subsumption_relations_final.ipynb

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    "colab": {
      "name": "subsumption-relations-final.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PHncwB-qClIU"
      },
      "source": [
        "# **Identifying Method-Level Mutant Subsumption Relations in Z3**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MrqeMMOJUE5m"
      },
      "source": [
        "### **Importing Libraries**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7uXQRP_kwgN8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dc562ff9-bb1f-4cc2-e06f-6525e11d8a3f"
      },
      "source": [
        "try:\n",
        "  import z3\n",
        "except:\n",
        "  !pip install z3-solver\n",
        "  import z3\n",
        "\n",
        "from z3 import *\n",
        "from graphviz import Digraph\n",
        "\n",
        "import math\n",
        "import pandas\n",
        "import random as rd\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting z3-solver\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/6d/51/86d4d708593b77dd43e1154f25b107d9d9a3300da49759c88254192a0a04/z3_solver-4.8.9.0-py2.py3-none-manylinux1_x86_64.whl (30.5MB)\n",
            "\u001b[K     |████████████████████████████████| 30.5MB 146kB/s \n",
            "\u001b[?25hInstalling collected packages: z3-solver\n",
            "Successfully installed z3-solver-4.8.9.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AWle2sLbSL5K"
      },
      "source": [
        "### **Declaring Z3 Utility Functions**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k8xeBdcN471q"
      },
      "source": [
        "def check(f):\n",
        "  s = Solver()\n",
        "  s.add(f)\n",
        "  r = s.check()\n",
        "# all your queries are in a decidable fragment\n",
        "  if r == unknown:\n",
        "    print(\"unexpected unknown result for \", f)\n",
        "  return r\n",
        "\n",
        "def is_sat(f):\n",
        "  return check(f) == sat\n",
        "\n",
        "def is_unsat(f):\n",
        "  return check(f) == unsat\n",
        "\n",
        "def kills(p, m):\n",
        "  return p != m\n",
        "\n",
        "#This function proves a theorem using the Z3 Python API.\n",
        "def prove(theorem):\n",
        "    s = Solver()\n",
        "    s.add(Not(theorem))\n",
        "    if s.check() == unsat:\n",
        "      return 1 # The theorem was proved\n",
        "    else:\n",
        "      if s.check() == unknown:\n",
        "        print(\"unexpected unknown result for \", theorem)\n",
        "        return 2 # Z3 does not know how to prove the theorem\n",
        "      else:\n",
        "        return 0 # It is not a valid theorem"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NYmpYbVLSZv_"
      },
      "source": [
        "### **Identifying Equivalent Mutants**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AFiKjV048ARl"
      },
      "source": [
        "# keeping the non equivalent mutants\n",
        "def keepNonEquivalentMutants(p, muts):\n",
        "  return [m for m in muts if prove(p==m)!=1]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d8wY8jfHS-6n"
      },
      "source": [
        "### **Identifying Redundant Mutants**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U5Qk9ZT-S-DP"
      },
      "source": [
        "# keeping the non redundant mutants\n",
        "def redundantMutants(m1,m2):\n",
        "  if prove(m1==m2) == 1:\n",
        "    print(str(m1)+\" is duplicate to \"+str(m2))  \n",
        "    return True\n",
        "  else:\n",
        "    return False\n",
        "\n",
        "def keepNonRedundantMutants(muts):\n",
        "  non_redundant = []\n",
        "  for m1 in muts:\n",
        "    if not any(redundantMutants(m1, m2) for m2 in non_redundant):\n",
        "      non_redundant.append(m1)\n",
        "  return non_redundant"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D2NlOrKXTEoa"
      },
      "source": [
        "### **Identifying Subsumption Relations**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sEc47OMJTLh2"
      },
      "source": [
        "# condition 1\n",
        "def is_non_empty(p, cond, m):\n",
        "  return is_sat(And(cond, kills(p, m)))\n",
        "\n",
        "# condition 2\n",
        "def is_subset(p, cond, m1, m2):\n",
        "  return is_unsat(And(cond, kills(p, m2), Not(kills(p, m1))))\n",
        "\n",
        "# condition 3\n",
        "def is_strict(p, cond, m1, m2):\n",
        "  return is_sat(And(cond, kills(p, m1), Not(kills(p, m2))))\n",
        "\n",
        "def subsumption(p,m1,m2,conds):\n",
        "  t1 = is_non_empty(p, conds, m2)\n",
        "  t2 = is_subset(p, conds, m1, m2)\n",
        "  if t1 == 1 and t2 == 1:\n",
        "    print(str(m2)+\" subsumes \"+str(m1))\n",
        "    return (m2,m1)\n",
        "  else:\n",
        "    return None\n",
        "\n",
        "def identifySubsumptions(p, muts, conds):\n",
        "  result = []\n",
        "  for i in range(len(muts)):\n",
        "    for j in range(len(muts)):\n",
        "      if i != j:\n",
        "        s = subsumption(p,muts[i], muts[j], conds)\n",
        "        if (s is not None):\n",
        "          result.append(s)\n",
        "  return result"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-eJ-4mJKTMra"
      },
      "source": [
        "#### **Creating a Subsumption Relation Graph**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wquBXTKdTPB8"
      },
      "source": [
        "def createSubsumptionRelationGraph(subsumptions, mutations, mutationNames):\n",
        "  graph = Digraph('G')\n",
        "  for m in mutations:\n",
        "      graph.node(mutationNames[str(m)])\n",
        "  for s in subsumptions:\n",
        "    x = mutationNames[str(s[0])]\n",
        "    y = mutationNames[str(s[1])]\n",
        "    graph.edge(x,y)\n",
        "  return graph"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zr98LChuwAyL"
