >-87.904800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_26677_row2_col0\" class=\"data row2 col0\" >AMS</td>\n",
       "      <td id=\"T_26677_row2_col1\" class=\"data row2 col1\" >Amsterdam</td>\n",
       "      <td id=\"T_26677_row2_col2\" class=\"data row2 col2\" >Amsterdam Airport Schiphol</td>\n",
       "      <td id=\"T_26677_row2_col3\" class=\"data row2 col3\" >NL-NH</td>\n",
       "      <td id=\"T_26677_row2_col4\" class=\"data row2 col4\" >6</td>\n",
       "      <td id=\"T_26677_row2_col5\" class=\"data row2 col5\" >52.308601</td>\n",
       "      <td id=\"T_26677_row2_col6\" class=\"data row2 col6\" >4.763890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_26677_row3_col0\" class=\"data row3 col0\" >BOS</td>\n",
       "      <td id=\"T_26677_row3_col1\" class=\"data row3 col1\" >Boston</td>\n",
       "      <td id=\"T_26677_row3_col2\" class=\"data row3 col2\" >Boston Logan</td>\n",
       "      <td id=\"T_26677_row3_col3\" class=\"data row3 col3\" >US-MA</td>\n",
       "      <td id=\"T_26677_row3_col4\" class=\"data row3 col4\" >6</td>\n",
       "      <td id=\"T_26677_row3_col5\" class=\"data row3 col5\" >42.364300</td>\n",
       "      <td id=\"T_26677_row3_col6\" class=\"data row3 col6\" >-71.005203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_26677_row4_col0\" class=\"data row4 col0\" >DEN</td>\n",
       "      <td id=\"T_26677_row4_col1\" class=\"data row4 col1\" >Denver</td>\n",
       "      <td id=\"T_26677_row4_col2\" class=\"data row4 col2\" >Denver International Airport</td>\n",
       "      <td id=\"T_26677_row4_col3\" class=\"data row4 col3\" >US-CO</td>\n",
       "      <td id=\"T_26677_row4_col4\" class=\"data row4 col4\" >6</td>\n",
       "      <td id=\"T_26677_row4_col5\" class=\"data row4 col5\" >39.861698</td>\n",
       "      <td id=\"T_26677_row4_col6\" class=\"data row4 col6\" >-104.672997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_26677_row5_col0\" class=\"data row5 col0\" >DTW</td>\n",
       "      <td id=\"T_26677_row5_col1\" class=\"data row5 col1\" >Detroit</td>\n",
       "      <td id=\"T_26677_row5_col2\" class=\"data row5 col2\" >Detroit Metropolitan, Wayne County</td>\n",
       "      <td id=\"T_26677_row5_col3\" class=\"data row5 col3\" >US-MI</td>\n",
       "      <td id=\"T_26677_row5_col4\" class=\"data row5 col4\" >6</td>\n",
       "      <td id=\"T_26677_row5_col5\" class=\"data row5 col5\" >42.212399</td>\n",
       "      <td id=\"T_26677_row5_col6\" class=\"data row5 col6\" >-83.353401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_26677_row6_col0\" class=\"data row6 col0\" >ATL</td>\n",
       "      <td id=\"T_26677_row6_col1\" class=\"data row6 col1\" >Atlanta</td>\n",
       "      <td id=\"T_26677_row6_col2\" class=\"data row6 col2\" >Hartsfield - Jackson Atlanta International Airport</td>\n",
       "      <td id=\"T_26677_row6_col3\" class=\"data row6 col3\" >US-GA</td>\n",
       "      <td id=\"T_26677_row6_col4\" class=\"data row6 col4\" >5</td>\n",
       "      <td id=\"T_26677_row6_col5\" class=\"data row6 col5\" >33.636700</td>\n",
       "      <td id=\"T_26677_row6_col6\" class=\"data row6 col6\" >-84.428101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_26677_row7_col0\" class=\"data row7 col0\" >GIS</td>\n",
       "      <td id=\"T_26677_row7_col1\" class=\"data row7 col1\" >Gisborne</td>\n",
       "      <td id=\"T_26677_row7_col2\" class=\"data row7 col2\" >Gisborne Airport</td>\n",
       "      <td id=\"T_26677_row7_col3\" class=\"data row7 col3\" >NZ-GIS</td>\n",
       "      <td id=\"T_26677_row7_col4\" class=\"data row7 col4\" >5</td>\n",
       "      <td id=\"T_26677_row7_col5\" class=\"data row7 col5\" >-38.663300</td>\n",
       "      <td id=\"T_26677_row7_col6\" class=\"data row7 col6\" >177.977997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_26677_row8_col0\" class=\"data row8 col0\" >HLZ</td>\n",
       "      <td id=\"T_26677_row8_col1\" class=\"data row8 col1\" >Hamilton</td>\n",
       "      <td id=\"T_26677_row8_col2\" class=\"data row8 col2\" >Hamilton International Airport</td>\n",
       "      <td id=\"T_26677_row8_col3\" class=\"data row8 col3\" >NZ-WKO</td>\n",
       "      <td id=\"T_26677_row8_col4\" class=\"data row8 col4\" >5</td>\n",
       "      <td id=\"T_26677_row8_col5\" class=\"data row8 col5\" >-37.866699</td>\n",
       "      <td id=\"T_26677_row8_col6\" class=\"data row8 col6\" >175.332001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_26677_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_26677_row9_col0\" class=\"data row9 col0\" >IAH</td>\n",
       "      <td id=\"T_26677_row9_col1\" class=\"data row9 col1\" >Houston</td>\n",
       "      <td id=\"T_26677_row9_col2\" class=\"data row9 col2\" >George Bush Intercontinental</td>\n",
       "      <td id=\"T_26677_row9_col3\" class=\"data row9 col3\" >US-TX</td>\n",
       "      <td id=\"T_26677_row9_col4\" class=\"data row9 col4\" >5</td>\n",
       "      <td id=\"T_26677_row9_col5\" class=\"data row9 col5\" >29.984400</td>\n",
       "      <td id=\"T_26677_row9_col6\" class=\"data row9 col6\" >-95.341400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b2980>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[code, city, desc, region, runways, lat, lon] := @airport{code, city, desc, region, runways, lat, lon}\n",
    "\n",
    ":order -runways\n",
    ":limit 10"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db45f1d4-e89a-449e-beb8-a9301acfa86c",
   "metadata": {},
   "source": [
    "How many airports are there in total?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "9cd0a6ba-4808-4812-b760-ac389c435610",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 15ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_f1836_row0_col0 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_f1836\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_f1836_level0_col0\" class=\"col_heading level0 col0\" >count(code)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_f1836_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_f1836_row0_col0\" class=\"data row0 col0\" >3504</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b1bd0>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[count(code)] := @airport{code}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7bf2676-4e79-49f0-9401-4bf60f2dc313",
   "metadata": {},
   "source": [
    "Let's get a distribution of the initials of the airport codes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "d9878f9c-1b43-426b-a8f5-5060f2476d86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 18ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "  color: #307fc1;\n",
       "}\n",
       "#T_b5f69_row0_col1, #T_b5f69_row1_col1, #T_b5f69_row2_col1, #T_b5f69_row3_col1, #T_b5f69_row4_col1, #T_b5f69_row5_col1, #T_b5f69_row6_col1, #T_b5f69_row7_col1, #T_b5f69_row8_col1, #T_b5f69_row9_col1, #T_b5f69_row10_col1, #T_b5f69_row11_col1, #T_b5f69_row12_col1, #T_b5f69_row13_col1, #T_b5f69_row14_col1, #T_b5f69_row15_col1, #T_b5f69_row16_col1, #T_b5f69_row17_col1, #T_b5f69_row18_col1, #T_b5f69_row19_col1, #T_b5f69_row20_col1, #T_b5f69_row21_col1, #T_b5f69_row22_col1, #T_b5f69_row23_col1, #T_b5f69_row24_col1, #T_b5f69_row25_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_b5f69\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_b5f69_level0_col0\" class=\"col_heading level0 col0\" >count(initial)</th>\n",
       "      <th id=\"T_b5f69_level0_col1\" class=\"col_heading level0 col1\" >initial</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_b5f69_row0_col0\" class=\"data row0 col0\" >212</td>\n",
       "      <td id=\"T_b5f69_row0_col1\" class=\"data row0 col1\" >A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_b5f69_row1_col0\" class=\"data row1 col0\" >235</td>\n",
       "      <td id=\"T_b5f69_row1_col1\" class=\"data row1 col1\" >B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_b5f69_row2_col0\" class=\"data row2 col0\" >214</td>\n",
       "      <td id=\"T_b5f69_row2_col1\" class=\"data row2 col1\" >C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_b5f69_row3_col0\" class=\"data row3 col0\" >116</td>\n",
       "      <td id=\"T_b5f69_row3_col1\" class=\"data row3 col1\" >D</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_b5f69_row4_col0\" class=\"data row4 col0\" >95</td>\n",
       "      <td id=\"T_b5f69_row4_col1\" class=\"data row4 col1\" >E</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_b5f69_row5_col0\" class=\"data row5 col0\" >76</td>\n",
       "      <td id=\"T_b5f69_row5_col1\" class=\"data row5 col1\" >F</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_b5f69_row6_col0\" class=\"data row6 col0\" >135</td>\n",
