Query Analysis -- 2hop_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from PW_explorer.load_worlds import load_worlds\n",
    "from PW_explorer.run_clingo import run_clingo\n",
    "from PW_explorer.visualize import PWEVisualization\n",
    "from PW_explorer.helper import pw_slicer, rel_slicer, rel_name_remapper\n",
    "from PW_explorer.export import PWEExport\n",
    "from PWE_NB_Extension.helper import ASPRules\n",
    "import pandas as pd\n",
    "import os\n",
    "from misc import *\n",
    "from DLV_Input_Parser.dlv_rules_parser import parse_dlv_rules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "from nxpd import draw\n",
    "import nxpd\n",
    "from nxpd import nxpdParams\n",
    "nxpdParams['show'] = 'ipynb'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "IPython.CodeCell.options_default.highlight_modes['prolog'] = {'reg':[/^%%(clingo|dlv)/]};"
      ]
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "%load_ext PWE_NB_Extension"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def save_query_figs(query_analysis, folder='2hop_2_all_patterns_new'):\n",
    "    fnames = {}\n",
    "    os.makedirs(folder, exist_ok=True)\n",
    "    for pw_id in range(1, len(query_analysis['pw_objs'])+1):\n",
    "        pw_rel_dfs, pw_objs = pw_slicer(query_analysis['pw_rel_dfs'], query_analysis['pw_objs'], [pw_id])\n",
    "        pw_obj = pw_objs[0]\n",
    "\n",
    "        node_fig_g = get_pattern_graph3(pw_rel_dfs, pw_obj, silent=True, \n",
    "                                        q_head='none', \n",
    "                                        chain_eq_node_labels=False)\n",
    "        q_str = print_rewritten_query_string(pw_rel_dfs, html=False, display_q=False, include_ineqls=False)\n",
    "        q_str = q_str.replace('thop', 'q')\n",
    "        node_fig_g.graph['label'] = q_str\n",
    "        node_fig_g.graph['labelloc'] = 't' # options 't', 'b'\n",
    "        fname = '{}.{}'.format('{}/pw_{}'.format(folder, pw_id), 'png')\n",
    "        fname_gv = '{}.{}'.format('{}/pw_{}'.format(folder, pw_id), 'gv')\n",
    "        draw(node_fig_g, filename=fname, show=False)\n",
    "        draw(node_fig_g, filename=fname_gv, show=False)\n",
    "        fnames[pw_id] = fname\n",
    "    return fnames"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Supplementary ASP Encodings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo --donot-display_input --donot-run -lci query_analysis_suppl\n",
    "\n",
    "% schema ruleOccTrue(ATOM, OCC)\n",
    "ruleOccTrue(R, OC) :- ruleOcc(R, OC).\n",
    "% schema ruleHTrue(HEAD)\n",
    "ruleHTrue(H)  :- ruleH(H).\n",
    "% schema newVar(VAR, DOMAIN)\n",
    "newVar(VAR, TYPE) :- var(VAR, TYPE), not eqOrd(_,VAR,TYPE).\n",
    "% schema eqOrdMinimal(VAR1, VAR2, DOMAIN)\n",
    "eqOrdMinimal(A,B,TYPE) :- eqOrd(A,B,TYPE), newVar(A,TYPE).\n",
    "% schema neqOrd(VAR1, VAR2, DOMAIN)\n",
    "neqOrd(A,B,TYPE) :- newVar(A,TYPE), newVar(B,TYPE), A<B.\n",
    "\n",
    "% New inferred edges\n",
    "% schema e(NODE1, NODE2)\n",
    "e(V1,V2) :- newArc(V1, 1, e, OCC), newArc(V2, 2, e, OCC).\n",
    "% schema e(OCC, NODE1, NODE2)\n",
    "e(OCC,V1,V2) :- newArc(V1, 1, e, OCC), newArc(V2, 2, e, OCC).\n",
    "    \n",
    "%graphviz graph graph_type=directed rankdir=LR\n",
    "%graphviz edge newArc(HEAD, _, TAIL) label=$2\n",
    "%graphviz node ruleOccTrue(N) color=green\n",
    "\n",
    "#show ruleOccTrue/2.\n",
    "#show ruleHTrue/1.\n",
    "#show var/2.\n",
    "#show newVar/2.\n",
    "#show ruleOcc/2.\n",
    "#show ruleH/1.\n",
    "#show eqOrd/3.\n",
    "#show neqOrd/3.\n",
    "#show eqOrdMinimal/3.\n",
    "#show arc/4.\n",
    "#show newArc/4.\n",
    "#show hArc/3.\n",
    "#show newHArc/3.\n",
    "#show e/2.\n",
    "#show e/3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Query Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Say we want to statically analyze the 2hop/2 query:\n",
    "\n",
    "__thop(X,Y) :- e(X,Z), e(Z,Y).__\n",
    "\n",
    "To do this, we first encode the query as a incidence graph as shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "query_str = \"thop(X,Y) :- e(X,Z), e(Z,Y).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_query_incidence_graph_encoding(asp_rule):\n",
    "    listener = parse_dlv_rules(asp_rule, print_parse_tree=False)\n",
    "    \n",
    "    schema_defs = [\n",
    "        '% schema var(VAR, DOMAIN).',\n",
    "        '% schema ruleOcc(ATOM, OCC).',\n",
    "        '% schema ruleH(HEAD).',\n",
    "        '% schema arc(VAR, POS, ATOM, OCC).',\n",
    "        '% schema hArc(VAR, POS, HEAD).',\n",
    "    ]\n",
    "    rule_vars = set([])\n",
    "    rule_occ_nodes = []\n",
    "    rule_inc_edges = []\n",
    "    rule_head_nodes = []\n",
    "    head_inc_edges = []\n",
    "    \n",
    "    \n",
    "    assert len(listener.rules) == 1\n",
    "    \n",
    "    for rule in listener.rules:\n",
    "        head_atoms, tail_atoms = rule[0], rule[1]\n",
    "        \n",
    "        for i, ruleOcc in enumerate(tail_atoms):\n",
    "            rule_vars.update(set(ruleOcc.vars))\n",
    "            rule_occ_nodes.append(f'ruleOcc({ruleOcc.rel_name}, {i+1}).')\n",
    "            for j, ruleOcc_v in enumerate(ruleOcc.vars):\n",
    "                rule_inc_edges.append(f'arc(\"{ruleOcc_v}\", {j+1}, {ruleOcc.rel_name}, {i+1}).')\n",
    "\n",
    "        for i, ruleH in enumerate(head_atoms):\n",
    "            rule_vars.update(set(ruleH.vars))\n",
    "            rule_head_nodes.append(f'ruleH({ruleH.rel_name}).')\n",
    "            for j, ruleH_v in enumerate(ruleH.vars):\n",
    "                head_inc_edges.append(f'hArc(\"{ruleH_v}\", {j+1}, {ruleH.rel_name}).')\n",
    "    \n",
    "    var_nodes = [f'var(\"{v}\", node).' for v in rule_vars]\n",
    "    \n",
    "    return schema_defs + var_nodes + rule_occ_nodes + rule_inc_edges + rule_head_nodes + head_inc_edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
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       "<div class=\"highlight\"><pre><span></span><span class=\"lineno\"> 1 </span><span class=\"c1\">% schema var(VAR, DOMAIN).</span>\n",
       "<span class=\"lineno\"> 2 </span><span class=\"c1\">% schema ruleOcc(ATOM, OCC).</span>\n",
       "<span class=\"lineno\"> 3 </span><span class=\"c1\">% schema ruleH(HEAD).</span>\n",
       "<span class=\"lineno\"> 4 </span><span class=\"c1\">% schema arc(VAR, POS, ATOM, OCC).</span>\n",
       "<span class=\"lineno\"> 5 </span><span class=\"c1\">% schema hArc(VAR, POS, HEAD).</span>\n",
       "<span class=\"lineno\"> 6 </span><span class=\"nf\">var</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span> <span class=\"s s-Atom\">node</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 7 </span><span class=\"nf\">var</span><span class=\"p\">(</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">,</span> <span class=\"s s-Atom\">node</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 8 </span><span class=\"nf\">var</span><span class=\"p\">(</span><span class=\"s2\">&quot;Z&quot;</span><span class=\"p\">,</span> <span class=\"s s-Atom\">node</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 9 </span><span class=\"nf\">ruleOcc</span><span class=\"p\">(</span><span class=\"s s-Atom\">e</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">10 </span><span class=\"nf\">ruleOcc</span><span class=\"p\">(</span><span class=\"s s-Atom\">e</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">11 </span><span class=\"nf\">arc</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"s s-Atom\">e</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">12 </span><span class=\"nf\">arc</span><span class=\"p\">(</span><span class=\"s2\">&quot;Z&quot;</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"s s-Atom\">e</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">13 </span><span class=\"nf\">arc</span><span class=\"p\">(</span><span class=\"s2\">&quot;Z&quot;</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"s s-Atom\">e</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">14 </span><span class=\"nf\">arc</span><span class=\"p\">(</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"s s-Atom\">e</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">15 </span><span class=\"nf\">ruleH</span><span class=\"p\">(</span><span class=\"s s-Atom\">thop</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">16 </span><span class=\"nf\">hArc</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"s s-Atom\">thop</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">17 </span><span class=\"nf\">hArc</span><span class=\"p\">(</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"s s-Atom\">thop</span><span class=\"p\">).</span>\n",
       "</pre></div>\n"
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      "text/plain": [
       "'% schema var(VAR, DOMAIN).\\n% schema ruleOcc(ATOM, OCC).\\n% schema ruleH(HEAD).\\n% schema arc(VAR, POS, ATOM, OCC).\\n% schema hArc(VAR, POS, HEAD).\\nvar(\"X\", node).\\nvar(\"Y\", node).\\nvar(\"Z\", node).\\nruleOcc(e, 1).\\nruleOcc(e, 2).\\narc(\"X\", 1, e, 1).\\narc(\"Z\", 2, e, 1).\\narc(\"Z\", 1, e, 2).\\narc(\"Y\", 2, e, 2).\\nruleH(thop).\\nhArc(\"X\", 1, thop).\\nhArc(\"Y\", 2, thop).'"