      },
      "source": [
        "**Declaring common functions**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_Q-RvrQbwLIj"
      },
      "source": [
        "def xor(a,b):\n",
        "    return Or(And(a,Not(b)),And(Not(a),b))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Z9x5Mv5GoYX"
      },
      "source": [
        "### **Using our approach to prove subsumption relations for 37 mutation targets**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TABi27L2Q6U4"
      },
      "source": [
        "**A.1 Arithmetic expressions with integers:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U1xdoUCYQ9bP"
      },
      "source": [
        "# 1) Declare variables and conditions\n",
        "x = Int('x')\n",
        "y = Int('y')\n",
        "conditions = And(x>0,y>0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OLv4IV_7RDKI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 572
        },
        "outputId": "329a7614-c454-4ea4-b961-454a655a60df"
      },
      "source": [
        "msg = \"A.1.1 lexp + rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x+y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x*y, x-y, x, y]\n",
        "mutationNames =\t{\n",
        "  \"x*y\": \"AORB *\",\n",
        "  \"x - y\": \"AORB -\",\n",
        "  \"x\": \"CDL/VDL/ODL y\",\n",
        "  \"y\": \"CDL/VDL/ODL x\",\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.1.1 lexp + rexp\n",
            "============================================\n",
            "x*y subsumes x - y\n",
            "x subsumes x - y\n",
            "y subsumes x - y\n",
            "x*y subsumes x\n",
            "x - y subsumes x\n",
            "y subsumes x\n",
            "x*y subsumes y\n",
            "x - y subsumes y\n",
            "x subsumes y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e4HQhpR7YS9j",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 572
        },
        "outputId": "361368d8-22a8-4928-a53b-a28e1f5a8c56"
      },
      "source": [
        "msg = \"A.1.2 lexp - rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x-y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x*y, x+y, x, y]\n",
        "mutationNames = {\n",
        "  \"x*y\": \"AORB *\",\n",
        "  \"x + y\": \"AORB +\",\n",
        "  \"x\": \"CDL/VDL/ODL y\",\n",
        "  \"y\": \"CDL/VDL/ODL x\", \n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.1.2 lexp - rexp\n",
            "============================================\n",
            "x + y subsumes x*y\n",
            "x subsumes x*y\n",
            "y subsumes x*y\n",
            "x*y subsumes x + y\n",
            "x subsumes x + y\n",
            "y subsumes x + y\n",
            "x*y subsumes x\n",
            "x + y subsumes x\n",
            "y subsumes x\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f2ZOjU9MaADf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 278
        },
        "outputId": "4d939ced-8b9b-4dfe-c054-ecabbcb3303b"
      },
      "source": [
        "msg = \"A.1.3 lexp * rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x*y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x-y, x+y, x, y]\n",
        "mutationNames = {\n",
        "  \"x - y\": \"AORB -\",\n",
        "  \"x + y\": \"AORB +\",\n",
        "  \"x\": \"CDL/VDL/ODL y\",\n",
        "  \"y\": \"CDL/VDL/ODL x\", \n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.1.3 lexp * rexp\n",
            "============================================\n",
            "x + y subsumes x - y\n",
            "x subsumes x - y\n",
            "y subsumes x - y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
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          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sx1vFVszbksd"
      },
      "source": [
        "**A.2 Logic expressions with booleans:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g1dRr4kMbwnm"
      },
      "source": [
        "# 1) Declare variables and conditions\n",
        "x = Bool('x')\n",
        "y = Bool('y')\n",
        "conditions = True"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9sx8smLOnUMb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 691
        },
        "outputId": "5756cd36-0418-4801-d7d1-072ec52a5b74"
      },
      "source": [
        "msg = \"A.2.1 lexp ^ rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = xor(x,y)\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True, False, Or(x,y), x, y, Not(program), x==y, \n",
        "             x!=y,And(x,y), xor(Not(x),y), xor(x,Not(y))]\n",
        "mutationNames = {\n",
        "    \"True\": \"COR true\",\n",
        "    \"False\": \"COR false\",\n",
        "    \"Or(x, y)\": \"COR ||\",\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\",\n",
        "    \"Not(Or(And(x, Not(y)), And(Not(x), y)))\": \"COI !()\",\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"x != y\": \"ROR !=\",\n",
        "    \"And(x, y)\": \"COR &&\",\n",
        "    \"Not(x)^y\": \"COI !x ^ y\",\n",
        "    \"x^Not(y)\": \"COI x ^ !y\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.2.1 lexp ^ rexp\n",
            "============================================\n",
            "x == y is duplicate to Not(Or(And(x, Not(y)), And(Not(x), y)))\n",
            "Or(And(Not(x), Not(y)), And(Not(Not(x)), y)) is duplicate to Not(Or(And(x, Not(y)), And(Not(x), y)))\n",
            "Or(And(x, Not(Not(y))), And(Not(x), Not(y))) is duplicate to Not(Or(And(x, Not(y)), And(Not(x), y)))\n",
            "Or(x, y) subsumes True\n",
            "Or(x, y) subsumes x\n",
            "Or(x, y) subsumes y\n",
            "True subsumes Not(Or(And(x, Not(y)), And(Not(x), y)))\n",
            "False subsumes Not(Or(And(x, Not(y)), And(Not(x), y)))\n",
            "Or(x, y) subsumes Not(Or(And(x, Not(y)), And(Not(x), y)))\n",
            "x subsumes Not(Or(And(x, Not(y)), And(Not(x), y)))\n",