       "      <td id=\"T_b5f69_row6_col1\" class=\"data row6 col1\" >G</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_b5f69_row7_col0\" class=\"data row7 col0\" >129</td>\n",
       "      <td id=\"T_b5f69_row7_col1\" class=\"data row7 col1\" >H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_b5f69_row8_col0\" class=\"data row8 col0\" >112</td>\n",
       "      <td id=\"T_b5f69_row8_col1\" class=\"data row8 col1\" >I</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_b5f69_row9_col0\" class=\"data row9 col0\" >80</td>\n",
       "      <td id=\"T_b5f69_row9_col1\" class=\"data row9 col1\" >J</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
       "      <td id=\"T_b5f69_row10_col0\" class=\"data row10 col0\" >197</td>\n",
       "      <td id=\"T_b5f69_row10_col1\" class=\"data row10 col1\" >K</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row11\" class=\"row_heading level0 row11\" >11</th>\n",
       "      <td id=\"T_b5f69_row11_col0\" class=\"data row11 col0\" >184</td>\n",
       "      <td id=\"T_b5f69_row11_col1\" class=\"data row11 col1\" >L</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row12\" class=\"row_heading level0 row12\" >12</th>\n",
       "      <td id=\"T_b5f69_row12_col0\" class=\"data row12 col0\" >228</td>\n",
       "      <td id=\"T_b5f69_row12_col1\" class=\"data row12 col1\" >M</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row13\" class=\"row_heading level0 row13\" >13</th>\n",
       "      <td id=\"T_b5f69_row13_col0\" class=\"data row13 col0\" >111</td>\n",
       "      <td id=\"T_b5f69_row13_col1\" class=\"data row13 col1\" >N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row14\" class=\"row_heading level0 row14\" >14</th>\n",
       "      <td id=\"T_b5f69_row14_col0\" class=\"data row14 col0\" >89</td>\n",
       "      <td id=\"T_b5f69_row14_col1\" class=\"data row14 col1\" >O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row15\" class=\"row_heading level0 row15\" >15</th>\n",
       "      <td id=\"T_b5f69_row15_col0\" class=\"data row15 col0\" >203</td>\n",
       "      <td id=\"T_b5f69_row15_col1\" class=\"data row15 col1\" >P</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row16\" class=\"row_heading level0 row16\" >16</th>\n",
       "      <td id=\"T_b5f69_row16_col0\" class=\"data row16 col0\" >7</td>\n",
       "      <td id=\"T_b5f69_row16_col1\" class=\"data row16 col1\" >Q</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row17\" class=\"row_heading level0 row17\" >17</th>\n",
       "      <td id=\"T_b5f69_row17_col0\" class=\"data row17 col0\" >121</td>\n",
       "      <td id=\"T_b5f69_row17_col1\" class=\"data row17 col1\" >R</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row18\" class=\"row_heading level0 row18\" >18</th>\n",
       "      <td id=\"T_b5f69_row18_col0\" class=\"data row18 col0\" >245</td>\n",
       "      <td id=\"T_b5f69_row18_col1\" class=\"data row18 col1\" >S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row19\" class=\"row_heading level0 row19\" >19</th>\n",
       "      <td id=\"T_b5f69_row19_col0\" class=\"data row19 col0\" >205</td>\n",
       "      <td id=\"T_b5f69_row19_col1\" class=\"data row19 col1\" >T</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row20\" class=\"row_heading level0 row20\" >20</th>\n",
       "      <td id=\"T_b5f69_row20_col0\" class=\"data row20 col0\" >77</td>\n",
       "      <td id=\"T_b5f69_row20_col1\" class=\"data row20 col1\" >U</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row21\" class=\"row_heading level0 row21\" >21</th>\n",
       "      <td id=\"T_b5f69_row21_col0\" class=\"data row21 col0\" >86</td>\n",
       "      <td id=\"T_b5f69_row21_col1\" class=\"data row21 col1\" >V</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row22\" class=\"row_heading level0 row22\" >22</th>\n",
       "      <td id=\"T_b5f69_row22_col0\" class=\"data row22 col0\" >59</td>\n",
       "      <td id=\"T_b5f69_row22_col1\" class=\"data row22 col1\" >W</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row23\" class=\"row_heading level0 row23\" >23</th>\n",
       "      <td id=\"T_b5f69_row23_col0\" class=\"data row23 col0\" >28</td>\n",
       "      <td id=\"T_b5f69_row23_col1\" class=\"data row23 col1\" >X</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row24\" class=\"row_heading level0 row24\" >24</th>\n",
       "      <td id=\"T_b5f69_row24_col0\" class=\"data row24 col0\" >211</td>\n",
       "      <td id=\"T_b5f69_row24_col1\" class=\"data row24 col1\" >Y</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_b5f69_level0_row25\" class=\"row_heading level0 row25\" >25</th>\n",
       "      <td id=\"T_b5f69_row25_col0\" class=\"data row25 col0\" >49</td>\n",
       "      <td id=\"T_b5f69_row25_col1\" class=\"data row25 col1\" >Z</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f320d30>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[count(initial), initial] := @airport{code}, initial = first(chars(code))\n",
    "\n",
    ":order initial"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34283880-46bb-4759-965e-5e3de5128c15",
   "metadata": {},
   "source": [
    "More useful are the statistics of runways:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "4d509508-02fa-4ec3-94a9-905dde2dda41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 20ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_90640_row0_col0, #T_90640_row0_col1, #T_90640_row0_col2, #T_90640_row0_col3, #T_90640_row0_col4, #T_90640_row0_col5, #T_90640_row0_col6 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_90640\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_90640_level0_col0\" class=\"col_heading level0 col0\" >count(r)</th>\n",
       "      <th id=\"T_90640_level0_col1\" class=\"col_heading level0 col1\" >count_unique(r)</th>\n",
       "      <th id=\"T_90640_level0_col2\" class=\"col_heading level0 col2\" >sum(r)</th>\n",
       "      <th id=\"T_90640_level0_col3\" class=\"col_heading level0 col3\" >min(r)</th>\n",
       "      <th id=\"T_90640_level0_col4\" class=\"col_heading level0 col4\" >max(r)</th>\n",
       "      <th id=\"T_90640_level0_col5\" class=\"col_heading level0 col5\" >mean(r)</th>\n",
       "      <th id=\"T_90640_level0_col6\" class=\"col_heading level0 col6\" >std_dev(r)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_90640_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_90640_row0_col0\" class=\"data row0 col0\" >3504</td>\n",
       "      <td id=\"T_90640_row0_col1\" class=\"data row0 col1\" >7</td>\n",
       "      <td id=\"T_90640_row0_col2\" class=\"data row0 col2\" >4980.000000</td>\n",
       "      <td id=\"T_90640_row0_col3\" class=\"data row0 col3\" >1</td>\n",
       "      <td id=\"T_90640_row0_col4\" class=\"data row0 col4\" >7</td>\n",
       "      <td id=\"T_90640_row0_col5\" class=\"data row0 col5\" >1.421233</td>\n",
       "      <td id=\"T_90640_row0_col6\" class=\"data row0 col6\" >0.743083</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b2b30>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[count(r), count_unique(r), sum(r), min(r), max(r), mean(r), std_dev(r)] := \n",
    "    @airport{runways: r}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c62269c6-9c23-4766-918d-aedb5cfe4bc3",
   "metadata": {},
   "source": [
    "Using `country`, we can find countries with no airports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "739902f6-902f-4261-878f-826291596399",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 12ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_eaffb_row0_col0, #T_eaffb_row1_col0, #T_eaffb_row2_col0, #T_eaffb_row3_col0, #T_eaffb_row4_col0 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_eaffb\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_eaffb_level0_col0\" class=\"col_heading level0 col0\" >desc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_eaffb_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_eaffb_row0_col0\" class=\"data row0 col0\" >Andorra</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_eaffb_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_eaffb_row1_col0\" class=\"data row1 col0\" >Liechtenstein</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_eaffb_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_eaffb_row2_col0\" class=\"data row2 col0\" >Monaco</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_eaffb_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_eaffb_row3_col0\" class=\"data row3 col0\" >Pitcairn</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_eaffb_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_eaffb_row4_col0\" class=\"data row4 col0\" >San Marino</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b1090>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[desc] := @country{code, desc}, not @airport{country: code}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f65e01a-b43f-48d2-9afa-0021262e6ada",