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     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "thop_query_desc = get_query_incidence_graph_encoding(query_str)\n",
    "ASPRules(thop_query_desc)"
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   "cell_type": "markdown",
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   "source": [
    "Next we encode the query analysis code that uses a query description such as the one above.\n",
    "\n",
    "Within this analysis, we create Bell-Number(n) (i.e. B<sub>n</sub>) many partitions where n is the number of distinct variable in the query.\n",
    "\n",
    "Then we recreate a new incidence graph where the we substitute each disjoint group in the partition with a representative variable (for simplicity, we use the lexicographically smallest variable)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo --donot-display_input -lci query_analysis_enc --donot-run\n",
    "\n",
    "% Create variable partitions\n",
    "% schema eq(VAR1, VAR2, DOMAIN)\n",
    "eq(A,B,TYPE) ; not eq(A,B,TYPE) :- var(A, TYPE), var(B, TYPE), A!=B.\n",
    "eq(A,B,TYPE) :- eq(B,A,TYPE).\n",
    "eq(A,B,TYPE) :- eq(A,C,TYPE), eq(C,B,TYPE), A!=B, B!=C, A!=C.\n",
    "\n",
    "% Order the individual partitions\n",
    "% schema eqOrd(VAR1, VAR2, DOMAIN)\n",
    "eqOrd(A,B,TYPE) :- eq(A,B,TYPE), A<B.\n",
    "\n",
    "% Find the new arcs, getting rid of the redundant variables as per the orderings\n",
    "% schema newArc(VAR, POS, ATOM, OCC)\n",
    "newArc(VAR, POS, ATOM, OCC) :- arc(VAR_ORIG, POS, ATOM, OCC), eqOrd(VAR,VAR_ORIG,TYPE), not eqOrd(_,VAR,TYPE).\n",
    "newArc(VAR, POS, ATOM, OCC) :- arc(VAR, POS, ATOM, OCC), not eqOrd(_,VAR,_).\n",
    "\n",
    "% schema newHArc(VAR, POS, HEAD)\n",
    "newHArc(VAR, POS, H) :- hArc(VAR_ORIG,POS,H), eqOrd(VAR,VAR_ORIG,TYPE), not eqOrd(_,VAR,TYPE).\n",
    "newHArc(VAR, POS, H) :- hArc(VAR, POS, H), not eqOrd(_,VAR,_)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these two encodings, we can create the specialized queries that make up the original query.\n",
    "\n",
    "For clarity, let's project out the resultant e/2 and thop/2 relation that make up the query:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output:\n"
     ]
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       "<div class=\"highlight\"><pre><span></span><span class=\"lineno\"> 1 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\"> 2 </span><span class=\"nf\">thop</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">)</span> <span class=\"nf\">e</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;Z&quot;</span><span class=\"p\">)</span> <span class=\"nf\">e</span><span class=\"p\">(</span><span class=\"s2\">&quot;Z&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 3 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">2</span>\n",
       "<span class=\"lineno\"> 4 </span><span class=\"nf\">thop</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">)</span> <span class=\"nf\">e</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">)</span> <span class=\"nf\">e</span><span class=\"p\">(</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 5 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">3</span>\n",
       "<span class=\"lineno\"> 6 </span><span class=\"nf\">thop</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">)</span> <span class=\"nf\">e</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">)</span> <span class=\"nf\">e</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;Y&quot;</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 7 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">4</span>\n",
       "<span class=\"lineno\"> 8 </span><span class=\"nf\">thop</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">)</span> <span class=\"nf\">e</span><span class=\"p\">(</span><span class=\"s2\">&quot;Z&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">)</span> <span class=\"nf\">e</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;Z&quot;</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\"> 9 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">5</span>\n",
       "<span class=\"lineno\">10 </span><span class=\"nf\">thop</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">)</span> <span class=\"nf\">e</span><span class=\"p\">(</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">,</span><span class=\"s2\">&quot;X&quot;</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">11 </span><span class=\"nv\">SATISFIABLE</span>\n",
       "<span class=\"lineno\">12 </span>\n",
       "<span class=\"lineno\">13 </span><span class=\"nv\">Models</span>       <span class=\"s s-Atom\">:</span> <span class=\"mi\">5</span>\n",
       "<span class=\"lineno\">14 </span><span class=\"nv\">Calls</span>        <span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\">15 </span><span class=\"nv\">Time</span>         <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.002</span><span class=\"nf\">s</span> <span class=\"p\">(</span><span class=\"nv\">Solving</span><span class=\"s s-Atom\">:</span> <span class=\"mf\">0.00</span><span class=\"s s-Atom\">s</span> <span class=\"mi\">1</span><span class=\"s s-Atom\">st</span> <span class=\"nv\">Model</span><span class=\"s s-Atom\">:</span> <span class=\"mf\">0.00</span><span class=\"s s-Atom\">s</span> <span class=\"nv\">Unsat</span><span class=\"s s-Atom\">:</span> <span class=\"mf\">0.00</span><span class=\"s s-Atom\">s</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">16 </span><span class=\"nv\">CPU</span> <span class=\"nv\">Time</span>     <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.002</span><span class=\"s s-Atom\">s</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'Answer: 1\\nthop(\"X\",\"Y\") e(\"X\",\"Z\") e(\"Z\",\"Y\")\\nAnswer: 2\\nthop(\"X\",\"Y\") e(\"X\",\"Y\") e(\"Y\",\"Y\")\\nAnswer: 3\\nthop(\"X\",\"Y\") e(\"X\",\"X\") e(\"X\",\"Y\")\\nAnswer: 4\\nthop(\"X\",\"X\") e(\"Z\",\"X\") e(\"X\",\"Z\")\\nAnswer: 5\\nthop(\"X\",\"X\") e(\"X\",\"X\")\\nSATISFIABLE\\n\\nModels       : 5\\nCalls        : 1\\nTime         : 0.002s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)\\nCPU Time     : 0.002s'"
      ]
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   ],
   "source": [
    "%%clingo --donot-display_input -l query_analysis_enc thop_query_desc\n",
    "\n",
    "e(V1,V2) :- newArc(V1, 1, e, OCC), newArc(V2, 2, e, OCC).\n",
    "thop(V1,V2) :- newHArc(V1,1,thop), newHArc(V2,2,thop).\n",
    "#show e/2.\n",
    "#show thop/2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, we get B<sub>4</sub> (= 15) PWs. The outputs above showcase a canonical database that would satisfy the specialized query that these PWs represent.\n",
    "\n",
    "First we load these PWs in using the PWE Tool."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "%clingo --donot-display_input --donot-display_output -l query_analysis_enc thop_query_desc query_analysis_suppl -exp query_analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Models: 5\n"
     ]
    }
   ],
   "source": [
    "query_analysis['pw_rel_dfs'], query_analysis['rel_schema'], query_analysis['pw_objs'] =load_worlds(query_analysis['asp_soln'],\n",
    "                                                                                                   query_analysis['meta_data'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "if 'hArc_3' not in query_analysis['pw_rel_dfs']:\n",
    "    query_analysis['pw_rel_dfs']['hArc_3'] = pd.DataFrame(columns=['pw', 'VAR', 'POS', 'HEAD'])\n",
    "if 'newHArc_3' not in query_analysis['pw_rel_dfs']:\n",
    "    query_analysis['pw_rel_dfs']['newHArc_3'] = pd.DataFrame(columns=['pw', 'VAR', 'POS', 'HEAD'])\n",
    "for i in range(len(query_analysis['pw_objs'])):\n",
    "    if 'hArc_3' not in query_analysis['pw_objs'][i].rls:\n",
    "        query_analysis['pw_objs'][i].rls['hArc_3'] = []\n",
    "    if 'newHArc_3' not in query_analysis['pw_objs'][i].rls:\n",
    "        query_analysis['pw_objs'][i].rls['newHArc_3'] = []\n",
    "    if 'ruleHTrue_1' not in query_analysis['pw_objs'][i].rls:\n",
    "        query_analysis['pw_objs'][i].rls['ruleHTrue_1'] = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With some simple python and ASP magic, we can create these specialized queries, their canonical databases and visualize the graph patterns these canonical databases represent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "\n",
      "PW: 1\n",
      "\n",
      "Partitioning Description:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>. % <text style=color:blue>[Z][X][Y]</text></text>"
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     "text": [
      "Specialized Query:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>, X != Y, X != Z, Y != Z.</text>"
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     "text": [
      "Canonical DB:\n",
      "e(\"X\",\"Z\"). e(\"Z\",\"Y\"). thop(\"X\",\"Y\").\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "------------------------------------------------------------\n",
      "\n",
      "PW: 2\n",
      "\n",
      "Partitioning Description:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>. % <text style=color:blue>[Y=Z][X]</text></text>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Specialized Query:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>, Y=Z, X != Y.</text>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Canonical DB:\n",
      "e(\"X\",\"Y\"). e(\"Y\",\"Y\"). thop(\"X\",\"Y\").\n"
     ]
    },
    {
     "data": {