            "y subsumes Not(Or(And(x, Not(y)), And(Not(x), y)))\n",
            "And(x, y) subsumes Not(Or(And(x, Not(y)), And(Not(x), y)))\n",
            "False subsumes And(x, y)\n",
            "Or(x, y) subsumes And(x, y)\n",
            "x subsumes And(x, y)\n",
            "y subsumes And(x, y)\n",
            "============================================\n"
          ],
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        },
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          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hct4ldaMztgR",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 861
        },
        "outputId": "d6956229-17ab-42ea-f348-b004f2d705d5"
      },
      "source": [
        "msg = \"A.2.2 lexp && rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = And(x,y)\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True, False, Or(x,y), x, y, Not(program), x==y, \n",
        "             x!=y,xor(x,y), And(Not(x),y), And(x, Not(y))]\n",
        "mutationNames = {\n",
        "    \"True\": \"COR true\",\n",
        "    \"False\": \"COR false\",\n",
        "    \"Or(x, y)\": \"COR ||\",\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\",\n",
        "    \"Not(And(x, y))\": \"COI !()\",\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"x != y\": \"ROR !=\",\n",
        "    \"Or(And(x, Not(y)), And(Not(x), y))\": \"COR ^\",\n",
        "    \"And(Not(x), y)\": \"COR !x && y\",\n",
        "    \"And(x, Not(y))\": \"COR x && !y\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.2.2 lexp && rexp\n",
            "============================================\n",
            "Or(And(x, Not(y)), And(Not(x), y)) is duplicate to x != y\n",
            "Or(x, y) subsumes True\n",
            "x subsumes True\n",
            "y subsumes True\n",
            "x == y subsumes True\n",
            "x subsumes Or(x, y)\n",
            "y subsumes Or(x, y)\n",
            "True subsumes Not(And(x, y))\n",
            "False subsumes Not(And(x, y))\n",
            "Or(x, y) subsumes Not(And(x, y))\n",
            "x subsumes Not(And(x, y))\n",
            "y subsumes Not(And(x, y))\n",
            "x == y subsumes Not(And(x, y))\n",
            "x != y subsumes Not(And(x, y))\n",
            "And(Not(x), y) subsumes Not(And(x, y))\n",
            "And(x, Not(y)) subsumes Not(And(x, y))\n",
            "False subsumes x != y\n",
            "Or(x, y) subsumes x != y\n",
            "x subsumes x != y\n",
            "y subsumes x != y\n",
            "And(Not(x), y) subsumes x != y\n",
            "And(x, Not(y)) subsumes x != y\n",
            "False subsumes And(Not(x), y)\n",
            "y subsumes And(Not(x), y)\n",
            "False subsumes And(x, Not(y))\n",
            "x subsumes And(x, Not(y))\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Nnsik_yd76UQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 861
        },
        "outputId": "52ae3bb5-738a-462e-b572-2dac6f3d39c3"
      },
      "source": [
        "msg = \"A.2.3 lexp || rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = Or(x,y)\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True, False, And(x,y), x, y, Not(program), x==y, \n",
        "             x!=y,xor(x,y), Or(Not(x),y), Or(x, Not(y))]\n",
        "mutationNames = {\n",
        "    \"True\": \"COR true\",\n",
        "    \"False\": \"COR false\",\n",
        "    \"And(x, y)\": \"COR &&\",\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\",\n",
        "    \"Not(Or(x, y))\": \"COI !()\",\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"x != y\": \"ROR !=\",\n",
        "    \"Or(And(x, Not(y)), And(Not(x), y))\": \"COR ^\",\n",
        "    \"Or(Not(x), y)\": \"COI !x || y\",\n",
        "    \"Or(x, Not(y))\": \"COI x || !y\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.2.3 lexp || rexp\n",
            "============================================\n",
            "Or(And(x, Not(y)), And(Not(x), y)) is duplicate to x != y\n",
            "And(x, y) subsumes False\n",
            "x subsumes False\n",
            "y subsumes False\n",
            "x != y subsumes False\n",
            "x subsumes And(x, y)\n",
            "y subsumes And(x, y)\n",
            "True subsumes Not(Or(x, y))\n",
            "False subsumes Not(Or(x, y))\n",
            "And(x, y) subsumes Not(Or(x, y))\n",
            "x subsumes Not(Or(x, y))\n",
            "y subsumes Not(Or(x, y))\n",
            "x == y subsumes Not(Or(x, y))\n",
            "x != y subsumes Not(Or(x, y))\n",
            "Or(Not(x), y) subsumes Not(Or(x, y))\n",
            "Or(x, Not(y)) subsumes Not(Or(x, y))\n",
            "True subsumes x == y\n",
            "And(x, y) subsumes x == y\n",
            "x subsumes x == y\n",
            "y subsumes x == y\n",
            "Or(Not(x), y) subsumes x == y\n",
            "Or(x, Not(y)) subsumes x == y\n",
            "True subsumes Or(Not(x), y)\n",
            "y subsumes Or(Not(x), y)\n",
            "True subsumes Or(x, Not(y))\n",
            "x subsumes Or(x, Not(y))\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f25b94446d8>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2bB0BsK0Fj6r",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "outputId": "6e654f18-2ce9-47a6-f3c7-6d4695549426"
      },
      "source": [
        "msg = \"A.2.4 (bool) lexp == rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x==y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [Not(program), x!=y,Not(x)==y,x==Not(y),x,y]\n",
        "mutationNames = {\n",
        "    \"Not(x == y)\": \"COI !()\",\n",
        "    \"x!=y\": \"ROR !=\",\n",
        "    \"Not(x) == y\": \"COI !x == y\",\n",
        "    \"x == Not(y)\": \"COI x == !y\",\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.2.4 (bool) lexp == rexp\n",
            "============================================\n",
            "x != y is duplicate to Not(x == y)\n",