   "metadata": {},
   "source": [
    "The `route` relation by itself is rather boring:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "9d297cc5-ba50-44d7-b834-46ffaa6c748d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_d1c60_row0_col0, #T_d1c60_row0_col1, #T_d1c60_row1_col0, #T_d1c60_row1_col1, #T_d1c60_row2_col0, #T_d1c60_row2_col1, #T_d1c60_row3_col0, #T_d1c60_row3_col1, #T_d1c60_row4_col0, #T_d1c60_row4_col1, #T_d1c60_row5_col0, #T_d1c60_row5_col1, #T_d1c60_row6_col0, #T_d1c60_row6_col1, #T_d1c60_row7_col0, #T_d1c60_row7_col1, #T_d1c60_row8_col0, #T_d1c60_row8_col1, #T_d1c60_row9_col0, #T_d1c60_row9_col1 {\n",
       "  color: black;\n",
       "}\n",
       "#T_d1c60_row0_col2, #T_d1c60_row1_col2, #T_d1c60_row2_col2, #T_d1c60_row3_col2, #T_d1c60_row4_col2, #T_d1c60_row5_col2, #T_d1c60_row6_col2, #T_d1c60_row7_col2, #T_d1c60_row8_col2, #T_d1c60_row9_col2 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_d1c60\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_d1c60_level0_col0\" class=\"col_heading level0 col0\" >fr</th>\n",
       "      <th id=\"T_d1c60_level0_col1\" class=\"col_heading level0 col1\" >to</th>\n",
       "      <th id=\"T_d1c60_level0_col2\" class=\"col_heading level0 col2\" >dist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_d1c60_row0_col0\" class=\"data row0 col0\" >AAA</td>\n",
       "      <td id=\"T_d1c60_row0_col1\" class=\"data row0 col1\" >FAC</td>\n",
       "      <td id=\"T_d1c60_row0_col2\" class=\"data row0 col2\" >48.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_d1c60_row1_col0\" class=\"data row1 col0\" >AAA</td>\n",
       "      <td id=\"T_d1c60_row1_col1\" class=\"data row1 col1\" >MKP</td>\n",
       "      <td id=\"T_d1c60_row1_col2\" class=\"data row1 col2\" >133.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_d1c60_row2_col0\" class=\"data row2 col0\" >AAA</td>\n",
       "      <td id=\"T_d1c60_row2_col1\" class=\"data row2 col1\" >PPT</td>\n",
       "      <td id=\"T_d1c60_row2_col2\" class=\"data row2 col2\" >270.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_d1c60_row3_col0\" class=\"data row3 col0\" >AAA</td>\n",
       "      <td id=\"T_d1c60_row3_col1\" class=\"data row3 col1\" >RAR</td>\n",
       "      <td id=\"T_d1c60_row3_col2\" class=\"data row3 col2\" >968.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_d1c60_row4_col0\" class=\"data row4 col0\" >AAE</td>\n",
       "      <td id=\"T_d1c60_row4_col1\" class=\"data row4 col1\" >ALG</td>\n",
       "      <td id=\"T_d1c60_row4_col2\" class=\"data row4 col2\" >254.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_d1c60_row5_col0\" class=\"data row5 col0\" >AAE</td>\n",
       "      <td id=\"T_d1c60_row5_col1\" class=\"data row5 col1\" >CDG</td>\n",
       "      <td id=\"T_d1c60_row5_col2\" class=\"data row5 col2\" >882.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_d1c60_row6_col0\" class=\"data row6 col0\" >AAE</td>\n",
       "      <td id=\"T_d1c60_row6_col1\" class=\"data row6 col1\" >IST</td>\n",
       "      <td id=\"T_d1c60_row6_col2\" class=\"data row6 col2\" >1161.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_d1c60_row7_col0\" class=\"data row7 col0\" >AAE</td>\n",
       "      <td id=\"T_d1c60_row7_col1\" class=\"data row7 col1\" >LYS</td>\n",
       "      <td id=\"T_d1c60_row7_col2\" class=\"data row7 col2\" >631.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_d1c60_row8_col0\" class=\"data row8 col0\" >AAE</td>\n",
       "      <td id=\"T_d1c60_row8_col1\" class=\"data row8 col1\" >MRS</td>\n",
       "      <td id=\"T_d1c60_row8_col2\" class=\"data row8 col2\" >477.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d1c60_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_d1c60_row9_col0\" class=\"data row9 col0\" >AAE</td>\n",
       "      <td id=\"T_d1c60_row9_col1\" class=\"data row9 col1\" >ORN</td>\n",
       "      <td id=\"T_d1c60_row9_col2\" class=\"data row9 col2\" >477.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f321c00>"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[fr, to, dist] := @route{fr, to, dist}\n",
    "\n",
    ":limit 10"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f037a30-6f67-4fd9-ba3a-968ebfe811ff",
   "metadata": {},
   "source": [
    "It just records the starting and ending airports of each route, together with the distance. This relation only becomes useful when used as a graph."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44135ecf-045e-41c2-9c76-fb8eaac8b15b",
   "metadata": {},
   "source": [
    "Airports with no routes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "e58de060-2f75-46fb-9ce0-98068e338c09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 77ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
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       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_35084\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_35084_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_35084_level0_col1\" class=\"col_heading level0 col1\" >desc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_35084_row0_col0\" class=\"data row0 col0\" >AFW</td>\n",
       "      <td id=\"T_35084_row0_col1\" class=\"data row0 col1\" >Fort Worth Alliance Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_35084_row1_col0\" class=\"data row1 col0\" >APA</td>\n",
       "      <td id=\"T_35084_row1_col1\" class=\"data row1 col1\" >Centennial Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_35084_row2_col0\" class=\"data row2 col0\" >APK</td>\n",
       "      <td id=\"T_35084_row2_col1\" class=\"data row2 col1\" >Apataki Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_35084_row3_col0\" class=\"data row3 col0\" >BID</td>\n",
       "      <td id=\"T_35084_row3_col1\" class=\"data row3 col1\" >Block Island State Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_35084_row4_col0\" class=\"data row4 col0\" >BVS</td>\n",
       "      <td id=\"T_35084_row4_col1\" class=\"data row4 col1\" >Breves Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_35084_row5_col0\" class=\"data row5 col0\" >BWU</td>\n",
       "      <td id=\"T_35084_row5_col1\" class=\"data row5 col1\" >Sydney Bankstown Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_35084_row6_col0\" class=\"data row6 col0\" >CRC</td>\n",
       "      <td id=\"T_35084_row6_col1\" class=\"data row6 col1\" >Santa Ana Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_35084_row7_col0\" class=\"data row7 col0\" >CVT</td>\n",
       "      <td id=\"T_35084_row7_col1\" class=\"data row7 col1\" >Coventry Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_35084_row8_col0\" class=\"data row8 col0\" >EKA</td>\n",
       "      <td id=\"T_35084_row8_col1\" class=\"data row8 col1\" >Murray Field</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_35084_row9_col0\" class=\"data row9 col0\" >GYZ</td>\n",
       "      <td id=\"T_35084_row9_col1\" class=\"data row9 col1\" >Gruyere Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
       "      <td id=\"T_35084_row10_col0\" class=\"data row10 col0\" >HFN</td>\n",
       "      <td id=\"T_35084_row10_col1\" class=\"data row10 col1\" >Hornafjordur Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row11\" class=\"row_heading level0 row11\" >11</th>\n",
       "      <td id=\"T_35084_row11_col0\" class=\"data row11 col0\" >HZK</td>\n",
       "      <td id=\"T_35084_row11_col1\" class=\"data row11 col1\" >Husavik Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row12\" class=\"row_heading level0 row12\" >12</th>\n",
       "      <td id=\"T_35084_row12_col0\" class=\"data row12 col0\" >ILG</td>\n",
       "      <td id=\"T_35084_row12_col1\" class=\"data row12 col1\" >New Castle Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row13\" class=\"row_heading level0 row13\" >13</th>\n",
       "      <td id=\"T_35084_row13_col0\" class=\"data row13 col0\" >INT</td>\n",
       "      <td id=\"T_35084_row13_col1\" class=\"data row13 col1\" >Smith Reynolds Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row14\" class=\"row_heading level0 row14\" >14</th>\n",
       "      <td id=\"T_35084_row14_col0\" class=\"data row14 col0\" >ISL</td>\n",
       "      <td id=\"T_35084_row14_col1\" class=\"data row14 col1\" >Ataturk International Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row15\" class=\"row_heading level0 row15\" >15</th>\n",
       "      <td id=\"T_35084_row15_col0\" class=\"data row15 col0\" >KGG</td>\n",
       "      <td id=\"T_35084_row15_col1\" class=\"data row15 col1\" >Kédougou Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row16\" class=\"row_heading level0 row16\" >16</th>\n",