      "image/png": 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ffZcA0IoVK3irj0g3fhkAdezYkffvWnWfj1knJBHR1KlTCQAtWrSIVCoVdevWjTiOo5MnTwoal5CfT2FhIZ0+fZqOHDlCDx8+NGpdMTdjyHaOLU36ehIdvH6QylV1e5Of74QkIoqPjyepVEohISGkVquJiCgxMZGkUikFBgbqNeUb48KFCySTycjJyckoY5ctNiHz8vLI29ubRCIRTZ48mQDQwoULBY2JyHw+H2OLuRlDmAGSvCEhbgZHDnMd6H++/R86eetkjW/UGyMhiYg++OADAkDr168nIqIhQ4YYvGo2xuPHj8nLy4tEIhEdPnyYt3KfVt3nY/YrKDs7O2Pbtm0YNmwYdu3ahc6dO+Of//yn0GFZnYp5SovKivD9he+xJXYL3Jq5YUrPKZjQfQL6+PUxSX/DsmXLsHv3bnz44YcQiUQ4fvw4oqKi8Pzzz1cek52djQ0bNtRa1vjx4/UeFalUKkyYMAGPHj3Cp59+ihdfNP4SdE8z+4QEAD8/P9ja2qKkpAQBAQEGH4MwpqNU66ZnzFZkY+OpjVj32zp4OXvhtV6v4fU+r6OjR0ej1W1jY4Ovv/4agwcPxpw5c+Dl5YVVq1ZVOSYrKwvLly+vtaz27dvrJeSCBQsQGxuLV155BR988AGvsdeF2SekVqtFZGQkSkpK0LlzZxw4cADff/+9eQzJsgd+TvwZLXNbCh2J0SRnJde4v2L5tkf5j7AmZg1WH12NIK8glDmVwYv4XcOxwqBBgzB+/Hj8+OOPWLlyJRwdHavs79ixI0pKSmotRyarOgHy1q1bsWHDBgQHB+Pbb7/lM+Q6M/uEXL16NWJjYzFz5kwsW7YMgYGBmDdvHsLDwwUZtFBFS2De/nnCxmBkXs51Tyq1RtesTXiUALgCxdpiXH14Fc/5PMd7XD4+umXjDH0HOI6DrW391o+Mi4vDnDlz4OLigv3798Pe3p6XOOvLrBPy2rVrWL58Odq0aYM1a9bAwcEBn332GWbPno3p06fj119/Few5KQDgLpASk1I5iqYpOp54HEPXDq31OJlEBqVaCf+W/ojoEYFfN/yKru26GiUZa5ORkYEVK1bUetz06dPRrVs3ZGZm4uWXX4ZarUZ0dLSg/59mm5BlZWWIiIiAWq3G1q1b4eDgAAB44403EB0djePHj+Orr77C3LlzBY7UelUkoYejByaGTcQ/nv9HZQKe/X9nBYsrPz8fmzdvrvW4AQMGoGvXrpgwYQLS0tKwZs0avcHepma2CblkyRIkJibizTffxKBBgyq3cxyHzZs3Izg4GEuWLMGwYcPQvn17ASO1LhKxBGqtGk42TpgUNgmv9X7NZD2sddWxY0eUl5fX6diVK1fizJkzaNasGW7fvo3Zs2cbPE4ikWD9+vV8hmm4HqPX0AAxMTH48ssv4efnh9WrV+vt9/X1xaeffoqFCxciMjISv//+O3urwNg4wF5mjwndJmBKzykY1HEQxCLL/8wrBngrFIoah93JZDLrTcihQ4dCq9XWeMyCBQuwYMECE0VkvWykNnil2yuY0nMKRgaNNMpS4g2xdu1arF27ttHlrFu3DuvWreMhIn6YZUIy5qOvf1/09e8rdBhWgy3YyjBmpNqElEh0F09TvRFvaSo+l4rPialKLBZDrVYLHYbZUqvVBvs9qk3IihVhLWEVZCHk5+cD0I21ZfQ5OTlVzvXD6CsoKDD43ak2Ib29vSGTyXD79m2jBmapkpKS4Orqqjdsi9Hx9fVFUlKS0GGYJa1Wizt37hgcgFBtQkqlUgQFBem9rc/oXLx4kU0AVoPnnnsON2/eZFdJA27cuIHi4mKD358aO3VGjBiBw4cPm2yaCkuhVCpx9OhR3qd1aEqGDBkCrVaLo0ePCh2K2Tl48CA8PDwQEhKit6/GhHz11Vdx//59HD9+3GjBWaJ9+/ahsLBQb35U5m+urq4YPnx4nYawWROtVoutW7fi1VdfNTy6qbY3mwcPHky9e/e2+pWvKqhUKurcuTNNmDBB6FDM3tGjR4njODp9+rTQoZiNTZs2kVQqpdu3bxvcX2tCJiQkkEQioe+++4734CzRF198QXK5vNoPlKnqhRdeoKCgIFKpVEKHIriCggLy8PCgBQsWVHtMnRZsjYqKIi8vrzotydyUpaamkrOzMy1dulToUCzGrVu3SCaTVbs6lzWJiooid3d3ysvLq/aYOiVkTk4OtWvXjvr161frksxNVVFREYWEhFBQUBApFPWfFtGaffLJJySVSikmJkboUATzzTffEMdxFB0dXeNxdUpIIl3T1cnJiSIjI63uflKtVtOYMWOoRYsWdO/ePaHDsTharZamTJlCzs7OdPPmTaHDMbmYmBiSSqW0fPnyWo+tc0IS6W7SpVIpTZo0iUpKShoan0UpLCykkSNHkq2tLZ07d07ocCxWaWkp9enTh9zc3AwuedBURUdHk62tLU2ZMqVOF7J6JSQR0YkTJ8jFxYV69uzZ5FfGvXv3LgUHB5OnpyddvHhR6HAsnkKhoHHjxpFcLqdvv/1W6HCMSqPR0Mcff0wcx9Fbb71VObFzbeqdkERESUlJ1L59e3JycqI1a9bwOmO0OSgpKaGPP/6Y7OzsKCQkxOizg1sTjUZDS5YsIY7jaMSIEUaZFVxo586do+7du5NUKqWNGzfW69wGJSQRUXFxMX300Udka2tLHTt2pE2bNlFRUVFDi6sTTfUTZfMiPz+f1q9fT23btiUHBwdatWoVlZfXbep8pn7OnDlDISEhJJVKKSoqiuLj44UOqVG0Wi3FxsbSxIkTieM4GjJkCCUkJNS7HI6ocePi7t+/j+XLlyM6Ohocx6F///7o3r072rZty/ubEIcPt8eoUfwNdici5OXl4d69e4iLi0NsbCykUikiIiLwv//7v/D09OStLmui0QBXrwInTgDPPQcMrWbSOo1Ggy1btuDzzz9HcnIyAgICEB4ejsDAQLi6ukIul5s28HoqKSlBVlYW4uPjceLECaSnp6Nbt25YunQpxo0b16AyG52QFXJycnDo0CHExMQgPj4eaWlpla8o8aM1gCQAXgD4K7d58+Zo3bo1QkJCMHz4cLz44ouVr54xdUME/PmnLgF//RU4fRpQKIDwcOD4caC26Y6ICLGxsThy5AguXbqEmzdvIj8/v84TVQnF1tYWLi4uCAwMRN++fTFmzBh07dq1UWXylpDG9tlnwLvvAlu2ANOnCx2NeSkqKsKOHTtw7949+Pv7Y8qUKUZfTfnOHeDkSeC334CYGCA3F5BKAa1Wd4V0cQESEgDWyKgfi0nI4GDdf3B4uO6LwOgkJSUhPDwcDg4OePDgAZRKJfz8/BAbGwsPDw/e6nnyBDhzRnfF++UXIDVVd+XjOODZiQE4Djh6FBg2jLfqrQdvd7VGlJhIpGsYEXEcUXq60BGZj5EjR9Iff/xBRESZmZk0Y8YMAkDTp0/npfxdu4j8/HSfvUhEJJX+/X9h6EcsJvroI16qtkoWMcnVjh265hCg+6u8Z4+w8ZiLK1euICIiAl26dAEAuLu74+OPP4ZIJMK5c+d4qWPgQCAnR3fV02oBlar6Y6VSoHdv4KOPeKnaKllEk7VdO+D+fd2/OQ4IDQWuXBE0JLOQk5MDFxcXvffqevToAYlEwltS7t4N1Pbqp0gEODnpbiu8jLPolVUw+yvkpUt/JyOgaxhdvQok17xKmlVwdXU1+JJramoqRo4cyVs9EycC48f/3UoxhAiIjmbJ2Fhmn5A7d+p/EaRS3X8+o+/MmTOQSCRYuHAhr+X+5z+Ag4PuSvgssVjXTK3ueSNTd2bdZNVqAQ8PICtLf5+vL5CSYvqYzJlGo8HgwYPxxRdfGGUCrgMHgJdeqrpNKgV69gROnar9eSNTO7O+Qp46ZTgZAeDuXeCPP0wajtlbvHgx3n77baPNhjd2LDBhwt8tFpFId9WMjmbJyBezTsine1efJZXqmrOMzjfffIPQ0FCMGTPGqPVs2KBLwopb1z172H0jn8w2IZVKXe9edd3sKhXw3Xe6zgRrt2/fPhARIiMjq2w/ffp0vctKSwNmzgSKiw3vd3MDNm3Sfe4ffQQ8tXQnwwOzvYc8cAAYN672hIuNBfr0MU1M5uj48eP48MMPMXXq1MptGo0GN2/eRFBQEObNm1fnsk6f1jVLW7YEDh8GAgKqP3b9emDOHMOdPEwjCDgooUYTJ+pGhtQ0KoTjiN58U+hIhXPlyhWyt7cnAHo/NjY2lJOTU6/ycnOJli0jspLJIMySWV4hlUqgWzcgL+/vbWq1bgCzq2vVDgRvb+D8+b/vaRjGkpllQhpy+TIQFqZ71GFgjRKGaRJMfgeQkZGBU6dO1fu84GBdMrZuzX9MDGMuTJaQWVlZWLx4MXx9fbFv3756ny+X666MNQ3fYmr2+DEweTJw757QkTDVMVlC3r9/H5GRkSgtLTVVlcxT/vwTCAoC4uJ09+KMeTLZetxhYWFQKpWmqo55RseOwPvvA1FRgL290NEw1TFZQjLCEouBxYuFjoKpDXusyzBmhCUkw5gRlpBNRGam7k2MY8eEjoRpDItJyBs3AD8/3WxnTFXZ2X/3oNrYCB0N0xgW06lTXq57B7KmSZaslZsbsGaNbmC4o6PQ0TCNYTEJaW+vG99q5rPLC+a114SOgOGDSRMy76/R4mVlZfU+t1Mn3XhWhmnKTHYP+csvv+Ctt94CAOzfvx+bN29GRkaGqapnGItgMW97WLP8fGDJEt1oG54nk2PMjMXcQ1orlQro3h0oK9PNoMA0bewKaQGOH9clJc/LbTJmiCUkw5gRixkYwDDWwGISsqREt8COmS+q22AajdARMObAYhLy5k3dfVR6utCR8KugAJg1SzcXKsOwXlaBjRqlWx7866+FjoQxBxaTkN7ewKpVurXrm5KvvtL9bk3t92IahvWyMowZsZh7SIaxBiwhTaABY+kZK8US0ogKC4E33gAGDNAtPsswtbGYTh1LNG8e8Msvuo4btkoUUxesU8eIHj0CJBKgRQuhI2EsBUtIhjEjFtOQSksD3nuPTYPPNG0Wk5AZGcDq1bqXdc2JucXDWDaz7NTREKFYRShRa1GuIRCAhwoAkOJ+kQqiIt0CrXIRB3upCPYSEUQmXrBVodC9xb9vH5CYCDg5mbZ+pmkS9B4yt1yDzBI1sss0yCrXILtUDYVKl4TPUis5FGaJ4NRSA7GBPyNysQgOUg4tbCVwsxHD1UYMDzsJnGRi/YN58PHHwLp1up8pU4xSBWOFTJqQOWUapBQqkapQIVWhRplGCw6AiOOgBYGPSDhOV56GCCDAViKCj4MUPvYS+DnK4CznJ0FLS3Vvanh48FIcwwAwQUKmF6uRmFeOpAIlipQaiDgORLpmqKlUNGe1BDSXi9HBWYbOzeVoYWuWLXbGihklIUvUWtzILcf17DLklWsg4nTJYC5EHActEVrYShDiaoNAFznkYhPfhDKMAbwmZIFSi7jMUlzPLoMWZFZJaBAHiEiXoCFuNujZ0hYO0r87ntPTgVatBIyPsTq8JGSxWovTj0pwI7cMIgAG+mTMnq5Zy6Gbuw1CHe2w4iMOGzcCCQmAv7/Q0THWolE3UVoCLmWW4veMEmhJ1yljqVPD6K7mhCtZZfjvD4T92+yx8T8cS0bGpBp8hcwu0+Dg/SJkl6nNv2naACV5IgR4izG6bTM4G+nRCcM8q0EJeTmrFCfTS0CWcJ/YCCKOgwjASJ9mCHRhy24xxlevhNQScCxVgT9yrO+N214tbTHAyx6sL5YxpjonpEpL2JNSiDSFCtb4ri0HDu2dZBjbzsHkw/QY61GnweVqLWFvSiHSitVWmYwAQCAkF5TjwL0iXkYUMYwhtSYkAfjpXhFSFSporfybqAWQXFiOn1MVQofCNFG1JuS5jBLcK7TOZqohWgJu5JThWrb13UczxldjQj5QqBD7WNebylQVk1aMJ6VqocNgmphqE1JLwNGHxm2a/XFsH64d2W3UOozJ2J8PY32qTcjLWaXIV799L5IAAAcuSURBVGp5uzY++CMOJzavhSInq3Jb7PcbcHLLv3mqwbS0RHhcqsafuU10OS5GEAYTUkvA+Sel4PNFkPvXziNmw0oUZT/hrUxzcDajROgQmCbEYELezi9HqcZ8u3HIXGYdJiC/XIOHCpXQkTBNhMHB5Tdyy8EBvDVXf/rkbdy5cAoAsPf/5qNtSE+Mfndl5f4nKbdwets6pMSdhVgmg19YP4xZsgpSuU3lMZn3buPntR8h7c9rKC8phod/JwyY9haCBo+qUtfOJTPg0T4Ivt374NyOr5ESdxb2Lu54btRE9I+cC47nGYtFHJCQWw6fZlJey2Wsk963kwhIVah4ffjt7uMHBzfdXBduPn5wbe1bua84Lweb3ngJqQlXEPLCK3Br7YvL+3/A3uXzKo+5f/0ivpo6FJn3bqPH+H9g0MxF4ERi/PDONJzYtKZKXXcuncWVAz/g23mToVar0GN8JGQ2tji6bgV++uRt/n6pv2gJuFek5L1cxjrpXSEzy9RQ8jxivF/km9BqNXgYH4fwaW/Bs0NQ5b6SglwMmfUuBs96p3LbhsjhSP7rikpEOPSvDyCRyTF7289wdNcldv9/zMW2NyfhxOa16DLsJbi18as8PyftPl5ctAJ9I2YDAIZGvY/NUeNx5cAO9JowDa06deX19ytSalGk0lZ5uZlhGkLvG5Rfbto3GjmRCAOmvVVlW6tOXVFamI+CJ4/w6FY8Ht2Kh29Y38pkBACxRIpuYyZDo1Ii+eKpKufbODihz5RZVeoYOH0BiAjJ508a5fcoMPHnxjRNeglZqiaTDp52dPeERCarss3GQTfJqbK0GNkP7wIAfLs9r3euV8cuAIDsBylVtrv5+ILjqv4SLf06AtBdPY2hWM0GTzCNp5eQKi2Z9BUjma1dtfuICCX5OQCA5l4+evs1Kt29m0hU9QViB7eW1dYjldno7WssjuOgasovhjImo5eQNhIRtGb01l9zrzYAgHtXL+jtexAfBwBw8W5TZXtO6j29Y/MepQIA3NryPycHEcFWYj6fGWO59BLSTsLxOiCgsbw6BkMsleHOM/eJAHD38u8QicQI6D2oyvbsBymVTd0Klw/s0JX3VIcSn+wkrEOHaTy9b5GxJg929mwNALj003dI+/Nanc9zdPdA70n/g0e3buDAynfx5E4isu7fwfH/rEbC8UMIeXEC3Hx8q5xDWg2+fzsSf548gicpt3Bi0xqc27UJXYaORdvQXrz+XoButnRXnmZEZ6ybXvY5SEVwkIlQpOR3NExArwHwCe6OC3u2IfPebcz8Zn+dzx0x70OQVoPfd3yDC3u2VW7v+crrGP3Op3rH+/XoD8cWnvjhnemVo3p8u/fB2A/+1fhfxAB3GwlkbKJlhgcGp/ComDfHGP0UhVkZkNs1g9y+Wb3PVeRm43HSDUhkcngEdIato7PeMSsGdoB3YAimrY9GaWE+0m5eh1MLT7Tw7cBH+HpEHNC7pR36eVbfOcUwdWWwfRriZmO0F3CffpZYX81c3BDQe2Cdj7d1dEZAr/AG11cXWgBdXNmMdAw/DPZEtLSVwMNOovcsj6lKxAF+DjKjLXnHWJ9quwaHtLI3q97WunJwbwl7Z1eT1KUFEO7FmqoMf2qcBnLf/SIk5yutfnIrQ0TgEOIuxzDv+t8LM0x1anx4NqyVPWzEHFjLtSoRBzjIRBjgaS90KEwTU2NC2ktFGNfOwVSxWAwROIz3dWBrSjK8q3V4SetmUgxnzbJKHAeMbtuMrb7MGEWdxnuFuNlgiDdrnoEDRrdxQAdn9piDMY56LbZzLbsMv6bppj60mn4e0l0VRRyHUW2aoVNzloyM8dR7Obp7RSr8dLcQGoJV9L6KOEAuFmGCryO87FkzlTGuBq0PmVeuwYH7Rcgs1TTppOSgu4ce3daBTc/BmESDV1DWEnDhSQli/5qXtCm9n1uxUOvAVnbo5m4rdDiMFWlwQlbIK9fgeFoxUgqV4DjzepeyvkQcBy0ROjeXI9zLHo4ydlVkTKvRCVnhfpEKZx6X4FGxqvKLbSlE4KAFoY2DDAM87di9IiMY3hKyQlqxCucySnHvryumOSemiNNNBt3BWY7eLW3Rkj1bZATGe0JWKFRqcSO3DNdzylGk1EDMARqhcpOAimmCRJzufre5XIxQNxsEushhz6bfYMyE0RLyaY9L1EguUCIpX4mcMjU46BLDKAn6VPIBgJjjoAEBpHutrIOzDP5OMjbShjFLJknIpxWptEhTqJBerMYDhQo5ZerKHloJx0GLhj3fFHO61Ugqklws4uBuI4ZPMyla2Uvh3UzCroSM2TN5Qj5LS0C+UoPsUg1yyjUoUmn+mpqfUKLWQKkFtFqCBoBGSxBzHMScLuGkIsBeIoajTIRmUhEcpCK42YjhZiOGk0zM3lJhLI7gCckwzN9YG45hzAhLSIYxIywhGcaMSADsEToIhmF0/j90yFVbm2m34QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "------------------------------------------------------------\n",
      "\n",
      "PW: 3\n",
      "\n",
      "Partitioning Description:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>. % <text style=color:blue>[X=Z][Y]</text></text>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Specialized Query:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>, X=Z, X != Y.</text>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Canonical DB:\n",
      "e(\"X\",\"X\"). e(\"X\",\"Y\"). thop(\"X\",\"Y\").\n"
     ]
    },
    {
     "data": {