            "Not(x) == y is duplicate to Not(x == y)\n",
            "x == Not(y) is duplicate to Not(x == y)\n",
            "x subsumes Not(x == y)\n",
            "y subsumes Not(x == y)\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zZeU3fdcHLCB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "outputId": "26c45867-d641-409c-a250-4e1f52d5a695"
      },
      "source": [
        "msg = \"A.2.5 (bool) lexp != rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x!=y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x==y,Not(program),Not(x)!=y,x!=Not(y),x,y]\n",
        "mutationNames = {\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"Not(x != y)\": \"COI ()\",\n",
        "    \"Not(x) != y\": \"COI !x != y\",\n",
        "    \"x != Not(y)\": \"COI x != !y\",\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.2.5 (bool) lexp != rexp\n",
            "============================================\n",
            "Not(x != y) is duplicate to x == y\n",
            "Not(x) != y is duplicate to x == y\n",
            "x != Not(y) is duplicate to x == y\n",
            "x subsumes x == y\n",
            "y subsumes x == y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
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          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aKg2bVONKcsC"
      },
      "source": [
        "**A.3 Relational expressions with integers:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qUNqzxYaKuNJ"
      },
      "source": [
        "# 1) Declare variables and conditions\n",
        "x = Int('x')\n",
        "y = Int('y')\n",
        "conditions = True"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2ZNiDkOkKvIO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "outputId": "e423508d-57f8-4791-a862-9d8bb76403ce"
      },
      "source": [
        "msg = \"A.3.1 lexp == rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x==y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True,False,x>=y,x<=y,x>y,x<y,x!=y,Not(program)]\n",
        "mutationNames = {\n",
        "    \"True\": \"ROR true\",\n",
        "    \"False\": \"ROR false\",\n",
        "    \"x >= y\": \"ROR >=\",\n",
        "    \"x <= y\": \"ROR <=\",\n",
        "    \"x > y\": \"ROR >\",\n",
        "    \"x < y\": \"ROR <\",\n",
        "    \"x != y\": \"ROR !=\",\n",
        "    \"Not(x == y)\": \"COI !()\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.3.1 lexp == rexp\n",
            "============================================\n",
            "Not(x == y) is duplicate to x != y\n",
            "x >= y subsumes True\n",
            "x <= y subsumes True\n",
            "False subsumes x > y\n",
            "x >= y subsumes x > y\n",
            "False subsumes x < y\n",
            "x <= y subsumes x < y\n",
            "True subsumes x != y\n",
            "False subsumes x != y\n",
            "x >= y subsumes x != y\n",
            "x <= y subsumes x != y\n",
            "x > y subsumes x != y\n",
            "x < y subsumes x != y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
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          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SrDeCzSQPAZl",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "outputId": "6d5cbf9c-3555-41e2-f186-24ff7f427ac1"
      },
      "source": [
        "msg = \"A.3.2 lexp != rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x!=y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True,False,x>=y,x<=y,x>y,x<y,x==y,Not(program)]\n",
        "mutationNames = {\n",
        "    \"True\": \"ROR true\",\n",
        "    \"False\": \"ROR false\",\n",
        "    \"x >= y\": \"ROR >=\",\n",
        "    \"x <= y\": \"ROR <=\",\n",
        "    \"x > y\": \"ROR >\",\n",
        "    \"x < y\": \"ROR <\",\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"Not(x != y)\": \"COI !()\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.3.2 lexp != rexp\n",
            "============================================\n",
            "Not(x != y) is duplicate to x == y\n",
            "x > y subsumes False\n",
            "x < y subsumes False\n",
            "True subsumes x >= y\n",
            "x > y subsumes x >= y\n",
            "True subsumes x <= y\n",
            "x < y subsumes x <= y\n",
            "True subsumes x == y\n",
            "False subsumes x == y\n",
            "x >= y subsumes x == y\n",
            "x <= y subsumes x == y\n",
            "x > y subsumes x == y\n",
            "x < y subsumes x == y\n",
            "============================================\n"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_wG54U6rQI09",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "outputId": "ca7326e4-baaa-4408-e0a6-e0036f093c38"
      },
      "source": [
        "msg = \"A.3.3 lexp > rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x>y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True,False,x>=y,x<=y,x<y,x==y,x!=y,Not(program)]\n",
        "mutationNames = {\n",
        "    \"True\": \"ROR true\",\n",
        "    \"False\": \"ROR false\",\n",
        "    \"x >= y\": \"ROR >=\",\n",
        "    \"x <= y\": \"ROR <=\",\n",
        "    \"x < y\": \"ROR <\",\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"x != y\": \"ROR !=\",\n",
        "    \"Not(x > y)\": \"COI !()\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.3.3 lexp > rexp\n",
            "============================================\n",
            "Not(x > y) is duplicate to x <= y\n",
            "x >= y subsumes True\n",
            "x != y subsumes True\n",
            "True subsumes x <= y\n",
            "False subsumes x <= y\n",
            "x >= y subsumes x <= y\n",
            "x < y subsumes x <= y\n",
            "x == y subsumes x <= y\n",
            "x != y subsumes x <= y\n",
            "False subsumes x < y\n",
            "x != y subsumes x < y\n",
            "False subsumes x == y\n",