       "      <td id=\"T_35084_row16_col0\" class=\"data row16 col0\" >NBW</td>\n",
       "      <td id=\"T_35084_row16_col1\" class=\"data row16 col1\" >Leeward Point Field</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row17\" class=\"row_heading level0 row17\" >17</th>\n",
       "      <td id=\"T_35084_row17_col0\" class=\"data row17 col0\" >NFO</td>\n",
       "      <td id=\"T_35084_row17_col1\" class=\"data row17 col1\" >Mata'aho Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row18\" class=\"row_heading level0 row18\" >18</th>\n",
       "      <td id=\"T_35084_row18_col0\" class=\"data row18 col0\" >PSY</td>\n",
       "      <td id=\"T_35084_row18_col1\" class=\"data row18 col1\" >Stanley Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row19\" class=\"row_heading level0 row19\" >19</th>\n",
       "      <td id=\"T_35084_row19_col0\" class=\"data row19 col0\" >RIG</td>\n",
       "      <td id=\"T_35084_row19_col1\" class=\"data row19 col1\" >Rio Grande Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row20\" class=\"row_heading level0 row20\" >20</th>\n",
       "      <td id=\"T_35084_row20_col0\" class=\"data row20 col0\" >SFD</td>\n",
       "      <td id=\"T_35084_row20_col1\" class=\"data row20 col1\" >San Fernando De Apure Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row21\" class=\"row_heading level0 row21\" >21</th>\n",
       "      <td id=\"T_35084_row21_col0\" class=\"data row21 col0\" >SFH</td>\n",
       "      <td id=\"T_35084_row21_col1\" class=\"data row21 col1\" >San Felipe International Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row22\" class=\"row_heading level0 row22\" >22</th>\n",
       "      <td id=\"T_35084_row22_col0\" class=\"data row22 col0\" >SXF</td>\n",
       "      <td id=\"T_35084_row22_col1\" class=\"data row22 col1\" >Berlin-Schönefeld International Airport *Closed*</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row23\" class=\"row_heading level0 row23\" >23</th>\n",
       "      <td id=\"T_35084_row23_col0\" class=\"data row23 col0\" >TUA</td>\n",
       "      <td id=\"T_35084_row23_col1\" class=\"data row23 col1\" >Teniente Coronel Luis a Mantilla Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row24\" class=\"row_heading level0 row24\" >24</th>\n",
       "      <td id=\"T_35084_row24_col0\" class=\"data row24 col0\" >TWB</td>\n",
       "      <td id=\"T_35084_row24_col1\" class=\"data row24 col1\" >Toowoomba Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row25\" class=\"row_heading level0 row25\" >25</th>\n",
       "      <td id=\"T_35084_row25_col0\" class=\"data row25 col0\" >TXL</td>\n",
       "      <td id=\"T_35084_row25_col1\" class=\"data row25 col1\" >Berlin, Tegel International Airport *Closed*</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row26\" class=\"row_heading level0 row26\" >26</th>\n",
       "      <td id=\"T_35084_row26_col0\" class=\"data row26 col0\" >VCV</td>\n",
       "      <td id=\"T_35084_row26_col1\" class=\"data row26 col1\" >Southern California Logistics Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_35084_level0_row27\" class=\"row_heading level0 row27\" >27</th>\n",
       "      <td id=\"T_35084_row27_col0\" class=\"data row27 col0\" >YEI</td>\n",
       "      <td id=\"T_35084_row27_col1\" class=\"data row27 col1\" >Bursa Yenişehir Airport</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b1270>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[code, desc] := @airport{code, desc}, not @route{fr: code}, not @route{to: code}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e26b06c3-3919-4a72-861d-e63318708496",
   "metadata": {},
   "source": [
    "Airports with the most out routes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "1b0a075d-5968-41e6-90df-27ee2034dc84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 108ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_a007e_row0_col0, #T_a007e_row1_col0, #T_a007e_row2_col0, #T_a007e_row3_col0, #T_a007e_row4_col0 {\n",
       "  color: black;\n",
       "}\n",
       "#T_a007e_row0_col1, #T_a007e_row1_col1, #T_a007e_row2_col1, #T_a007e_row3_col1, #T_a007e_row4_col1 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_a007e\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_a007e_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_a007e_level0_col1\" class=\"col_heading level0 col1\" >n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_a007e_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_a007e_row0_col0\" class=\"data row0 col0\" >FRA</td>\n",
       "      <td id=\"T_a007e_row0_col1\" class=\"data row0 col1\" >310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a007e_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_a007e_row1_col0\" class=\"data row1 col0\" >IST</td>\n",
       "      <td id=\"T_a007e_row1_col1\" class=\"data row1 col1\" >309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a007e_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_a007e_row2_col0\" class=\"data row2 col0\" >CDG</td>\n",
       "      <td id=\"T_a007e_row2_col1\" class=\"data row2 col1\" >293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a007e_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_a007e_row3_col0\" class=\"data row3 col0\" >AMS</td>\n",
       "      <td id=\"T_a007e_row3_col1\" class=\"data row3 col1\" >283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a007e_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_a007e_row4_col0\" class=\"data row4 col0\" >MUC</td>\n",
       "      <td id=\"T_a007e_row4_col1\" class=\"data row4 col1\" >270</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b1b10>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "route_count[fr, count(fr)] := @route{fr}\n",
    "?[code, n] := route_count[code, n]\n",
    "\n",
    ":sort -n\n",
    ":limit 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4154c1e-78f8-4621-9a32-05363d1b13cf",
   "metadata": {},
   "source": [
    "How many routes are there from the European Union to the US?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "7de94407-206b-42d9-ac3b-cd9a3277bfe3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 56ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_14f11_row0_col0 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_14f11\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_14f11_level0_col0\" class=\"col_heading level0 col0\" >n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_14f11_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_14f11_row0_col0\" class=\"data row0 col0\" >435</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
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       "<pandas.io.formats.style.Styler at 0x11f321cc0>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "routes[unique(r)] := @contain['EU', fr],\n",
    "                     @route{fr, to},\n",
    "                     @airport{code: to, country: 'US'},\n",
    "                     r = [fr, to]\n",
    "?[n] := routes[rs], n = length(rs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "528bc6eb-064d-418f-8aa1-98aeedd64ace",
   "metadata": {},
   "source": [
    "How many airports are there in the US with routes from the EU?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "7ecfd10d-f05f-443e-a0e9-73480d67dcf1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 55ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_60391_row0_col0 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_60391\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_60391_level0_col0\" class=\"col_heading level0 col0\" >count_unique(to)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_60391_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_60391_row0_col0\" class=\"data row0 col0\" >45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b1150>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[count_unique(to)] := @contain['EU', fr],\n",
    "                       @route{fr, to},\n",
    "                       @airport{code: to, country: 'US'}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a13fa07-aaa4-47c1-aefb-0a93c80e3c18",
   "metadata": {},
   "source": [
    "How many routes are there for each airport in London, UK?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "52f6c021-1ac7-42a6-910a-7686eb2c653d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 18ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_abca9_row0_col0, #T_abca9_row1_col0, #T_abca9_row2_col0, #T_abca9_row3_col0, #T_abca9_row4_col0 {\n",
       "  color: black;\n",
       "}\n",
       "#T_abca9_row0_col1, #T_abca9_row1_col1, #T_abca9_row2_col1, #T_abca9_row3_col1, #T_abca9_row4_col1 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_abca9\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_abca9_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_abca9_level0_col1\" class=\"col_heading level0 col1\" >count(code)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_abca9_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_abca9_row0_col0\" class=\"data row0 col0\" >LCY</td>\n",