      "image/png": 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iq1Dd52PVhCQimjRpEgGgefPmkVarpR49ehDHcXT48GFe6yEiOnXqFCkUCnJxceG9/6lQCUlkHOB79OhR2rt3L929e9eidSVcTSD7mfY04ZsJ9PPFn6lcW7eR/EImJBHR5cuXSS6XU2hoKOl0OiIiunbtGsnlcgoKCjK57Lc20SRkfn4++fr6kkQioZdeeokA0Ny5c3mtg4jo/v375OPjQxKJhPbs2cN7+UImpDUlXE0gTAXJ3pARN5Ujp1lO9PqG1+nw9cM1zsYgdEISEX344YcEgFauXElEREOHDjV71hRCdZ+P1VdQdnV1xfr16zF8+HD8+OOP6Nq1Kz777DOT43Jzc7Fq1apayxs3blyV5n4A0Gq1GD9+PLKysrB06VI8+yxbgq6xdAYdAEBVpsL3p77H2sS18HD0wMReEzG+53j09e8rupnhFy5ciK1bt+Ljjz+GRCLBwYMHERMTg6efflro0KolyJLm/v7+sLe3R0lJCQIDA80+BsnJycGiRYtqLatjx44mCTlnzhwkJibihRdewIcffshb3IyRRmecnjFXnYvVR1Zjxf9WwMfVB6/0fgWv9X0Nnb07CxyhkZ2dHb755hsMGTIEM2fOhI+PD5YtWyZ0WDWyekIaDAZER0ejpKQEXbt2xa5du/D999/jlVdeqXJc586dUVJSUmt5CoWiyv/XrVuHVatWISQkxKSFjXcOwL5r++D1yMuy9QjoZs7NGvdXzA6fVZCFuIQ4fL7/cwT7BKPMpQw+5GONEGs0ePBgjBs3Dv/3f/+H2NhYODuLezl7qyfk559/jsTEREybNg0LFy5EUFAQZs+ejYiIiCoPkjmOg729fb3KTkpKwsyZM+Hm5oadO3fCwcGB7/Cr8gJm75xt2ToE5uNa96TS6Y2XtclZyYA7UGwoxvm75wVfdayiY4QQHRXqy6oJeeHCBSxatAjt27dHXFwcnJyc8MUXX2DGjBmYMmUKDhw4UHkf8uDBAyxevLjWMqdMmYIePXogOzsbzz//PHQ6HbZs2VLZs8WibgFpCWnWqUsgB68dxLDlw2o9TiFTQKPTIMArAFFPReHAqgPo/kR3wZPR1lgtIcvKyhAVFQWdTod169bByckJAPDGG29gy5YtOHjwIL766ivMmjULgLEv7Zo1a2otd+DAgejevTvGjx+PzMxMxMXFWbXPZnNWkYTezt54MfxFvPr0q5UJ+Nt/fhM4OttktYRcsGABrl27hjfffBODBw+u3M5xHNasWYOQkBAsWLAAw4cPR8eOHdG5c2eUl5fXqezY2FgcO3YMjo6OuHHjBmbMmGH2OJlMhpUrV/LyfpormVQGnUEHFzsXTAifgFf6vCLKFlZbZZWETEhIwH//+1/4+/vj888/N9nv5+eHpUuXYu7cuYiOjsbx48frNUqgopOuWq2usTuUQqFgCdlQHOCgcMD4HuMxsddEDO48GFIJG8nBN6sk5LBhw6rtZ1phzpw5mDNnToPKX7FiBVasWNGg1zI1s5Pb4YUeL2Bir4kYETzCJpf1W758OZYvXy50GHUiyHNIxnb0C+iHfgH9hA6j2RBkwVaGYcyrNiFlMuPJ01oj4m1NxedS8TkxVUmlUuh0OqHDEC2dTme2naTahKxYEba6VZCbu4KCAgDGvrmMKRcXl8q5fhhThYWFZr871Sakr68vFAoFbty4YdHAbFVKSgrc3d1F3xVLKH5+fkhJSRE6DFEyGAxITU0126Gk2oSUy+UIDg7GyZMnLRqcrTp9+jSbAKwGTz75JK5evcrOkmZcuXIFxcXFZr8/NTbqREZGYs+ePVabpsJWaDQa7N+/n9cpQZqaoUOHwmAwYP/+/UKHIjo///wzvL29ERoaarKvxoR8+eWXcfv2bRw8eNBiwdmiHTt2oKioyGR+VOYxd3d3PPPMM3Xq/ticGAwGrFu3Di+//LL53k21jWweMmQI9enTp9mvfFVBq9VS165dafz48UKHInr79+8njuPo6NGjQociGvHx8SSXy+nGjRtm99eakMnJySSTycwu3tIcffnll6RUKqv9QJmq/va3v1FwcDBptVqhQxFcYWEheXt705w5c6o9pk4LtsbExJCPj0+dlmRuyjIyMsjV1ZU++ugjoUOxGdevXyeFQlG5OldzFhMTQ56enpSfn1/tMXVKyLy8PHriiSeof//+tS7J3FSpVCoKDQ2l4OBgs4ukMNVbsmQJyeVySkhIEDoUwXz77bfEcRxt2bKlxuPqlJBExktXFxcXio6Obnb3kzqdjkaPHk2tWrWi9PR0ocOxOQaDgSZOnEiurq509epVocOxuoSEBJLL5bRo0aJaj61zQhIZb9LlcjlNmDCBSkpKGhqfTSkqKqIRI0aQvb09nThxQuhwbFZpaSn17duXPDw8Kpc8aA62bNlC9vb2NHHixDqdyOqVkEREhw4dIjc3N+rVq1eTXxn31q1bFBISQq1bt6bTp08LHY7NU6vVNHbsWFIqlbRhwwahw7EovV5Pn376KXEcR2+//XblZM21qXdCEhGlpKRQx44dycXFheLi4gSfBZpvJSUl9Omnn1KLFi0oNDTU4rODNyd6vZ4WLFhAHMdRZGQk7zPKi8GJEyeoZ8+eJJfLafXq1fV6bYMSkoiouLiYPvnkE7K3t6fOnTtTfHw8qVSqhhZXJ/rqJ8rmRUFBAa1cuZI6dOhATk5OtGzZMiovr9vU+Uz9HDt2jEJDQ0kul1NMTIzVllm3FIPBQImJifTiiy8Sx3E0dOhQSk5Ornc5HFHj+sXdvn0bixYtwpYtW8BxHAYMGICePXuiQ4cOvI+E2LOnI0aO5K+zOxEhPz8f6enpSEpKQmJiIuRyOaKiovD3v/8drVu35q2u5kSvB86fBw4dAp58EhhWzaR1er0ea9euxb/+9S/cvHkTgYGBiIiIQFBQENzd3aFUKq0beD2VlJQgJycHly9fxqFDh3Dv3j306NEDH330EcaOHdugMhudkBXy8vKwe/duJCQk4PLly8jMzKwcosSPtgBSAPgA4K/cli1bom3btggNDcUzzzyDZ599tnLoGVM3RMDvvxsT8MAB4OhRQK0GIiKAgweB2qZHIiIkJiZi7969OHPmDK5evYqCgoI6T3ImFHt7e7i5uSEoKAj9+vXD6NGj0b1790aVyVtCWtoXXwDz5wNr1wJTpggdjbioVCps2rQJ6enpCAgIwMSJEytXU7aU1FTg8GHgf/8DEhKAR48AuRwwGIxnSDc3IDkZYBcZ9WMzCRkSYvwFR0QYvwiMUUpKCiIiIuDk5IQ7d+5Ao9HA398fiYmJ8Pb25q2ehw+BY8eMZ7xffgEyMoxnPo4D/joxAMcB+/cDw4fzVn3zwdtdrQVdu0ZkvDAi4jiie/eEjkg8RowYQZcuXSIiouzsbJo6dSoBoClTpvBS/o8/Evn7Gz97iYRILn/8uzD3I5USffIJL1U3SzYxydWmTcbLIcD4V3nbNmHjEYtz584hKioK3bp1AwB4enri008/hUQiwYkTJ3ipY9AgIC/PeNYzGACttvpj5XKgTx/gk094qbpZsolL1ieeAG7fNv6b44CwMODcOUFDEoW8vDy4ubmZjKt76qmnIJPJeEvKrVuB2oZ+SiSAi4vxtsJH+EWvbJboz5BnzjxORsB4YXT+PHCz5lXSmgV3d3ezg1wzMjIwYsQI3up58UVg3LjHVynmEAFbtrBkbCzRJ+TmzaZfBLnc+MtnTB07dgwymQxz587ltdyvvwacnIxnwr+SSo2XqdU9b2TqTtSXrAYD4O0N5OSY7vPzA9LSrB+TmOn1egwZMgRffvmlRSbg2rULeO65qtvkcqBXL+DIkdqfNzK1E/UZ8sgR88kIALduAZcuWTUc0Xv33XfxzjvvWGw2vDFjgPHjH1+xSCTGs+aWLSwZ+SLqhPxz6+pfyeXGy1nG6Ntvv0VYWBhGjx5t0XpWrTImYcWt67Zt7L6RT6JNSI3G2LpXXTO7Vgt8952xMaG527FjB4gI0dHRVbYfPXq03mVlZgLTpgHFxeb3e3gA8fHGz/2TT4A/LfXJ8EC095C7dgFjx9aecImJQN++1olJjA4ePIiPP/4YkyZNqtym1+tx9epVBAcHY/bs2XUu6+hR42WplxewZw8QGFj9sStXAjNnmm/kYRpBwE4JNXrxRWPPkJp6hXAc0ZtvCh2pcM6dO0cODg4EwOTHzs6O8vLy6lXeo0dECxcSNZPJIERJlGdIjQbo0QPIz3+8TaczdmB2d6/agODrC5w8+fiehmFsmSgT0pyzZ4HwcOOjDjNrlDBMk2D1O4AHDx7gyJEj9X5dSIgxGdu25T8mhhELqyVkTk4O3n33Xfj5+WHHjh31fr1SaTwz1tR9i6nZ/fvASy8B6elCR8JUx2oJefv2bURHR6O0tNRaVTJ/8vvvQHAwkJRkvBdnxMlq63GHh4dDo9FYqzrmLzp3Bj74AIiJARwchI6GqY7VEpIRllQKvPuu0FEwtWGPdRlGRFhCMoyIsIRsIrKzjSMxfv1V6EiYxrCZhLxyBfD3N852xlSVm/u4BdXOTuhomMawmUad8nLjGMiaJllqrjw8gLg4Y8dwZ2eho2Eaw2YS0sHB2L9V5LPLC+aVV4SOgOGDVRMy/4/e4mVlZfV+bZcuxv6sDNOUWe0e8pdffsHbb78NANi5cyfWrFmDBw8eWKt6hrEJNjPaozkrKAAWLDD2tuF5MjlGZGzmHrK50mqBnj2BsjLjDApM08bOkDbg4EFjUvK83CYjQiwhGUZEbKZjAMM0BzaTkCUlxgV2RL6oboPp9UJHwIiBzSTk1avG+6h794SOhF+FhcD06ca5UBmGtbIKbORI4/Lg33wjdCSMGNhMQvr6AsuWGdeub0q++sr43pra+2IahrWyMoyI2Mw9JMM0BywhraABfemZZoolpAUVFQFvvAEMHGhcfJZhamMzjTq2aPZs4JdfjA03bJUopi5Yo44FZWUBMhnQqpXQkTC2giUkw4iIzVxIZWYC77/PpsFnmjabScgHD4DPPzcO1hUTscXD2DZRNuroiVCsJZToDCjXEwjAXTUAyHFbpYVEZVygVSnh4CCXwEEmgcTKC7aq1cZR/Dt2ANeuAS4u1q2faZoEvYd8VK5HdokOuWV65JTrkVuqg1prTMK/0mk4FOVI4OKlh9TMnxGlVAInOYdW9jJ42EnhbieFdwsZXBRS04N58OmnwIoVxp+JEy1SBdMMWTUh88r0SCvSIEOtRYZahzK9ARwACcfBAAIfkXCcsTw9EUCAvUyCdk5ytHOQwd9ZAVclPwlaWmocqeHtzUtxDAPACgl5r1iHa/nlSCnUQKXRQ8JxIDJehlpLxeWsgYCWSik6uSrQtaUSrexFecXONGMWScgSnQFXHpXjYm4Z8sv1kHDGZBALCcfBQIRW9jKEutshyE0JpdTKN6EMYwavCVmoMSApuxQXc8tgAIkqCc3iAAkZEzTUww69vOzhJH/c8HzvHtCmjYDxMc0OLwlZrDPgaFYJrjwqgwSAmTYZ0TNe1nLo4WmHMOcWWPwJh9WrgeRkICBA6OiY5qJRN1EGAs5kl+L4gxIYyNgoY6tTwxjP5oRzOWX4fz8Qdq53wOqvOZaMjFU1+AyZW6bHz7dVyC3Tif/StAFK8iUI9JViVAdHuFro0QnD/FWDEvJsTikO3ysB2cJ9YiNIOA4SACPaOSLIjS27xVhevRLSQMCvGWpcymt+I257e9ljoI8DWFssY0l1TkitgbAtrQiZai2a41hbDhw6uigw5gknq3fTY5qPOnUu1xkI29OKkFmsa5bJCAAEws3CcuxKV/HSo4hhzKk1IQnAT+kqZKi1MDTzb6IBwM2icuzLUAsdCtNE1ZqQJx6UIL2oeV6mmmMg4EpeGS7kNr/7aMbyakzIO2otEu8bW1OZqhIyi/GwVCd0GEwTU21CGgjYf9eyl2aXft2BC3u3WrQOS7L058M0P9Um5NmcUhRoDLydG+9cSsKhNcuhzsup3Jb4/SocXvtvnmqwLpCeHwkAAAcQSURBVAMR7pfq8PujJrocFyMIswlpIODkw1LwORDk9oWTSFgVC1XuQ97KFIPfHpQIHQLThJhNyBsF5SjVi7cZh8Qy6zABBeV63FVrhY6EaSLMdi6/8qgcHMDb5epPS95B6qkjAIDt/3gLHUJ7YdT82Mr9D9Ou4+j6FUhL+g1ShQL+4f0xesEyyJV2lcdkp9/AvuWfIPP3CygvKYZ3QBcMnPw2goeMrFLX5gVT4d0xGH49++LEpm+QlvQbHNw88eTIFzEgehY4nmcslnBA8qNytHOU81ou0zyZfDuJgAy1lteH357t/OHkYZzrwqOdP9zb+lXuK87PQ/wbzyEj+RxC//YCPNr64ezOH7B90ezKY25fPI2vJg1DdvoNPDXuVQyeNg+cRIof3puMQ/FxVepKPfMbzu36ARtmvwSdTounxkVDYWeP/SsW46cl7/D3pv5gICBdpeG9XKZ5MjlDZpfpoOG5x3j/6DdhMOhx93ISIia/jdadgiv3lRQ+wtDp8zFk+nuV21ZFP4Obf5xRiQi7//khZAolZqzfB2dPY2IPeHUW1r85AYfWLEe34c/Bo71/5evzMm/j2XmL0S9qBgBgWMwHWBMzDud2bULv8ZPRpkt3Xt+fSmOASmuoMriZYRrC5BtUUG7dEY2cRIKBk9+usq1Nl+4oLSpA4cMsZF2/jKzrl+EX3q8yGQFAKpOjx+iXoNdqcPP0kSqvt3NyQd+J06vUMWjKHBARbp48bJH3UWjlz41pmkwSslRHVu087ezZGjKFoso2OyfjJKea0mLk3r0FAPDr8bTJa306dwMA5N5Jq7Ldo50fOK7qm/Dy7wzAePa0hGId6zzBNJ5JQmoNZNUhRgr7FtXuIyKUFOQBAFr6tDPZr9ca790kkqoDiJ08vKqtR66wM9nXWBzHQduUB4YyVmOSkHYyCQwiGvXX0qc9ACD9/CmTfXcuJwEA3HzbV9mel5Fucmx+VgYAwKMD/3NyEBHsZeL5zBjbZZKQLWQcrx0CGsuncwikcgVS/3KfCAC3zh6HRCJFYJ/BVbbn3kmrvNStcHbXJmN5f2pQ4lMLGWvQYRrP5FtkqcmDXVu3BQCc+ek7ZP5+oc6vc/b0Rp8JryPr+hXsip2Ph6nXkHM7FQe//hzJB3cj9Nnx8GjnV+U1ZNDj+3ei8fvhvXiYdh2H4uNw4sd4dBs2Bh3CevP6vgDjbOnuPM2IzjRvJtnnJJfASSGBSsNvb5jA3gPRLqQnTm1bj+z0G5j27c46vzZy9scggx7HN32LU9vWV27v9cJrGPXeUpPj/Z8aAOdWrfHDe1Mqe/X49eyLMR/+s/FvxAxPOxkUbKJlhgdmp/ComDfHEu0URTkPoGzhCKWDY71fq36Ui/spVyBTKOEd2BX2zq4mxywe1Am+QaGYvHILSosKkHn1IlxatUYrv058hG9CwgF9vFqgf+vqG6cYpq7MXp+GethZbADun58l1pejmwcC+wyq8/H2zq4I7B3R4PrqwgCgmzubkY7hh9mWCC97GbxbyEye5TFVSTjA30lhsSXvmOan2qbBoW0cRNXaWldOnl5wcHW3Sl0GABE+7FKV4U+N00DuuK3CzQJNs5/cyhwJOIR6KjHct/73wgxTnRofng1v4wA7KQd25VqVhAOcFBIMbO0gdChME1NjQjrIJRj7hJO1YrEZEnAY5+fE1pRkeFdr95K2jnI8wy7LKnEcMKqDI1t9mbGIOvX3CvWww1BfdnkGDhjV3gmdXNljDsYy6rXYzoXcMhzINE592Gzaech4VpRwHEa2d0SXliwZGcup93J06SotfrpVBD2hWbS+SjhAKZVgvJ8zfBzYZSpjWQ1aHzK/XI9dt1XILtU36aTkYLyHHtXBiU3PwVhFg1dQNhBw6mEJEv+Yl7Qpjc+tWKh1UJsW6OFpL3Q4TDPS4ISskF+ux8HMYqQVacBx4hpLWV8SjoOBCF1bKhHh4wBnBTsrMtbV6ISscFulxbH7Jcgq1lZ+sW2FBBwMILR3UmBg6xbsXpERDG8JWSGzWIsTD0qR/scZU8yJKeGMk0F3clWij5c9vNizRUZgvCdkhSKNAVceleFiXjlUGj2kHKAXKjcJqJgmSMIZ73dbKqUI87BDkJsSDmz6DUYkLJaQf3a/RIebhRqkFGiQV6YDB2NiWCRB/5R8ACDlOOhBABmHlXVyVSDARcF62jCiZJWE/DOV1oBMtRb3inW4o9Yir0xX2UIr4zgY0LDnm1LOuBpJRZJLJRw87aRo5yhHGwc5fB1l7EzIiJ7VE/KvDAQUaPTILdUjr1wPlVb/x9T8hBKdHhoDYDAQ9AD0BoKU4yDljAknlwAOMimcFRI4yiVwkkvgYSeFh50ULgopG6XC2BzBE5JhmMfYNRzDiAhLSIYREZaQDCMiMgDbhA6CYRij/w+Idvi2ePimHQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "------------------------------------------------------------\n",
      "\n",
      "PW: 4\n",
      "\n",
      "Partitioning Description:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>. % <text style=color:blue>[X=Y][Z]</text></text>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Specialized Query:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>, X=Y, X != Z.</text>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Canonical DB:\n",
      "e(\"Z\",\"X\"). e(\"X\",\"Z\"). thop(\"X\",\"X\").\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "------------------------------------------------------------\n",
      "\n",
      "PW: 5\n",
      "\n",
      "Partitioning Description:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>. % <text style=color:blue>[X=Y=Z]</text></text>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Specialized Query:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<text style=color:black><text style=color:green>thop(X,Y)</text> :- <text style=color:green>e(X,Z)</text>, <text style=color:green>e(Z,Y)</text>, X=Y, X=Z.</text>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Canonical DB:\n",
      "e(\"X\",\"X\"). thop(\"X\",\"X\").\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, len(query_analysis['pw_objs'])+1):\n",
    "    print('-'*60)\n",
    "    print(\"\\nPW:\", i)\n",
    "    pw_rel_dfs, pw_objs = pw_slicer(query_analysis['pw_rel_dfs'], query_analysis['pw_objs'], [i])\n",
    "    pw_obj = pw_objs[0]\n",
    "    \n",
    "    print(\"\\nPartitioning Description:\")\n",
    "    print_fancy_rewrite(pw_rel_dfs)\n",
    "    \n",
    "    print(\"Specialized Query:\")\n",
    "    print_explicit_rewritten_query_string(pw_rel_dfs, chain_eq=False)\n",
    "    \n",
    "    print(\"Canonical DB:\")\n",
    "    pw_edge_facts = get_edge_facts(pw_obj)\n",
    "    pw_head_facts = get_query_head_facts(pw_obj)\n",
    "    print(\" \".join(pw_edge_facts+pw_head_facts))\n",
    "    g = get_pattern_graph3(pw_rel_dfs, pw_obj, silent=True, q_head='hyperedge')\n",
    "    # draw(g, filename='{}.{}'.format('3hop_all_patterns_new/pw_{}'.format(i), 'png'), show=False)\n",
    "    display(draw(g))\n",
    "    print('-'*60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "pw_id_to_head_encoding = {\n",