            "x >= y subsumes x == y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
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          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q44FzvfqS8JC",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "outputId": "a279d1cf-75dd-47ae-d6ac-583ff23bd507"
      },
      "source": [
        "msg = \"A.3.4 lexp >= rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x>=y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True,False,x<=y,x<y,x>y,x==y,x!=y,Not(program)]\n",
        "mutationNames = {\n",
        "    \"True\": \"ROR true\",\n",
        "    \"False\": \"ROR false\",\n",
        "    \"x > y\": \"ROR >\",\n",
        "    \"x <= y\": \"ROR <=\",\n",
        "    \"x < y\": \"ROR <\",\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"x != y\": \"ROR !=\",\n",
        "    \"Not(x >= y)\": \"COI !()\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.3.4 lexp >= rexp\n",
            "============================================\n",
            "Not(x >= y) is duplicate to x < y\n",
            "x > y subsumes False\n",
            "x == y subsumes False\n",
            "True subsumes x <= y\n",
            "x == y subsumes x <= y\n",
            "True subsumes x < y\n",
            "False subsumes x < y\n",
            "x <= y subsumes x < y\n",
            "x > y subsumes x < y\n",
            "x == y subsumes x < y\n",
            "x != y subsumes x < y\n",
            "True subsumes x != y\n",
            "x > y subsumes x != y\n",
            "============================================\n"
          ],
          "name": "stdout"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h9_wpljNTuyj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "outputId": "fa0054e2-ee5f-4a57-c2fc-6de1e89448b3"
      },
      "source": [
        "msg = \"A.3.5 lexp < rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x<y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True,False,x<=y,x>=y,x>y,x==y,x!=y,Not(program)]\n",
        "mutationNames = {\n",
        "    \"True\": \"ROR true\",\n",
        "    \"False\": \"ROR false\",\n",
        "    \"x > y\": \"ROR >\",\n",
        "    \"x <= y\": \"ROR <=\",\n",
        "    \"x >= y\": \"ROR >=\",\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"x != y\": \"ROR !=\",\n",
        "    \"Not(x < y)\": \"COI !()\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.3.5 lexp < rexp\n",
            "============================================\n",
            "Not(x < y) is duplicate to x >= y\n",
            "x <= y subsumes True\n",
            "x != y subsumes True\n",
            "True subsumes x >= y\n",
            "False subsumes x >= y\n",
            "x <= y subsumes x >= y\n",
            "x > y subsumes x >= y\n",
            "x == y subsumes x >= y\n",
            "x != y subsumes x >= y\n",
            "False subsumes x > y\n",
            "x != y subsumes x > y\n",
            "False subsumes x == y\n",
            "x <= y subsumes x == y\n",
            "============================================\n"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rhxhkbm_VU_m",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "outputId": "cd7a8028-c44d-46dc-da5f-35b95ea76203"
      },
      "source": [
        "msg = \"A.3.6 lexp <= rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x<=y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True,False,x>=y,x<y,x>y,x==y,x!=y,Not(program)]\n",
        "mutationNames = {\n",
        "    \"True\": \"ROR true\",\n",
        "    \"False\": \"ROR false\",\n",
        "    \"x < y\": \"ROR <\",\n",
        "    \"x > y\": \"ROR >\",\n",
        "    \"x >= y\": \"ROR >=\",\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"x != y\": \"ROR !=\",\n",
        "    \"Not(x < y)\": \"COI !()\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.3.6 lexp <= rexp\n",
            "============================================\n",
            "Not(x <= y) is duplicate to x > y\n",
            "x < y subsumes False\n",
            "x == y subsumes False\n",
            "True subsumes x >= y\n",
            "x == y subsumes x >= y\n",
            "True subsumes x > y\n",
            "False subsumes x > y\n",
            "x >= y subsumes x > y\n",
            "x < y subsumes x > y\n",
            "x == y subsumes x > y\n",
            "x != y subsumes x > y\n",
            "True subsumes x != y\n",
            "x < y subsumes x != y\n",
            "============================================\n"
          ],
          "name": "stdout"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ICzxGguKWSm_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "outputId": "2880e2c5-7f81-4185-da57-0e465aec4751"
      },
      "source": [
        "msg = \"A.3.7 (obj) lexp != rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x!=y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [True,False,x>y,x<y,x==y,x<=y,x>=y,Not(program)]\n",
        "mutationNames = {\n",
        "    \"True\": \"ROR true\",\n",
        "    \"False\": \"ROR false\",\n",
        "    \"x < y\": \"ROR <\",\n",
        "    \"x > y\": \"ROR >\",\n",
        "    \"x >= y\": \"ROR >=\",\n",
        "    \"x <= y\": \"ROR <=\",\n",
        "    \"x == y\": \"ROR ==\",\n",
        "    \"Not(x x!= y)\": \"COI !()\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.3.7 (obj) lexp != rexp\n",
            "============================================\n",
            "Not(x != y) is duplicate to x == y\n",
            "x > y subsumes False\n",
            "x < y subsumes False\n",
            "True subsumes x == y\n",
            "False subsumes x == y\n",
            "x > y subsumes x == y\n",
            "x < y subsumes x == y\n",
            "x <= y subsumes x == y\n",
            "x >= y subsumes x == y\n",
            "True subsumes x <= y\n",
            "x < y subsumes x <= y\n",