       "      <td id=\"T_abca9_row0_col1\" class=\"data row0 col1\" >51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_abca9_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_abca9_row1_col0\" class=\"data row1 col0\" >LGW</td>\n",
       "      <td id=\"T_abca9_row1_col1\" class=\"data row1 col1\" >232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_abca9_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_abca9_row2_col0\" class=\"data row2 col0\" >LHR</td>\n",
       "      <td id=\"T_abca9_row2_col1\" class=\"data row2 col1\" >221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_abca9_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_abca9_row3_col0\" class=\"data row3 col0\" >LTN</td>\n",
       "      <td id=\"T_abca9_row3_col1\" class=\"data row3 col1\" >130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_abca9_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_abca9_row4_col0\" class=\"data row4 col0\" >STN</td>\n",
       "      <td id=\"T_abca9_row4_col1\" class=\"data row4 col1\" >211</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f323550>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[code, count(code)] := @airport{code, city: 'London', region: 'GB-ENG'}, @route{fr: code}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19ecd6fa-04e0-4a03-9834-f0dfea861e9a",
   "metadata": {},
   "source": [
    "We need to specify the region, because there is another city called London, not in the UK."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d393dfbb-5ceb-412d-bc71-24db4bcf3261",
   "metadata": {},
   "source": [
    "How many airports are reachable from London, UK in two hops?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "0689fddc-e02d-4b4c-a621-b17f0431ccf4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 87ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_12c5b_row0_col0 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_12c5b\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_12c5b_level0_col0\" class=\"col_heading level0 col0\" >count_unique(a3)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_12c5b_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_12c5b_row0_col0\" class=\"data row0 col0\" >2353</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f322050>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lon_uk_airports[code] := @airport{code, city: 'London', region: 'GB-ENG'}\n",
    "one_hop[to] := lon_uk_airports[fr], @route{fr, to}, not lon_uk_airports[to];\n",
    "?[count_unique(a3)] := one_hop[a2], @route{fr: a2, to: a3}, not lon_uk_airports[a3];"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4be5b2d5-8aa9-4109-94f4-ccb75e109935",
   "metadata": {},
   "source": [
    "What are the cities directly reachable from LGW, but furthermost away?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "9ac99669-84dc-4a7a-b985-d1e333a41065",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 4ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_cb7a5_row0_col0, #T_cb7a5_row1_col0, #T_cb7a5_row2_col0, #T_cb7a5_row3_col0, #T_cb7a5_row4_col0, #T_cb7a5_row5_col0, #T_cb7a5_row6_col0, #T_cb7a5_row7_col0, #T_cb7a5_row8_col0, #T_cb7a5_row9_col0 {\n",
       "  color: black;\n",
       "}\n",
       "#T_cb7a5_row0_col1, #T_cb7a5_row1_col1, #T_cb7a5_row2_col1, #T_cb7a5_row3_col1, #T_cb7a5_row4_col1, #T_cb7a5_row5_col1, #T_cb7a5_row6_col1, #T_cb7a5_row7_col1, #T_cb7a5_row8_col1, #T_cb7a5_row9_col1 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_cb7a5\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_cb7a5_level0_col0\" class=\"col_heading level0 col0\" >city</th>\n",
       "      <th id=\"T_cb7a5_level0_col1\" class=\"col_heading level0 col1\" >dist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_cb7a5_row0_col0\" class=\"data row0 col0\" >Buenos Aires</td>\n",
       "      <td id=\"T_cb7a5_row0_col1\" class=\"data row0 col1\" >6908.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_cb7a5_row1_col0\" class=\"data row1 col0\" >Singapore</td>\n",
       "      <td id=\"T_cb7a5_row1_col1\" class=\"data row1 col1\" >6751.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_cb7a5_row2_col0\" class=\"data row2 col0\" >Langkawi</td>\n",
       "      <td id=\"T_cb7a5_row2_col1\" class=\"data row2 col1\" >6299.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_cb7a5_row3_col0\" class=\"data row3 col0\" >Duong Dong</td>\n",
       "      <td id=\"T_cb7a5_row3_col1\" class=\"data row3 col1\" >6264.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_cb7a5_row4_col0\" class=\"data row4 col0\" >Taipei</td>\n",
       "      <td id=\"T_cb7a5_row4_col1\" class=\"data row4 col1\" >6080.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_cb7a5_row5_col0\" class=\"data row5 col0\" >Port Louis</td>\n",
       "      <td id=\"T_cb7a5_row5_col1\" class=\"data row5 col1\" >6053.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_cb7a5_row6_col0\" class=\"data row6 col0\" >Rayong</td>\n",
       "      <td id=\"T_cb7a5_row6_col1\" class=\"data row6 col1\" >6008.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_cb7a5_row7_col0\" class=\"data row7 col0\" >Cape Town</td>\n",
       "      <td id=\"T_cb7a5_row7_col1\" class=\"data row7 col1\" >5987.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_cb7a5_row8_col0\" class=\"data row8 col0\" >Hong Kong</td>\n",
       "      <td id=\"T_cb7a5_row8_col1\" class=\"data row8 col1\" >5982.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_cb7a5_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_cb7a5_row9_col0\" class=\"data row9 col0\" >Shanghai</td>\n",
       "      <td id=\"T_cb7a5_row9_col1\" class=\"data row9 col1\" >5745.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3201c0>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[city, dist] := @route{fr: 'LGW', to, dist},\n",
    "                 @airport{code: to, city}\n",
    ":order -dist\n",
    ":limit 10"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "121df2dd-1926-47eb-80d3-c90fe56b253d",
   "metadata": {},
   "source": [
    "What airports are within 0.1 degrees of the Greenwich meridian?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "5ac6dee6-c475-4db9-824d-2cbcc774aa23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 15ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_f745a_row0_col0, #T_f745a_row0_col1, #T_f745a_row1_col0, #T_f745a_row1_col1, #T_f745a_row2_col0, #T_f745a_row2_col1, #T_f745a_row3_col0, #T_f745a_row3_col1 {\n",
       "  color: black;\n",
       "}\n",
       "#T_f745a_row0_col2, #T_f745a_row0_col3, #T_f745a_row1_col2, #T_f745a_row1_col3, #T_f745a_row2_col2, #T_f745a_row2_col3, #T_f745a_row3_col2, #T_f745a_row3_col3 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_f745a\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_f745a_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_f745a_level0_col1\" class=\"col_heading level0 col1\" >desc</th>\n",
       "      <th id=\"T_f745a_level0_col2\" class=\"col_heading level0 col2\" >lon</th>\n",
       "      <th id=\"T_f745a_level0_col3\" class=\"col_heading level0 col3\" >lat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_f745a_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_f745a_row0_col0\" class=\"data row0 col0\" >CDT</td>\n",
       "      <td id=\"T_f745a_row0_col1\" class=\"data row0 col1\" >Castellon De La Plana Airport</td>\n",
       "      <td id=\"T_f745a_row0_col2\" class=\"data row0 col2\" >0.026111</td>\n",
       "      <td id=\"T_f745a_row0_col3\" class=\"data row0 col3\" >39.999199</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f745a_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_f745a_row1_col0\" class=\"data row1 col0\" >LCY</td>\n",
       "      <td id=\"T_f745a_row1_col1\" class=\"data row1 col1\" >London City Airport</td>\n",
       "      <td id=\"T_f745a_row1_col2\" class=\"data row1 col2\" >0.055278</td>\n",
       "      <td id=\"T_f745a_row1_col3\" class=\"data row1 col3\" >51.505278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f745a_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_f745a_row2_col0\" class=\"data row2 col0\" >LDE</td>\n",
       "      <td id=\"T_f745a_row2_col1\" class=\"data row2 col1\" >Tarbes-Lourdes-Pyrénées Airport</td>\n",
       "      <td id=\"T_f745a_row2_col2\" class=\"data row2 col2\" >-0.006439</td>\n",
       "      <td id=\"T_f745a_row2_col3\" class=\"data row2 col3\" >43.178699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f745a_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_f745a_row3_col0\" class=\"data row3 col0\" >LEH</td>\n",