    "    1: \"abc\",\n",
    "    2: \"abb\",\n",
    "    3: \"aab\",\n",
    "    4: \"aba\",\n",
    "    5: \"aaa\",\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pw_id_to_encoding = pw_id_to_head_encoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above, we can see for each PW, the variable partitions (in blue), followed by the specialized query the PW represents, followed by a textual and visual representation of the canonical database of the specialized query.\n",
    "\n",
    "These visual representations of the canonical databases are what we call ___graph-patterns___.\n",
    "\n",
    "One outstanding issue is that these specialized queries/patterns aren't disjoint, _yet_, i.e. some of them are equivalent. To find the set of disjoint set of these specialized queries/patterns, we check for isomorphisms between these canonical databases. If there exists an isomorphism between two canonical databases (and hence the graph patterns), the two specialized queries (and the graph patterns) are equivalent, and can be grouped together.\n",
    "\n",
    "Below is the encoding that checks if there exists such an isomorphism for two such canonical databases:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_isomorphism_equivalence_encoding(asp_rule, show_nothing_rule=True):\n",
    "    listener = parse_dlv_rules(asp_rule, print_parse_tree=False)\n",
    "    \n",
    "    logic_atom_types = set([])\n",
    "    \n",
    "    assert len(listener.rules) == 1\n",
    "    \n",
    "    for rule in listener.rules:\n",
    "        head_atoms, tail_atoms = rule[0], rule[1]\n",
    "        for ruleOcc in head_atoms+tail_atoms:\n",
    "            logic_atom_types.add((ruleOcc.rel_name, ruleOcc.rel_arity))\n",
    "    \n",
    "    gnode_rules = []\n",
    "    vmap_rules = ['vmap(X,Y) ; not vmap(X,Y) :- gnode1(X), gnode2(Y).']\n",
    "    many_to_one_cond_rule = [\n",
    "        ':- gnode1(X), #count {Y: vmap(X,Y)} != 1.',\n",
    "        ':- gnode2(Y), #count {X: vmap(X,Y)} != 1.',\n",
    "    ]\n",
    "    show_rule = ['#show.'] if show_nothing_rule else []\n",
    "    \n",
    "    for logic_atom, arity in logic_atom_types:\n",
    "        \n",
    "        for qid in [1,2]:\n",
    "            t = ['_' for _ in range(arity)]\n",
    "            for pos in range(arity):\n",
    "                t[pos] = 'X'\n",
    "                body = ','.join(t)\n",
    "                gnode_rules.append(f'gnode{qid}(X) :- {logic_atom}{qid}({body}).')\n",
    "                t[pos] = '_'\n",
    "        \n",
    "        tx, ty = [f'X{i+1}' for i in range(arity)], [f'Y{i+1}' for i in range(arity)]\n",
    "        l_vmaps = ', '.join([f'vmap({ti_x},{ti_y})' for ti_x, ti_y in zip(tx,ty)])\n",
    "        tx_j, ty_j = ','.join(tx), ','.join(ty)\n",
    "        if arity > 0:\n",
    "            vmap_rules.append(f':- {l_vmaps}, {logic_atom}1({tx_j}), not {logic_atom}2({ty_j}).')\n",
    "            vmap_rules.append(f':- {l_vmaps}, not {logic_atom}1({tx_j}), {logic_atom}2({ty_j}).')\n",
    "        elif arity == 0:\n",
    "            vmap_rules.append(f':- {logic_atom}1, not {logic_atom}2.')\n",
    "            vmap_rules.append(f':- not {logic_atom}1, {logic_atom}2.')\n",
    "        \n",
    "\n",
    "        \n",
    "    return gnode_rules + vmap_rules + many_to_one_cond_rule + show_rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
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       "<div class=\"highlight\"><pre><span></span><span class=\"lineno\"> 1 </span><span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">e1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 2 </span><span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">e1</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 3 </span><span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">e2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 4 </span><span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">e2</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 5 </span><span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">thop1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 6 </span><span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">thop1</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 7 </span><span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">thop2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 8 </span><span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">thop2</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 9 </span><span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"o\">not</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">10 </span><span class=\"p\">:-</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">Y1</span><span class=\"p\">),</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X2</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">),</span> <span class=\"nf\">e1</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">X2</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">e2</span><span class=\"p\">(</span><span class=\"nv\">Y1</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">11 </span><span class=\"p\">:-</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">Y1</span><span class=\"p\">),</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X2</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">e1</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">X2</span><span class=\"p\">),</span> <span class=\"nf\">e2</span><span class=\"p\">(</span><span class=\"nv\">Y1</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">12 </span><span class=\"p\">:-</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">Y1</span><span class=\"p\">),</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X2</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">),</span> <span class=\"nf\">thop1</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">X2</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">thop2</span><span class=\"p\">(</span><span class=\"nv\">Y1</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">13 </span><span class=\"p\">:-</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">Y1</span><span class=\"p\">),</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X2</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">thop1</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">X2</span><span class=\"p\">),</span> <span class=\"nf\">thop2</span><span class=\"p\">(</span><span class=\"nv\">Y1</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">14 </span><span class=\"p\">:-</span> <span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">Y</span><span class=\"s s-Atom\">:</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">!</span><span class=\"o\">=</span> <span class=\"mf\">1.</span>\n",
       "<span class=\"lineno\">15 </span><span class=\"p\">:-</span> <span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">),</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">X</span><span class=\"s s-Atom\">:</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">!</span><span class=\"o\">=</span> <span class=\"mf\">1.</span>\n",
       "<span class=\"lineno\">16 </span><span class=\"c1\">#show.</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'gnode1(X) :- e1(X,_).\\ngnode1(X) :- e1(_,X).\\ngnode2(X) :- e2(X,_).\\ngnode2(X) :- e2(_,X).\\ngnode1(X) :- thop1(X,_).\\ngnode1(X) :- thop1(_,X).\\ngnode2(X) :- thop2(X,_).\\ngnode2(X) :- thop2(_,X).\\nvmap(X,Y) ; not vmap(X,Y) :- gnode1(X), gnode2(Y).\\n:- vmap(X1,Y1), vmap(X2,Y2), e1(X1,X2), not e2(Y1,Y2).\\n:- vmap(X1,Y1), vmap(X2,Y2), not e1(X1,X2), e2(Y1,Y2).\\n:- vmap(X1,Y1), vmap(X2,Y2), thop1(X1,X2), not thop2(Y1,Y2).\\n:- vmap(X1,Y1), vmap(X2,Y2), not thop1(X1,X2), thop2(Y1,Y2).\\n:- gnode1(X), #count {Y: vmap(X,Y)} != 1.\\n:- gnode2(Y), #count {X: vmap(X,Y)} != 1.\\n#show.'"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qep_eq_check = create_isomorphism_equivalence_encoding(query_str)\n",
    "qep_eq_check = '\\n'.join(qep_eq_check)\n",
    "ASPRules(qep_eq_check)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now use PWE to compute the disjoint groups efficiently using the above encoding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "sets = get_equivalent_sets(query_analysis['pw_objs'], lambda pw1, pw2: are_equivalent_patterns(pw1,pw2,qep_eq_check))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1}\n",
      "{2}\n",
      "{3}\n",
      "{4}\n",
      "{5}\n"
     ]
    }
   ],
   "source": [
    "for s in sets:\n",
    "    print({pw.pw_id for pw in s})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(sets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "for s in sets:\n",
    "    if len(s) > 1:\n",
    "        print('-'*90)\n",
    "        for pw in s:\n",
    "            i = pw.pw_id\n",
    "            print('-'*60)\n",
    "            print(\"\\nPW:\", i)\n",
    "            pw_rel_dfs, pw_objs = pw_slicer(query_analysis['pw_rel_dfs'], query_analysis['pw_objs'], [i])\n",
    "            pw_obj = pw_objs[0]\n",
    "\n",
    "            print(\"Canonical DB:\")\n",
    "            pw_edge_facts = get_edge_facts(pw_obj)\n",
    "            pw_head_facts = get_query_head_facts(pw_obj)\n",
    "            print(\" \".join(pw_edge_facts+pw_head_facts))\n",
    "            g = get_pattern_graph3(pw_rel_dfs, pw_obj, silent=True, q_head='hyperedge')\n",
    "            display(draw(g))\n",
    "            print('-'*60)\n",
    "        print('-'*90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building a hierarchy of _semi_-specialized queries\n",
    "\n",