            "True subsumes x >= y\n",
            "x > y subsumes x >= y\n",
            "============================================\n"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SESbfG4j9p_W"
      },
      "source": [
        "**A.4 Logic expressions with bits:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aKkr562C9ta5"
      },
      "source": [
        "# 1) Declare variables and conditions\n",
        "x, y = BitVecs('x y', 32)\n",
        "conditions = True"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xTpb_iO-95mD",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 442
        },
        "outputId": "6957ffdc-71eb-4d6a-d564-b89979546ad6"
      },
      "source": [
        "msg = \"A.4.1 lexp & rexp'\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x & y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x, y, x|y, x^y, x<<y, x>>y]\n",
        "mutationNames = {\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\",\n",
        "    \"x | y\": \"LOR |\",\n",
        "    \"x ^ y\": \"LOR ^\",\n",
        "    \"x << y\": \"SOR <<\",\n",
        "    \"x >> y\": \"SOR >>\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.4.1 lexp & rexp'\n",
            "============================================\n",
            "x subsumes x | y\n",
            "y subsumes x | y\n",
            "x subsumes x ^ y\n",
            "y subsumes x ^ y\n",
            "x | y subsumes x ^ y\n",
            "x << y subsumes x ^ y\n",
            "x >> y subsumes x ^ y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8yEjnWz9_l_S",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "outputId": "8d7c8f00-9aa6-4f4e-aa89-c2cd5394ef8f"
      },
      "source": [
        "msg = \"A.4.2 lexp | rexp'\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x | y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x, y, x&y, x^y, x<<y, x>>y]\n",
        "mutationNames = {\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\",\n",
        "    \"x & y\": \"LOR &\",\n",
        "    \"x ^ y\": \"LOR ^\",\n",
        "    \"x << y\": \"SOR <<\",\n",
        "    \"x >> y\": \"SOR >>\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.4.2 lexp | rexp'\n",
            "============================================\n",
            "x subsumes x & y\n",
            "y subsumes x & y\n",
            "x subsumes x << y\n",
            "x ^ y subsumes x << y\n",
            "x >> y subsumes x << y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DECaIQZMASeP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 408
        },
        "outputId": "3c63b62a-8763-4e96-ac56-c47379376fe7"
      },
      "source": [
        "msg = \"A.4.3 lexp ^ rexp'\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x ^ y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x, y, x&y, x|y]\n",
        "mutationNames = {\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\",\n",
        "    \"x & y\": \"LOR &\",\n",
        "    \"x | y\": \"LOR |\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.4.3 lexp ^ rexp'\n",
            "============================================\n",
            "x | y subsumes x\n",
            "x | y subsumes y\n",
            "x subsumes x & y\n",
            "y subsumes x & y\n",
            "x | y subsumes x & y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
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          "output_type": "execute_result",
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          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Eb9-C_DYBtG-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        },
        "outputId": "e7fe5860-d347-40cf-c82f-c075855f9a7c"
      },
      "source": [
        "msg = \"A.4.4 lexp >> rexp'\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x >> y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x, y, x&y, x|y, x^y, x<<y]\n",
        "mutationNames = {\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\",\n",
        "    \"x & y\": \"LOR &\",\n",
        "    \"x ^ y\": \"LOR ^\",\n",
        "    \"x | y\": \"LOR |\",\n",
        "    \"x << y\": \"SOR <<\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.4.4 lexp >> rexp'\n",
            "============================================\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nitD57u1Crep",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 572
        },
        "outputId": "9edeec7f-3590-4aee-fb9a-c2646ac0c474"
      },
      "source": [
        "msg = \"A.4.5 lexp << rexp'\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x << y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x, y, x&y, x|y, x^y, x>>y]\n",
        "mutationNames = {\n",
        "    \"y\": \"CDL/VDL/ODL x\", \n",
        "    \"x\": \"CDL/VDL/ODL y\",\n",
        "    \"x & y\": \"LOR &\",\n",
        "    \"x ^ y\": \"LOR ^\",\n",
        "    \"x | y\": \"LOR |\",\n",
        "    \"x >> y\": \"SOR >>\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.4.5 lexp << rexp'\n",
            "============================================\n",
            "x >> y subsumes x\n",
            "x subsumes y\n",
            "x & y subsumes y\n",
            "x | y subsumes y\n",
            "x ^ y subsumes y\n",
            "x >> y subsumes y\n",
            "x subsumes x | y\n",
            "x ^ y subsumes x | y\n",
            "x >> y subsumes x | y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
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          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GrKFwP_4DA7f"
      },
      "source": [
        "**A.5 Unary expressions with bits:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "svoFZwoJDKWP"
      },
      "source": [
        "# 1) Declare variables and conditions\n",
        "x, y = BitVecs('x y', 32)\n",
        "conditions = True"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FXuGhjbADLY1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 572