       "      <td id=\"T_f745a_row3_col1\" class=\"data row3 col1\" >Le Havre Octeville Airport</td>\n",
       "      <td id=\"T_f745a_row3_col2\" class=\"data row3 col2\" >0.088056</td>\n",
       "      <td id=\"T_f745a_row3_col3\" class=\"data row3 col3\" >49.533901</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b2500>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "?[code, desc, lon, lat] := @airport{lon, lat, code, desc}, lon > -0.1, lon < 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "015a1743-edd4-490d-b02f-462fa2506bed",
   "metadata": {},
   "source": [
    "Airports in a box drawn around London Heathrow, UK:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "9ced92e0-ced4-4e55-a547-c8b06fa50756",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 15ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_edf2e_row0_col0, #T_edf2e_row0_col1, #T_edf2e_row1_col0, #T_edf2e_row1_col1, #T_edf2e_row2_col0, #T_edf2e_row2_col1, #T_edf2e_row3_col0, #T_edf2e_row3_col1, #T_edf2e_row4_col0, #T_edf2e_row4_col1, #T_edf2e_row5_col0, #T_edf2e_row5_col1 {\n",
       "  color: black;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_edf2e\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_edf2e_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_edf2e_level0_col1\" class=\"col_heading level0 col1\" >desc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_edf2e_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_edf2e_row0_col0\" class=\"data row0 col0\" >LCY</td>\n",
       "      <td id=\"T_edf2e_row0_col1\" class=\"data row0 col1\" >London City Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_edf2e_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_edf2e_row1_col0\" class=\"data row1 col0\" >LGW</td>\n",
       "      <td id=\"T_edf2e_row1_col1\" class=\"data row1 col1\" >London Gatwick</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_edf2e_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_edf2e_row2_col0\" class=\"data row2 col0\" >LHR</td>\n",
       "      <td id=\"T_edf2e_row2_col1\" class=\"data row2 col1\" >London Heathrow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_edf2e_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_edf2e_row3_col0\" class=\"data row3 col0\" >LTN</td>\n",
       "      <td id=\"T_edf2e_row3_col1\" class=\"data row3 col1\" >London Luton Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_edf2e_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_edf2e_row4_col0\" class=\"data row4 col0\" >SOU</td>\n",
       "      <td id=\"T_edf2e_row4_col1\" class=\"data row4 col1\" >Southampton Airport</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_edf2e_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_edf2e_row5_col0\" class=\"data row5 col0\" >STN</td>\n",
       "      <td id=\"T_edf2e_row5_col1\" class=\"data row5 col1\" >London Stansted Airport</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3dd9f0>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_box[lon, lat] := @airport{code: 'LHR', lon, lat}\n",
    "?[code, desc] := h_box[lhr_lon, lhr_lat], @airport{code, lon, lat, desc},\n",
    "                 abs(lhr_lon - lon) < 1, abs(lhr_lat - lat) < 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20046b0e-cd8f-4de6-8f87-a49dcc8b8f7f",
   "metadata": {},
   "source": [
    "For some spherical geometry: what is the angle subtended by SFO and NRT on the surface of the earth?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "6d133cc5-23cb-47c6-9cc0-2c6bebf049eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<p style=\"font-size: 75%\">Completed in 0ms</p>"
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       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_46c24_level0_col0\" class=\"col_heading level0 col0\" >deg_diff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_46c24_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_46c24_row0_col0\" class=\"data row0 col0\" >73.992112</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
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     "execution_count": 81,
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   ],
   "source": [
    "?[deg_diff] := @airport{code: 'SFO', lat: a_lat, lon: a_lon},\n",
    "               @airport{code: 'NRT', lat: b_lat, lon: b_lon},\n",
    "               deg_diff = rad_to_deg(haversine_deg_input(a_lat, a_lon, b_lat, b_lon))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "184bc863-b2a7-4dd3-9d27-648315098ec8",
   "metadata": {},
   "source": [
    "We mentioned before that aggregations in Cozo are powerful. More powerful than in traditional SQL databases. The power comes from the fact that aggregations can be used in recursions (some restrictions apply).\n",
    "\n",
    "Let's say we want to find the distance of the _shortest route_ between two airports. One way to calculate is to enumerate all the routes between the two airports, and then apply `min` aggregation to the results. This cannot be implemented as stated, since the routes may contain cycles and hence there can be an infinite number of routes between two airports.\n",
    "\n",
    "Instead, let's think recursively. If we already have all the shortest routes between all nodes, can we derive an _equation_ satisfied by the shortest route? Yes, the shortest route between `a` and `b` is either the distance of a direct route or the sum of the shortest distance from `a` to `c` and the distance of a direct route from `c` to `d`. We apply our `min` aggregation to this recursive set instead. \n",
    "\n",
    "Let's write it out and try to find the shortest route between the airports `LHR` and `YPO`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "207a6e99-1e4a-466d-9492-859a680d9207",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_481aa_level0_col0\" class=\"col_heading level0 col0\" >dist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
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       "</table>\n"
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     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "shortest[b, min(dist)] := @route{fr: 'LHR', to: b, dist} \n",
    "                          # Start with the airport 'LHR', retrieve a direct route from 'LHR' to b\n",
    "\n",
    "shortest[b, min(dist)] := shortest[c, d1], # Start with an existing shortest route from 'LHR' to c\n",
    "                          @route{fr: c, to: b, dist: d2},  # Retrieve a direct route from c to b\n",
    "                          dist = d1 + d2 # Add the distances\n",
    "\n",
    "?[dist] := shortest['YPO', dist] # Extract the answer for 'YPO'. \n",
    "                                 # We chose it since it is the hardest airport to get to from 'LHR'."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73d28120-ee91-4893-a796-6cddec3426ad",
   "metadata": {},
   "source": [
    "It works. Since path-finding is such a common operation on graphs, Cozo has several fixed rules for that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "e1d8328f-87e5-4884-9f77-f6379c46465b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 65ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_d8900_row0_col0, #T_d8900_row0_col1 {\n",
       "  color: black;\n",
       "}\n",
       "#T_d8900_row0_col2 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "#T_d8900_row0_col3 {\n",
       "  color: #bf5b3d;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_d8900\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_d8900_level0_col0\" class=\"col_heading level0 col0\" >starting</th>\n",
       "      <th id=\"T_d8900_level0_col1\" class=\"col_heading level0 col1\" >goal</th>\n",
       "      <th id=\"T_d8900_level0_col2\" class=\"col_heading level0 col2\" >distance</th>\n",
       "      <th id=\"T_d8900_level0_col3\" class=\"col_heading level0 col3\" >path</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_d8900_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_d8900_row0_col0\" class=\"data row0 col0\" >LHR</td>\n",
       "      <td id=\"T_d8900_row0_col1\" class=\"data row0 col1\" >YPO</td>\n",
       "      <td id=\"T_d8900_row0_col2\" class=\"data row0 col2\" >4147.000000</td>\n",
       "      <td id=\"T_d8900_row0_col3\" class=\"data row0 col3\" >['LHR', 'YUL', 'YVO', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
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       "<pandas.io.formats.style.Styler at 0x11f3dc520>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "starting[] <- [['LHR']]\n",
    "goal[] <- [['YPO']]\n",
    "?[starting, goal, distance, path] <~ ShortestPathDijkstra(@route[], starting[], goal[])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af89a4d7-2260-466c-a119-bb0ae0a84ebf",