    "In the specialized queries above, we explicitly encode the equalities and in/dis-equalities between the variables in the query. Say we only encode the equalities but not the in/dis-equalities. This gives us a set of _semi_-specialized queries which can be arranged in a hierarchy based on query containment relations. We build these queries and their hierarchy below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is an ASP encoding to check for query containment between two queries Q1 and Q2 (is Q2 contained in Q1?) based on their canonical databases:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_homomorphism_containment_encoding(asp_rule, show_nothing_rule=True):\n",
    "    listener = parse_dlv_rules(asp_rule, print_parse_tree=False)\n",
    "    \n",
    "    logic_atom_types = set([])\n",
    "    \n",
    "    assert len(listener.rules) == 1\n",
    "    \n",
    "    for rule in listener.rules:\n",
    "        head_atoms, tail_atoms = rule[0], rule[1]\n",
    "        for ruleOcc in head_atoms+tail_atoms:\n",
    "            logic_atom_types.add((ruleOcc.rel_name, ruleOcc.rel_arity))\n",
    "    \n",
    "    gnode_rules = []\n",
    "    vmap_rules = ['vmap(X,Y) ; not vmap(X,Y) :- gnode1(X), gnode2(Y).']\n",
    "    vmap_q1_q2_rules = []\n",
    "    vmap_q2_q1_rules = []\n",
    "    many_to_one_cond_rule = [':- gnode1(X), #count {Y: vmap(X,Y)} != 1.']\n",
    "    show_rule = ['#show.'] if show_nothing_rule else []\n",
    "    \n",
    "    for logic_atom, arity in logic_atom_types:\n",
    "        \n",
    "        for qid in [1,2]:\n",
    "            t = ['_' for _ in range(arity)]\n",
    "            for pos in range(arity):\n",
    "                t[pos] = 'X'\n",
    "                body = ','.join(t)\n",
    "                gnode_rules.append(f'gnode{qid}(X) :- {logic_atom}{qid}({body}).')\n",
    "                t[pos] = '_'\n",
    "        \n",
    "        tx, ty = [f'X{i+1}' for i in range(arity)], [f'Y{i+1}' for i in range(arity)]\n",
    "        l_vmaps = ', '.join([f'vmap({ti_x},{ti_y})' for ti_x, ti_y in zip(tx,ty)])\n",
    "        tx_j, ty_j = ','.join(tx), ','.join(ty)\n",
    "        l_gnode2s = ', '.join([f'gnode2({ti_y})' for ti_y in ty])\n",
    "        \n",
    "        if arity > 0:\n",
    "            vmap_q1_q2_rules.append(f':- {l_vmaps}, {logic_atom}1({tx_j}), not {logic_atom}2({ty_j}).')\n",
    "            #vmap_q2_q1_rules.append(f'{logic_atom}2_mapped({ty_j}) :- {l_vmaps}, {logic_atom}1({tx_j}), {logic_atom}2({ty_j}).')\n",
    "            #vmap_q2_q1_rules.append(f':- {l_gnode2s}, {logic_atom}2({ty_j}), not {logic_atom}2_mapped({ty_j}).')\n",
    "        elif arity == 0:\n",
    "            vmap_q1_q2_rules.append(f':- {logic_atom}1, not {logic_atom}2.')\n",
    "            #vmap_q2_q1_rules.append(f'{logic_atom}2_mapped :- {logic_atom}1, {logic_atom}2.')\n",
    "            #vmap_q2_q1_rules.append(f':- {logic_atom}2, not {logic_atom}2_mapped.')\n",
    "\n",
    "        \n",
    "    return gnode_rules + vmap_rules + vmap_q1_q2_rules + vmap_q2_q1_rules + many_to_one_cond_rule + show_rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
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       "<div class=\"highlight\"><pre><span></span><span class=\"lineno\"> 1 </span><span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">e1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 2 </span><span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">e1</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 3 </span><span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">e2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 4 </span><span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">e2</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 5 </span><span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">thop1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 6 </span><span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">thop1</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 7 </span><span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">thop2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"k\">_</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 8 </span><span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">thop2</span><span class=\"p\">(</span><span class=\"k\">_</span><span class=\"p\">,</span><span class=\"nv\">X</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\"> 9 </span><span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">;</span> <span class=\"o\">not</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"nf\">gnode2</span><span class=\"p\">(</span><span class=\"nv\">Y</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">10 </span><span class=\"p\">:-</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">Y1</span><span class=\"p\">),</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X2</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">),</span> <span class=\"nf\">e1</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">X2</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">e2</span><span class=\"p\">(</span><span class=\"nv\">Y1</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">11 </span><span class=\"p\">:-</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">Y1</span><span class=\"p\">),</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X2</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">),</span> <span class=\"nf\">thop1</span><span class=\"p\">(</span><span class=\"nv\">X1</span><span class=\"p\">,</span><span class=\"nv\">X2</span><span class=\"p\">),</span> <span class=\"o\">not</span> <span class=\"nf\">thop2</span><span class=\"p\">(</span><span class=\"nv\">Y1</span><span class=\"p\">,</span><span class=\"nv\">Y2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">12 </span><span class=\"p\">:-</span> <span class=\"nf\">gnode1</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">),</span> <span class=\"s s-Atom\">#count</span> <span class=\"p\">{</span><span class=\"nv\">Y</span><span class=\"s s-Atom\">:</span> <span class=\"nf\">vmap</span><span class=\"p\">(</span><span class=\"nv\">X</span><span class=\"p\">,</span><span class=\"nv\">Y</span><span class=\"p\">)}</span> <span class=\"p\">!</span><span class=\"o\">=</span> <span class=\"mf\">1.</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'gnode1(X) :- e1(X,_).\\ngnode1(X) :- e1(_,X).\\ngnode2(X) :- e2(X,_).\\ngnode2(X) :- e2(_,X).\\ngnode1(X) :- thop1(X,_).\\ngnode1(X) :- thop1(_,X).\\ngnode2(X) :- thop2(X,_).\\ngnode2(X) :- thop2(_,X).\\nvmap(X,Y) ; not vmap(X,Y) :- gnode1(X), gnode2(Y).\\n:- vmap(X1,Y1), vmap(X2,Y2), e1(X1,X2), not e2(Y1,Y2).\\n:- vmap(X1,Y1), vmap(X2,Y2), thop1(X1,X2), not thop2(Y1,Y2).\\n:- gnode1(X), #count {Y: vmap(X,Y)} != 1.'"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qep_containment_check = create_homomorphism_containment_encoding(query_str, show_nothing_rule=False)\n",
    "qep_containment_check = '\\n'.join(qep_containment_check)\n",
    "ASPRules(qep_containment_check)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to test whether query Q1 (represented by pw1) contains query Q2 (represented by pw2)\n",
    "# using the above encoding\n",
    "def q1_contains_q2(pw1, pw2):\n",
    "    return are_equivalent_patterns(pw1, pw2, qep_containment_check)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_canonical_db(pw_rel_dfs, include_head=True):\n",
    "    canonical_db = {}\n",
    "    for _, row in pw_rel_dfs['newArc_4'].iterrows():\n",
    "        rule = (row['ATOM'], int(row['OCC']))\n",
    "        pos = int(row['POS'])\n",
    "        var = row['VAR']\n",
    "        if rule not in canonical_db:\n",
    "            canonical_db[rule] = {}\n",
    "        canonical_db[rule][pos] = var\n",
    "    \n",
    "    if include_head:\n",
    "        if 'ruleH_1' in pw_rel_dfs:\n",
    "            for _, row in pw_rel_dfs['ruleH_1'].iterrows():\n",
    "                rule = row['HEAD']\n",
    "                if rule not in canonical_db:\n",
    "                    canonical_db[rule] = {}\n",
    "        if 'newHArc_3' in pw_rel_dfs:\n",
    "            for _, row in pw_rel_dfs['newHArc_3'].iterrows():\n",
    "                rule = row['HEAD']\n",
    "                pos = int(row['POS'])\n",
    "                var = row['VAR']\n",
    "                if rule not in canonical_db:\n",
    "                    canonical_db[rule] = {}\n",
    "                canonical_db[rule][pos] = var\n",
    "\n",
    "    canonical_db_fact_strs = []\n",
    "    for rule, rule_desc in canonical_db.items():\n",
    "        if isinstance(rule, tuple):\n",
    "            rule = rule[0]\n",
    "        r_body = [rule_desc[k] for k in sorted(rule_desc.keys())]\n",
    "        if len(r_body) > 0:\n",
    "            r_body_j = ', '.join(r_body)\n",
    "            canonical_db_fact_strs.append(f'{rule}({r_body_j}).')\n",
    "        else:\n",
    "            canonical_db_fact_strs.append(f'{rule}.')\n",
    "        \n",
    "    return canonical_db_fact_strs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def canonical_db_containment_check(pw1_rel_dfs, pw2_rel_dfs):\n",
    "    \"\"\"\n",
    "    Q1 (pw1) contains Q2 (pw2)\n",
    "    \"\"\"\n",
    "    pw1_q_str = print_rewritten_query_string(pw1_rel_dfs, html=False, display_q=False, include_ineqls=False)\n",
    "    pw2_canonical_db = get_canonical_db(pw2_rel_dfs, include_head=True)\n",
    "    sat_req_rule = ''\n",
    "    show_rule = ''\n",
    "    assert len(pw1_rel_dfs['ruleH_1']) > 0\n",
    "    q1_head = pw1_rel_dfs['ruleH_1']['HEAD'][0]\n",
    "    \n",
    "    pw1_q_str = pw1_q_str.replace(q1_head, f'{q1_head}_q')\n",
    "    \n",
    "    if 'newHArc_3' in pw1_rel_dfs and len(pw1_rel_dfs['newHArc_3']) > 0:\n",
    "        q1_head_arity = len(pw1_rel_dfs['newHArc_3']['POS'])\n",
    "        h_vars = [f'A{i}' for i in range(q1_head_arity)]\n",
    "        h_vars_j = ','.join(h_vars)\n",