        },
        "outputId": "92eec8ad-d91f-43ef-9dd2-243cfac98d65"
      },
      "source": [
        "msg = \"A.5.1 exp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [-x,~x,x+1,x-1,x]\n",
        "# AOIS exp++ e AOIS exp-- are equivalents to the program\n",
        "mutationNames = {\n",
        "    \"-x\": \"AOIU -x\",\n",
        "    \"~x\": \"LOI ~x\",\n",
        "    \"x + 1\": \"AOIS ++x\",\n",
        "    \"x - 1\": \"AOIS --x\",\n",
        "    \"x\": \"AOIS x++/x--\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.5.1 exp\n",
            "============================================\n",
            "-x subsumes ~x\n",
            "x + 1 subsumes ~x\n",
            "x - 1 subsumes ~x\n",
            "-x subsumes x + 1\n",
            "~x subsumes x + 1\n",
            "x - 1 subsumes x + 1\n",
            "-x subsumes x - 1\n",
            "~x subsumes x - 1\n",
            "x + 1 subsumes x - 1\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x5p3K72sEZn5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        },
        "outputId": "a2be3e22-c93d-42d3-86c6-7d33670bdeda"
      },
      "source": [
        "msg = \"A.5.2 +exp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = +x\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x, ~program]\n",
        "mutationNames = {\n",
        "    \"x\": \"AODU/ODL x\",\n",
        "    \"~x\": \"LOI ~x\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.5.2 +exp\n",
            "============================================\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wIfeQf0zFBpT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 244
        },
        "outputId": "3a5e87ac-139e-4f8a-9f8b-e95394a91c35"
      },
      "source": [
        "msg = \"A.5.3 -exp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = -x\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x,~program]\n",
        "mutationNames = {\n",
        "    \"x\": \"AODU/ODL x\",\n",
        "    \"~(-x)\": \"LOI ~x\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.5.3 -exp\n",
            "============================================\n",
            "x subsumes ~(-x)\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J7rd4mYCFqmB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 182
        },
        "outputId": "dbeac532-845e-48ac-c5af-b265f7fd1785"
      },
      "source": [
        "def subsumption(p,m1,m2,conds):\n",
        "  t1 = is_non_empty(p, conds, m2)\n",
        "  t2 = is_subset(p, conds, m1, m2)\n",
        "  t3 = is_strict(p, conds, m1, m2)\n",
        "  #if t1 == 1 and t2 == 1:\n",
        "  if t1 == 1 and t2 == 1 and t3 == 1:\n",
        "    print(str(m2)+\" subsumes \"+str(m1))\n",
        "    return (m2,m1)\n",
        "  else:\n",
        "    return None\n",
        "\n",
        "msg = \"A.5.4 ++exp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x+1\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x,~program]\n",
        "mutationNames = {\n",
        "    \"x\": \"AORS/AODS/ODL x\",\n",
        "    \"~(x + 1)\": \"LOI ~x\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "print(str((mutations)))\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "print(str((mutations)))\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print(str(subsumptions))\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.5.4 ++exp\n",
            "============================================\n",
            "[x, ~(x + 1)]\n",
            "[x, ~(x + 1)]\n",
            "[]\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
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              "<graphviz.dot.Digraph at 0x7f25b9442780>"
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            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"288pt\" height=\"44pt\"\n viewBox=\"0.00 0.00 288.29 44.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 40)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-40 284.2884,-40 284.2884,4 -4,4\"/>\n<!-- AORS/AODS/ODL x -->\n<g id=\"node1\" class=\"node\">\n<title>AORS/AODS/ODL x</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"92.9418\" cy=\"-18\" rx=\"92.8835\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"92.9418\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">AORS/AODS/ODL x</text>\n</g>\n<!-- LOI ~x -->\n<g id=\"node2\" class=\"node\">\n<title>LOI ~x</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"241.9418\" cy=\"-18\" rx=\"38.1938\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"241.9418\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">LOI ~x</text>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AUyKm8zNGIw2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        },
        "outputId": "7c191362-0491-4597-c039-df50e342170a"
      },
      "source": [
        "msg = \"A.5.5 exp++\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x,~program]\n",
        "# AORS, AODS e ODL são mutantes equivalentes ao programa\n",
        "mutationNames = {\n",
        "    \"x\": \"AORS/AODS/ODL x\",\n",
        "    \"~x\": \"LOI ~x\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.5.5 exp++\n",
            "============================================\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f25b93fdb00>"
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            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"85pt\" height=\"44pt\"\n viewBox=\"0.00 0.00 84.69 44.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 40)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-40 80.6932,-40 80.6932,4 -4,4\"/>\n<!-- LOI ~x -->\n<g id=\"node1\" class=\"node\">\n<title>LOI ~x</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"38.3466\" cy=\"-18\" rx=\"38.1938\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"38.3466\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">LOI ~x</text>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bW7tuPHEGtXM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        },