   "metadata": {},
   "source": [
    "Not only is it more efficient, but we also get a path for the shortest route.\n",
    "\n",
    "Not content with the shortest path, the following calculates the shortest ten paths:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "050a7fe1-9b6f-4cc8-96b7-9cebac55bdbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 89ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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       "#T_83cc4_row0_col2, #T_83cc4_row1_col2, #T_83cc4_row2_col2, #T_83cc4_row3_col2, #T_83cc4_row4_col2, #T_83cc4_row5_col2, #T_83cc4_row6_col2, #T_83cc4_row7_col2, #T_83cc4_row8_col2, #T_83cc4_row9_col2 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "#T_83cc4_row0_col3, #T_83cc4_row1_col3, #T_83cc4_row2_col3, #T_83cc4_row3_col3, #T_83cc4_row4_col3, #T_83cc4_row5_col3, #T_83cc4_row6_col3, #T_83cc4_row7_col3, #T_83cc4_row8_col3, #T_83cc4_row9_col3 {\n",
       "  color: #bf5b3d;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_83cc4\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_83cc4_level0_col0\" class=\"col_heading level0 col0\" >starting</th>\n",
       "      <th id=\"T_83cc4_level0_col1\" class=\"col_heading level0 col1\" >goal</th>\n",
       "      <th id=\"T_83cc4_level0_col2\" class=\"col_heading level0 col2\" >distance</th>\n",
       "      <th id=\"T_83cc4_level0_col3\" class=\"col_heading level0 col3\" >path</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_83cc4_row0_col0\" class=\"data row0 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row0_col1\" class=\"data row0 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row0_col2\" class=\"data row0 col2\" >4147.000000</td>\n",
       "      <td id=\"T_83cc4_row0_col3\" class=\"data row0 col3\" >['LHR', 'YUL', 'YVO', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_83cc4_row1_col0\" class=\"data row1 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row1_col1\" class=\"data row1 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row1_col2\" class=\"data row1 col2\" >4150.000000</td>\n",
       "      <td id=\"T_83cc4_row1_col3\" class=\"data row1 col3\" >['LHR', 'DUB', 'YUL', 'YVO', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_83cc4_row2_col0\" class=\"data row2 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row2_col1\" class=\"data row2 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row2_col2\" class=\"data row2 col2\" >4164.000000</td>\n",
       "      <td id=\"T_83cc4_row2_col3\" class=\"data row2 col3\" >['LHR', 'YUL', 'YMT', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_83cc4_row3_col0\" class=\"data row3 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row3_col1\" class=\"data row3 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row3_col2\" class=\"data row3 col2\" >4167.000000</td>\n",
       "      <td id=\"T_83cc4_row3_col3\" class=\"data row3 col3\" >['LHR', 'DUB', 'YUL', 'YMT', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_83cc4_row4_col0\" class=\"data row4 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row4_col1\" class=\"data row4 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row4_col2\" class=\"data row4 col2\" >4187.000000</td>\n",
       "      <td id=\"T_83cc4_row4_col3\" class=\"data row4 col3\" >['LHR', 'MAN', 'DUB', 'YUL', 'YVO', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_83cc4_row5_col0\" class=\"data row5 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row5_col1\" class=\"data row5 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row5_col2\" class=\"data row5 col2\" >4202.000000</td>\n",
       "      <td id=\"T_83cc4_row5_col3\" class=\"data row5 col3\" >['LHR', 'IOM', 'DUB', 'YUL', 'YVO', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_83cc4_row6_col0\" class=\"data row6 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row6_col1\" class=\"data row6 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row6_col2\" class=\"data row6 col2\" >4204.000000</td>\n",
       "      <td id=\"T_83cc4_row6_col3\" class=\"data row6 col3\" >['LHR', 'MAN', 'DUB', 'YUL', 'YMT', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_83cc4_row7_col0\" class=\"data row7 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row7_col1\" class=\"data row7 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row7_col2\" class=\"data row7 col2\" >4209.000000</td>\n",
       "      <td id=\"T_83cc4_row7_col3\" class=\"data row7 col3\" >['LHR', 'YUL', 'YMT', 'YNS', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_83cc4_row8_col0\" class=\"data row8 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row8_col1\" class=\"data row8 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row8_col2\" class=\"data row8 col2\" >4211.000000</td>\n",
       "      <td id=\"T_83cc4_row8_col3\" class=\"data row8 col3\" >['LHR', 'MAN', 'IOM', 'DUB', 'YUL', 'YVO', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_83cc4_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_83cc4_row9_col0\" class=\"data row9 col0\" >LHR</td>\n",
       "      <td id=\"T_83cc4_row9_col1\" class=\"data row9 col1\" >YPO</td>\n",
       "      <td id=\"T_83cc4_row9_col2\" class=\"data row9 col2\" >4212.000000</td>\n",
       "      <td id=\"T_83cc4_row9_col3\" class=\"data row9 col3\" >['LHR', 'DUB', 'YUL', 'YMT', 'YNS', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3df700>"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "starting[] <- [['LHR']]\n",
    "goal[] <- [['YPO']]\n",
    "?[starting, goal, distance, path] <~ KShortestPathYen(@route[], starting[], goal[], k: 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b3a398d-95ee-4e4f-91a7-5c95f82c8bd3",
   "metadata": {},
   "source": [
    "On the other hand, if efficiency is really important to you, you can use the A* algorithm with a really good heuristic function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "311a46cf-ba33-483a-ae60-c9a4ff2a071b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 32ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
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       "  color: #307fc1;\n",
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       "#T_fa38d_row0_col3 {\n",
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       "</style>\n",
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       "      <td id=\"T_fa38d_row0_col0\" class=\"data row0 col0\" >LHR</td>\n",
       "      <td id=\"T_fa38d_row0_col1\" class=\"data row0 col1\" >YPO</td>\n",
       "      <td id=\"T_fa38d_row0_col2\" class=\"data row0 col2\" >4147.000000</td>\n",
       "      <td id=\"T_fa38d_row0_col3\" class=\"data row0 col3\" >['LHR', 'YUL', 'YVO', 'YKQ', 'YMO', 'YFA', 'ZKE', 'YAT', 'YPO']</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3de320>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "code_lat_lon[code, lat, lon] := @airport{code, lat, lon}\n",
    "starting[code, lat, lon] := code = 'LHR', @airport{code, lat, lon};\n",
    "goal[code, lat, lon] := code = 'YPO', @airport{code, lat, lon};\n",
    "?[] <~ ShortestPathAStar(@route[], \n",
    "                         code_lat_lon[node, lat1, lon1], \n",
    "                         starting[], \n",
    "                         goal[goal, lat2, lon2], \n",
    "                         heuristic: haversine_deg_input(lat1, lon1, lat2, lon2) * 3963);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18a35f6d-7d31-412d-9ab0-abb79655b0d9",
   "metadata": {},
   "source": [
    "There's a lot more setup required in this case: we need to retrieve the latitudes and longitudes of airports and do processing on them first.\n",
    "The number `3963` above is the radius of the earth in miles. \n",
    "See [here](https://cozodb.github.io/current/manual/algorithms.html#Algo.ShortestPathAStar) for what is going on."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c522cee1-d4ad-4c75-aa91-9c5e2852eecd",
   "metadata": {},
   "source": [
    "The most important airports, by PageRank:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "a42d018b-ba09-4e27-9b1a-e780ca0bcc1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p style=\"font-size: 75%\">Completed in 91ms</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
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     "data": {
      "text/html": [
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       "#T_a78bd_row0_col2, #T_a78bd_row1_col2, #T_a78bd_row2_col2, #T_a78bd_row3_col2, #T_a78bd_row4_col2, #T_a78bd_row5_col2, #T_a78bd_row6_col2, #T_a78bd_row7_col2, #T_a78bd_row8_col2, #T_a78bd_row9_col2 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_a78bd\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_a78bd_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_a78bd_level0_col1\" class=\"col_heading level0 col1\" >desc</th>\n",