    "        sat_req_rule = f':- not {q1_head}_q({h_vars_j}), {q1_head}({h_vars_j}).'\n",
    "    else:\n",
    "        sat_req_rule = f':- not {q1_head}_q, {q1_head}.'\n",
    "    \n",
    "    #print(\"\\n\".join([pw1_q_str]+pw2_canonical_db+[sat_req_rule]))\n",
    "    asp_out, _ = run_clingo([pw1_q_str]+pw2_canonical_db+[sat_req_rule, show_rule], num_solutions=1)\n",
    "    #print(asp_out)\n",
    "    _,_,eq_check_pws = load_worlds(asp_out, silent=True)\n",
    "    \n",
    "    return len(eq_check_pws) >= 1\n",
    "\n",
    "def canonical_db_containment_check_wrapper(pw_rel_dfs, pw1_id, pw2_id):\n",
    "    \n",
    "    pw1_rel_dfs = pw_slicer(query_analysis['pw_rel_dfs'], None, [pw1_id])[0]\n",
    "    pw2_rel_dfs = pw_slicer(query_analysis['pw_rel_dfs'], None, [pw2_id])[0]\n",
    "    return canonical_db_containment_check(pw1_rel_dfs, pw2_rel_dfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figures for each PW (to build the hierarchy)\n",
    "\n",
    "query_fig_fnames = save_query_figs(query_analysis, folder='2hop_2_all_patterns_new')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we create the hierarchy of the queries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = nx.DiGraph()\n",
    "for pw_id in range(1, len(query_analysis['pw_objs'])+1):\n",
    "    fname = query_fig_fnames[pw_id]\n",
    "    g.add_node(pw_id, image=os.path.abspath(fname),\n",
    "               shape='box', fixedsize='true', imagescale='true', size=2, label=\" \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's add edges based on query containment between all the queries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for pw_id1 in range(1, len(query_analysis['pw_objs'])+1):\n",
    "    for pw_id2 in range(1, len(query_analysis['pw_objs'])+1):\n",
    "        if pw_id1 == pw_id2:\n",
    "            continue\n",
    "        if canonical_db_containment_check_wrapper(query_analysis['pw_rel_dfs'], pw_id1, pw_id2):\n",
    "            g.add_edge(pw_id1, pw_id2, dir='back')\n",
    "\n",
    "draw(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "keep_running = True\n",
    "\n",
    "while keep_running:\n",
    "    keep_running=False\n",
    "    for eu, ev in list(g.edges):\n",
    "        if (ev,eu) in list(g.edges):\n",
    "            print(f\"Merging {eu} and {ev}\")\n",
    "            g = nx.contracted_nodes(g, min(eu,ev), max(eu,ev), self_loops=False)\n",
    "            keep_running = True\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draw(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_ = nx.algorithms.dag.transitive_reduction(g)\n",
    "\n",
    "# Copy over the style properties (the nx.algorithms.dag.transitive_reduction loses these)\n",
    "for n in g.nodes:\n",
    "    for k,v in g.nodes[n].items():\n",
    "        g_.nodes[n][k] = v\n",
    "for e in g_.edges:\n",
    "    g_.edges[e]['dir'] = 'back'\n",
    "draw(g_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2hop_2_query_hierarchy_can_db_v2.pdf'"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draw(g_, filename='2hop_2_query_hierarchy_can_db_v2.pdf', show=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2hop_2_query_hierarchy_can_db_v2.gv'"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draw(g_, filename='2hop_2_query_hierarchy_can_db_v2.gv', show=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = nx.DiGraph()\n",
    "for pw_id in range(1, len(query_analysis['pw_objs'])+1):\n",
    "    fname = query_fig_fnames[pw_id]\n",
    "    g.add_node(pw_id, image=os.path.abspath(fname),\n",
    "               shape='box', fixedsize='true', imagescale='true', size=2, label=\" \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for pw_id1 in range(1, len(query_analysis['pw_objs'])+1):\n",
    "    for pw_id2 in range(1, len(query_analysis['pw_objs'])+1):\n",
    "        if pw_id1 == pw_id2:\n",
    "            continue\n",
    "        if q1_contains_q2(query_analysis['pw_objs'][pw_id1-1], query_analysis['pw_objs'][pw_id2-1]):\n",
    "            g.add_edge(pw_id1, pw_id2, dir='back')\n",
    "\n",
    "draw(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "keep_running = True\n",
    "\n",
    "while keep_running:\n",
    "    keep_running=False\n",
    "    for eu, ev in list(g.edges):\n",
    "        if (ev,eu) in list(g.edges):\n",
    "            print(f\"Merging {eu} and {ev}\")\n",
    "            g = nx.contracted_nodes(g, min(eu,ev), max(eu,ev), self_loops=False)\n",
    "            keep_running = True\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draw(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make the hierarchy easier to analyze, we remove the redundant transitive edges using a transitive reduction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_ = nx.algorithms.dag.transitive_reduction(g)\n",
    "\n",
    "# Copy over the style properties (the nx.algorithms.dag.transitive_reduction loses these)\n",
    "for n in g.nodes:\n",
    "    for k,v in g.nodes[n].items():\n",
    "        g_.nodes[n][k] = v\n",
    "for e in g_.edges:\n",
    "    g_.edges[e]['dir'] = 'back'\n",
    "draw(g_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The arrows can be iterpreted as ___'isa'___ relations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2hop_2_query_hierarchy_homomorphism.pdf'"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draw(g_, filename='2hop_2_query_hierarchy_homomorphsim.gv', show=False)\n",
    "draw(g_, filename='2hop_2_query_hierarchy_homomorphism.pdf', show=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_canonical_db_mod(pw_rel_dfs, include_head=True, pw_id=None):\n",
    "    canonical_db = {}\n",
    "    for _, row in pw_rel_dfs['newArc_4'].iterrows():\n",
    "        rule = (row['ATOM'], int(row['OCC']))\n",
    "        pos = int(row['POS'])\n",
    "        var = row['VAR']\n",
    "        if rule not in canonical_db:\n",
    "            canonical_db[rule] = {}\n",
    "        canonical_db[rule][pos] = var\n",
    "        \n",
    "    if include_head:\n",
    "        if 'ruleH_1' in pw_rel_dfs:\n",
    "            for _, row in pw_rel_dfs['ruleH_1'].iterrows():\n",
    "                rule = row['HEAD']\n",
    "                if rule not in canonical_db:\n",
    "                    canonical_db[rule] = {}\n",
    "        if 'newHArc_3' in pw_rel_dfs:\n",
    "            for _, row in pw_rel_dfs['newHArc_3'].iterrows():\n",
    "                rule = row['HEAD']\n",
    "                pos = int(row['POS'])\n",
    "                var = row['VAR']\n",
    "                if rule not in canonical_db:\n",
    "                    canonical_db[rule] = {}\n",
    "                canonical_db[rule][pos] = var\n",
    "    \n",
    "#     if include_head and ('newHArc_3' in pw_rel_dfs):\n",
    "#         for _, row in pw_rel_dfs['newHArc_3'].iterrows():\n",
    "#             rule = row['HEAD']\n",
    "#             pos = int(row['POS'])\n",
    "#             var = row['VAR']\n",
    "#             if rule not in canonical_db:\n",
    "#                 canonical_db[rule] = {}\n",
    "#             canonical_db[rule][pos] = var\n",
    "\n",
    "    canonical_db_fact_strs = []\n",
    "    for rule, rule_desc in canonical_db.items():\n",
    "        if isinstance(rule, tuple):\n",
    "            rule = rule[0]\n",
    "        r_body = [rule_desc[k] for k in sorted(rule_desc.keys())]\n",
    "        if pw_id is not None:\n",
    "            r_body.insert(0, str(pw_id))\n",
    "        if len(r_body) > 0:\n",
    "            r_body_j = ', '.join(r_body)\n",
    "            canonical_db_fact_strs.append(f'{rule}({r_body_j}).')\n",
    "        else:\n",
    "            canonical_db_fact_strs.append(f'{rule}.')\n",
    "        \n",
    "    return canonical_db_fact_strs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "can_dbs = []\n",
    "q_strs = []\n",
    "for i in range(1, len(query_analysis['pw_objs'])+1):\n",
    "    \n",
    "    pw_rel_dfs, pw_objs = pw_slicer(query_analysis['pw_rel_dfs'], query_analysis['pw_objs'], [i])\n",
    "    pw_obj = pw_objs[0]\n",
    "    pw_can_db = get_canonical_db_mod(pw_rel_dfs, pw_id=i)\n",
    "    can_dbs.extend(pw_can_db)\n",
    "    #print(pw_can_db)\n",
    "    pw_q_str = print_rewritten_query_string(pw_rel_dfs, html=False, display_q=False, include_ineqls=False)\n",
    "    pw_q_str = pw_q_str.replace('thop(', f'q({i},QID,')\n",
    "    pw_q_str = pw_q_str.replace('e(', f'e(QID,')\n",
    "    pw_q_str = pw_q_str.replace('.', ', qid(QID).')\n",
    "    q_strs.append(pw_q_str)\n",
    "    #print(pw_q_str)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "e(1, \"X\", \"Z\").\n",
      "e(1, \"Z\", \"Y\").\n",
      "thop(1, \"X\", \"Y\").\n",
      "e(2, \"X\", \"Y\").\n",
      "e(2, \"Y\", \"Y\").\n",
      "thop(2, \"X\", \"Y\").\n",
      "e(3, \"X\", \"X\").\n",
      "e(3, \"X\", \"Y\").\n",
      "thop(3, \"X\", \"Y\").\n",
      "e(4, \"X\", \"Z\").\n",
      "e(4, \"Z\", \"X\").\n",
      "thop(4, \"X\", \"X\").\n",
      "e(5, \"X\", \"X\").\n",
      "e(5, \"X\", \"X\").\n",
      "thop(5, \"X\", \"X\").\n",
      "q(1,QID,X,Y) :- e(QID,X,Z), e(QID,Z,Y), qid(QID).\n",
      "q(2,QID,X,Y) :- e(QID,X,Y), e(QID,Y,Y), qid(QID).\n",
      "q(3,QID,X,Y) :- e(QID,X,X), e(QID,X,Y), qid(QID).\n",
      "q(4,QID,X,X) :- e(QID,X,Z), e(QID,Z,X), qid(QID).\n",
      "q(5,QID,X,X) :- e(QID,X,X), e(QID,X,X), qid(QID).\n"
     ]
    }
   ],
   "source": [
    "print(\"\\n\".join(can_dbs+q_strs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_containment_aio_encoding(query_str, num_queries):\n",
    "    listener = parse_dlv_rules(query_str, print_parse_tree=False)\n",
    "    logic_atom_types = set([])\n",
    "    \n",
    "    qid_dec_rule = f'qid(1..{num_queries}).'\n",
    "    \n",
    "    assert len(listener.rules) == 1\n",
    "    rule = listener.rules[0]\n",
    "    head_atoms = rule[0]\n",
    "    assert len(head_atoms) == 1\n",
    "    head_atom = head_atoms[0]\n",
    "    head_atom_name, head_atom_arity = head_atom.rel_name, head_atom.rel_arity\n",
    "    \n",
    "    q_args = ['QID1', 'QID2'] + [f'A{i}' for i in range(head_atom_arity)]\n",
    "    \n",
    "    doesnt_contain_rule = 'doesnt_contain(QID1, QID2) :- not q({}), {}({}), qid(QID1), qid(QID2).'.format(','.join(q_args), head_atom_name, ','.join(q_args[1:]))\n",
    "    contains_rule = 'contains(QID1, QID2) :- not doesnt_contain(QID1, QID2), qid(QID1), qid(QID2), QID1 != QID2.'\n",
    "    contains_transitive_rule = 'contains(QID1, QID3) :- contains(QID1, QID2), contains(QID2, QID3), qid(QID1), qid(QID2), qid(QID3).'\n",
    "    \n",
    "    graphviz_annotations = [\n",
    "        '%graphviz graph graph_type=directed rankdir=TB',\n",
    "        '%graphviz edge contains(HEAD, TAIL)'\n",
    "    ]\n",
    "    show_rule = '#show contains/2.'\n",
    "    \n",
    "    return [qid_dec_rule, doesnt_contain_rule, contains_rule, contains_transitive_rule, *graphviz_annotations, show_rule]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
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       "<div class=\"highlight\"><pre><span></span><span class=\"lineno\">1 </span><span class=\"nf\">qid</span><span class=\"p\">(</span><span class=\"mf\">1..5</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">2 </span><span class=\"nf\">doesnt_contain</span><span class=\"p\">(</span><span class=\"nv\">QID1</span><span class=\"p\">,</span> <span class=\"nv\">QID2</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"o\">not</span> <span class=\"nf\">q</span><span class=\"p\">(</span><span class=\"nv\">QID1</span><span class=\"p\">,</span><span class=\"nv\">QID2</span><span class=\"p\">,</span><span class=\"nv\">A0</span><span class=\"p\">,</span><span class=\"nv\">A1</span><span class=\"p\">),</span> <span class=\"nf\">thop</span><span class=\"p\">(</span><span class=\"nv\">QID2</span><span class=\"p\">,</span><span class=\"nv\">A0</span><span class=\"p\">,</span><span class=\"nv\">A1</span><span class=\"p\">),</span> <span class=\"nf\">qid</span><span class=\"p\">(</span><span class=\"nv\">QID1</span><span class=\"p\">),</span> <span class=\"nf\">qid</span><span class=\"p\">(</span><span class=\"nv\">QID2</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">3 </span><span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"nv\">QID1</span><span class=\"p\">,</span> <span class=\"nv\">QID2</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"o\">not</span> <span class=\"nf\">doesnt_contain</span><span class=\"p\">(</span><span class=\"nv\">QID1</span><span class=\"p\">,</span> <span class=\"nv\">QID2</span><span class=\"p\">),</span> <span class=\"nf\">qid</span><span class=\"p\">(</span><span class=\"nv\">QID1</span><span class=\"p\">),</span> <span class=\"nf\">qid</span><span class=\"p\">(</span><span class=\"nv\">QID2</span><span class=\"p\">),</span> <span class=\"nv\">QID1</span> <span class=\"p\">!</span><span class=\"o\">=</span> <span class=\"nv\">QID2</span><span class=\"p\">.</span>\n",
       "<span class=\"lineno\">4 </span><span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"nv\">QID1</span><span class=\"p\">,</span> <span class=\"nv\">QID3</span><span class=\"p\">)</span> <span class=\"p\">:-</span> <span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"nv\">QID1</span><span class=\"p\">,</span> <span class=\"nv\">QID2</span><span class=\"p\">),</span> <span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"nv\">QID2</span><span class=\"p\">,</span> <span class=\"nv\">QID3</span><span class=\"p\">),</span> <span class=\"nf\">qid</span><span class=\"p\">(</span><span class=\"nv\">QID1</span><span class=\"p\">),</span> <span class=\"nf\">qid</span><span class=\"p\">(</span><span class=\"nv\">QID2</span><span class=\"p\">),</span> <span class=\"nf\">qid</span><span class=\"p\">(</span><span class=\"nv\">QID3</span><span class=\"p\">).</span>\n",
       "<span class=\"lineno\">5 </span><span class=\"c1\">%graphviz graph graph_type=directed rankdir=TB</span>\n",
       "<span class=\"lineno\">6 </span><span class=\"c1\">%graphviz edge contains(HEAD, TAIL)</span>\n",
       "<span class=\"lineno\">7 </span><span class=\"c1\">#show contains/2.</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'qid(1..5).\\ndoesnt_contain(QID1, QID2) :- not q(QID1,QID2,A0,A1), thop(QID2,A0,A1), qid(QID1), qid(QID2).\\ncontains(QID1, QID2) :- not doesnt_contain(QID1, QID2), qid(QID1), qid(QID2), QID1 != QID2.\\ncontains(QID1, QID3) :- contains(QID1, QID2), contains(QID2, QID3), qid(QID1), qid(QID2), qid(QID3).\\n%graphviz graph graph_type=directed rankdir=TB\\n%graphviz edge contains(HEAD, TAIL)\\n#show contains/2.'"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "containment_aio = '\\n'.join(create_containment_aio_encoding(query_str, len(query_analysis['pw_objs'])))\n",
    "ASPRules(containment_aio)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output:\n"
     ]
    },
    {
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      "text/html": [
       "<div class=\"highlight\"><pre><span></span><span class=\"lineno\">1 </span><span class=\"nv\">Answer</span><span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\">2 </span><span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">)</span> <span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">4</span><span class=\"p\">)</span> <span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">5</span><span class=\"p\">)</span> <span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">5</span><span class=\"p\">)</span> <span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span><span class=\"mi\">5</span><span class=\"p\">)</span> <span class=\"nf\">contains</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">,</span><span class=\"mi\">5</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">3 </span><span class=\"nv\">SATISFIABLE</span>\n",
       "<span class=\"lineno\">4 </span>\n",
       "<span class=\"lineno\">5 </span><span class=\"nv\">Models</span>       <span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\">6 </span><span class=\"nv\">Calls</span>        <span class=\"s s-Atom\">:</span> <span class=\"mi\">1</span>\n",
       "<span class=\"lineno\">7 </span><span class=\"nv\">Time</span>         <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.002</span><span class=\"nf\">s</span> <span class=\"p\">(</span><span class=\"nv\">Solving</span><span class=\"s s-Atom\">:</span> <span class=\"mf\">0.00</span><span class=\"s s-Atom\">s</span> <span class=\"mi\">1</span><span class=\"s s-Atom\">st</span> <span class=\"nv\">Model</span><span class=\"s s-Atom\">:</span> <span class=\"mf\">0.00</span><span class=\"s s-Atom\">s</span> <span class=\"nv\">Unsat</span><span class=\"s s-Atom\">:</span> <span class=\"mf\">0.00</span><span class=\"s s-Atom\">s</span><span class=\"p\">)</span>\n",
       "<span class=\"lineno\">8 </span><span class=\"nv\">CPU</span> <span class=\"nv\">Time</span>     <span class=\"s s-Atom\">:</span> <span class=\"mf\">0.002</span><span class=\"s s-Atom\">s</span>\n",
       "</pre></div>\n"
      ],
      "text/plain": [
       "'Answer: 1\\ncontains(1,2) contains(1,3) contains(1,4) contains(1,5) contains(2,5) contains(3,5) contains(4,5)\\nSATISFIABLE\\n\\nModels       : 1\\nCalls        : 1\\nTime         : 0.002s (Solving: 0.00s 1st Model: 0.00s Unsat: 0.00s)\\nCPU Time     : 0.002s'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%clingo --donot-display_input -l can_dbs q_strs containment_aio -exp containment_exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Models: 1\n"
     ]
    }
   ],
   "source": [
    "containment_exp['pw_rel_dfs'], containment_exp['rel_schema'], containment_exp['pw_objs'] =load_worlds(containment_exp['asp_soln'],\n",
    "                                                                                                   containment_exp['meta_data'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "containment_exp_g = nx.DiGraph()\n",
    "containment_exp_g.add_nodes_from(range(1, len(query_analysis['pw_objs'])+1))\n",
    "for _, row in containment_exp['pw_rel_dfs']['contains_2'].iterrows():\n",
    "    if int(row['x1']) != int(row['x2']):\n",
    "        containment_exp_g.add_edge(int(row['x1']), int(row['x2']))\n",
    "\n",
    "draw(containment_exp_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "keep_running = True\n",
    "while keep_running:\n",
    "    keep_running=False\n",
    "    for eu, ev in list(containment_exp_g.edges):\n",
    "        if eu == ev:\n",
    "            continue\n",
    "        if (ev,eu) in list(containment_exp_g.edges):\n",
    "            print(f\"Merging {eu} and {ev}\")\n",
    "            containment_exp_g = nx.contracted_nodes(containment_exp_g, min(eu,ev), max(eu,ev), self_loops=False)\n",
    "            keep_running = True\n",
    "            break\n",
    "\n",
    "draw(containment_exp_g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_ = nx.algorithms.dag.transitive_reduction(containment_exp_g)\n",
    "\n",
    "# Copy over the style properties (the nx.algorithms.dag.transitive_reduction loses these)\n",
    "# for n in g.nodes:\n",
    "#     for k,v in g.nodes[n].items():\n",
    "#         g_.nodes[n][k] = v\n",
    "for e in g_.edges:\n",
    "    g_.edges[e]['dir'] = 'back'\n",
    "draw(g_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_head_encoding = g_.copy()\n",
    "for n in g_head_encoding.nodes.keys():\n",
    "    g_head_encoding.nodes[n]['label'] = pw_id_to_head_encoding[int(n)]\n",
    "draw(g_head_encoding)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}