       "      <th id=\"T_a78bd_level0_col2\" class=\"col_heading level0 col2\" >score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_a78bd_row0_col0\" class=\"data row0 col0\" >FRA</td>\n",
       "      <td id=\"T_a78bd_row0_col1\" class=\"data row0 col1\" >Frankfurt am Main</td>\n",
       "      <td id=\"T_a78bd_row0_col2\" class=\"data row0 col2\" >1.265292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_a78bd_row1_col0\" class=\"data row1 col0\" >IST</td>\n",
       "      <td id=\"T_a78bd_row1_col1\" class=\"data row1 col1\" >Istanbul International Airport</td>\n",
       "      <td id=\"T_a78bd_row1_col2\" class=\"data row1 col2\" >1.260846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_a78bd_row2_col0\" class=\"data row2 col0\" >CDG</td>\n",
       "      <td id=\"T_a78bd_row2_col1\" class=\"data row2 col1\" >Paris Charles de Gaulle</td>\n",
       "      <td id=\"T_a78bd_row2_col2\" class=\"data row2 col2\" >1.251049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_a78bd_row3_col0\" class=\"data row3 col0\" >AMS</td>\n",
       "      <td id=\"T_a78bd_row3_col1\" class=\"data row3 col1\" >Amsterdam Airport Schiphol</td>\n",
       "      <td id=\"T_a78bd_row3_col2\" class=\"data row3 col2\" >1.243261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_a78bd_row4_col0\" class=\"data row4 col0\" >MUC</td>\n",
       "      <td id=\"T_a78bd_row4_col1\" class=\"data row4 col1\" >Munich International Airport</td>\n",
       "      <td id=\"T_a78bd_row4_col2\" class=\"data row4 col2\" >1.230537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_a78bd_row5_col0\" class=\"data row5 col0\" >ORD</td>\n",
       "      <td id=\"T_a78bd_row5_col1\" class=\"data row5 col1\" >Chicago O'Hare International Airport</td>\n",
       "      <td id=\"T_a78bd_row5_col2\" class=\"data row5 col2\" >1.220283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_a78bd_row6_col0\" class=\"data row6 col0\" >DFW</td>\n",
       "      <td id=\"T_a78bd_row6_col1\" class=\"data row6 col1\" >Dallas/Fort Worth International Airport</td>\n",
       "      <td id=\"T_a78bd_row6_col2\" class=\"data row6 col2\" >1.208827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_a78bd_row7_col0\" class=\"data row7 col0\" >DXB</td>\n",
       "      <td id=\"T_a78bd_row7_col1\" class=\"data row7 col1\" >Dubai International Airport</td>\n",
       "      <td id=\"T_a78bd_row7_col2\" class=\"data row7 col2\" >1.208430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_a78bd_row8_col0\" class=\"data row8 col0\" >PEK</td>\n",
       "      <td id=\"T_a78bd_row8_col1\" class=\"data row8 col1\" >Beijing Capital International Airport</td>\n",
       "      <td id=\"T_a78bd_row8_col2\" class=\"data row8 col2\" >1.208074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_a78bd_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_a78bd_row9_col0\" class=\"data row9 col0\" >ATL</td>\n",
       "      <td id=\"T_a78bd_row9_col1\" class=\"data row9 col1\" >Hartsfield - Jackson Atlanta International Airport</td>\n",
       "      <td id=\"T_a78bd_row9_col2\" class=\"data row9 col2\" >1.199858</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3df940>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rank[code, score] <~ PageRank(@route[a, b])\n",
    "?[code, desc, score] := rank[code, score], @airport{code, desc}\n",
    "\n",
    ":limit 10;\n",
    ":order -score"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2be4f97-5173-456e-a0d9-b7cf99bf9786",
   "metadata": {},
   "source": [
    "The following example takes a long time to run since it calculates the betweenness centrality.\n",
    "Algorithms for calculating the betweenness centrality have high complexity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "aaad3658-f2c2-4dde-bfe4-9b52e2b3f589",
   "metadata": {},
   "outputs": [
    {
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       "<p style=\"font-size: 75%\">Completed in 2902ms</p>"
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       "  color: black;\n",
       "}\n",
       "#T_2bfcd_row0_col2, #T_2bfcd_row1_col2, #T_2bfcd_row2_col2, #T_2bfcd_row3_col2, #T_2bfcd_row4_col2, #T_2bfcd_row5_col2, #T_2bfcd_row6_col2, #T_2bfcd_row7_col2, #T_2bfcd_row8_col2, #T_2bfcd_row9_col2 {\n",
       "  color: #307fc1;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_2bfcd\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_2bfcd_level0_col0\" class=\"col_heading level0 col0\" >code</th>\n",
       "      <th id=\"T_2bfcd_level0_col1\" class=\"col_heading level0 col1\" >desc</th>\n",
       "      <th id=\"T_2bfcd_level0_col2\" class=\"col_heading level0 col2\" >score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_2bfcd_row0_col0\" class=\"data row0 col0\" >ANC</td>\n",
       "      <td id=\"T_2bfcd_row0_col1\" class=\"data row0 col1\" >Anchorage Ted Stevens</td>\n",
       "      <td id=\"T_2bfcd_row0_col2\" class=\"data row0 col2\" >1074869.260952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_2bfcd_row1_col0\" class=\"data row1 col0\" >KEF</td>\n",
       "      <td id=\"T_2bfcd_row1_col1\" class=\"data row1 col1\" >Reykjavik, Keflavik International Airport</td>\n",
       "      <td id=\"T_2bfcd_row1_col2\" class=\"data row1 col2\" >928449.975037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_2bfcd_row2_col0\" class=\"data row2 col0\" >HEL</td>\n",
       "      <td id=\"T_2bfcd_row2_col1\" class=\"data row2 col1\" >Helsinki Ventaa</td>\n",
       "      <td id=\"T_2bfcd_row2_col2\" class=\"data row2 col2\" >581588.490562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_2bfcd_row3_col0\" class=\"data row3 col0\" >PEK</td>\n",
       "      <td id=\"T_2bfcd_row3_col1\" class=\"data row3 col1\" >Beijing Capital International Airport</td>\n",
       "      <td id=\"T_2bfcd_row3_col2\" class=\"data row3 col2\" >532020.425300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_2bfcd_row4_col0\" class=\"data row4 col0\" >DEL</td>\n",
       "      <td id=\"T_2bfcd_row4_col1\" class=\"data row4 col1\" >Indira Gandhi International Airport</td>\n",
       "      <td id=\"T_2bfcd_row4_col2\" class=\"data row4 col2\" >472979.963291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_2bfcd_row5_col0\" class=\"data row5 col0\" >IST</td>\n",
       "      <td id=\"T_2bfcd_row5_col1\" class=\"data row5 col1\" >Istanbul International Airport</td>\n",
       "      <td id=\"T_2bfcd_row5_col2\" class=\"data row5 col2\" >457882.076744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_2bfcd_row6_col0\" class=\"data row6 col0\" >PKC</td>\n",
       "      <td id=\"T_2bfcd_row6_col1\" class=\"data row6 col1\" >Yelizovo Airport</td>\n",
       "      <td id=\"T_2bfcd_row6_col2\" class=\"data row6 col2\" >408571.027619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_2bfcd_row7_col0\" class=\"data row7 col0\" >MSP</td>\n",
       "      <td id=\"T_2bfcd_row7_col1\" class=\"data row7 col1\" >Minneapolis-St.Paul International Airport</td>\n",
       "      <td id=\"T_2bfcd_row7_col2\" class=\"data row7 col2\" >396433.049206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_2bfcd_row8_col0\" class=\"data row8 col0\" >LAX</td>\n",
       "      <td id=\"T_2bfcd_row8_col1\" class=\"data row8 col1\" >Los Angeles International Airport</td>\n",
       "      <td id=\"T_2bfcd_row8_col2\" class=\"data row8 col2\" >393310.114286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_2bfcd_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_2bfcd_row9_col0\" class=\"data row9 col0\" >DEN</td>\n",
       "      <td id=\"T_2bfcd_row9_col1\" class=\"data row9 col1\" >Denver International Airport</td>\n",
       "      <td id=\"T_2bfcd_row9_col2\" class=\"data row9 col2\" >374339.835975</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x11f3b24a0>"
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     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centrality[code, score] <~ BetweennessCentrality(@route[a, b])\n",
    "?[code, desc, score] := centrality[code, score], @airport{code, desc}\n",
    "\n",
    ":limit 10;\n",
    ":order -score"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02ef7f3e-50c5-41bd-8879-17127a0369cc",
   "metadata": {},
   "source": [
    "These are the airports that, if disconnected from the network, cause the most disruption."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27763722-f643-42cb-af4e-1f56277e194b",
   "metadata": {},
   "source": [
    "That's it for the tutorial. Continue with the [Manual](https://cozodb.github.io/current/manual/index.html) if you want more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f2c6f0c-e6a4-4eeb-b33b-288bdfc8863d",
   "metadata": {},
   "outputs": [],
   "source": []
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