        "outputId": "3ff835bf-f15c-4661-d06f-09aed599a287"
      },
      "source": [
        "msg = \"A.5.6 --exp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x-1\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x,~program]\n",
        "# AORS, AODS e ODL são mutantes equivalentes ao programa\n",
        "mutationNames = {\n",
        "    \"x\": \"AORS/AODS/ODL x\",\n",
        "    \"~(x - 1)\": \"LOI ~x\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.5.6 --exp\n",
            "============================================\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f25b93f5748>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"288pt\" height=\"44pt\"\n viewBox=\"0.00 0.00 288.29 44.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 40)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-40 284.2884,-40 284.2884,4 -4,4\"/>\n<!-- AORS/AODS/ODL x -->\n<g id=\"node1\" class=\"node\">\n<title>AORS/AODS/ODL x</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"92.9418\" cy=\"-18\" rx=\"92.8835\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"92.9418\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">AORS/AODS/ODL x</text>\n</g>\n<!-- LOI ~x -->\n<g id=\"node2\" class=\"node\">\n<title>LOI ~x</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"241.9418\" cy=\"-18\" rx=\"38.1938\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"241.9418\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">LOI ~x</text>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K2Afo2xTHMRp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        },
        "outputId": "312d7c1a-37f6-4ac6-8fe1-7fb3f41d30cb"
      },
      "source": [
        "msg = \"A.5.7 exp--\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x,~program]\n",
        "# AORS, AODS e ODL são mutantes equivalentes ao programa\n",
        "mutationNames = {\n",
        "    \"x\": \"AORS/AODS/ODL x\",\n",
        "    \"~x\": \"LOI ~x\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.5.7 exp--\n",
            "============================================\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f25b93fdfd0>"
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            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"85pt\" height=\"44pt\"\n viewBox=\"0.00 0.00 84.69 44.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 40)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-40 80.6932,-40 80.6932,4 -4,4\"/>\n<!-- LOI ~x -->\n<g id=\"node1\" class=\"node\">\n<title>LOI ~x</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"38.3466\" cy=\"-18\" rx=\"38.1938\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"38.3466\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">LOI ~x</text>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IiD0j0XiHsvO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        },
        "outputId": "eeb7f2c6-5e38-456e-a2f4-688920df3cbd"
      },
      "source": [
        "msg = \"A.5.9 ~exp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = ~x\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x]\n",
        "mutationNames = {\n",
        "    \"x\": \"LOD/ODL/AODU X\",\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.5.9 ~exp\n",
            "============================================\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f25b9444f98>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"190pt\" height=\"44pt\"\n viewBox=\"0.00 0.00 189.98 44.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 40)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-40 185.9839,-40 185.9839,4 -4,4\"/>\n<!-- LOD/ODL/AODU X -->\n<g id=\"node1\" class=\"node\">\n<title>LOD/ODL/AODU X</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"90.9919\" cy=\"-18\" rx=\"90.9839\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"90.9919\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">LOD/ODL/AODU X</text>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V8oBWrEwIG-D"
      },
      "source": [
        "Unary expression with boolean:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uOlL63rCIQl7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        },
        "outputId": "564590b7-2b0a-48e1-ebbc-16f8307a8645"
      },
      "source": [
        "x, y = Bools('x y')\n",
        "msg = \"A.5.8 !exp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = Not(x)\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "mutations = [x]\n",
        "mutationNames = {\n",
        "    \"x\": \"COD/ODL x\",\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.5.8 !exp\n",
            "============================================\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f25b93f5390>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"128pt\" height=\"44pt\"\n viewBox=\"0.00 0.00 127.59 44.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 40)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-40 123.5894,-40 123.5894,4 -4,4\"/>\n<!-- COD/ODL x -->\n<g id=\"node1\" class=\"node\">\n<title>COD/ODL x</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"59.7947\" cy=\"-18\" rx=\"59.5901\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"59.7947\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">COD/ODL x</text>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "34jcJbOoI645"
      },
      "source": [
        "**A.6 Assigment operator expressions with integers:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WrQJtcudI--Z"
      },
      "source": [
        "# 1) Declare variables and conditions\n",
        "x = Int('x')\n",
        "y = Int('y')\n",
        "conditions = And(x>0,y>0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IU5ffe18JP_Z",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 278
        },
        "outputId": "7ec8dedb-c16b-40ed-f9e4-30b4ab5de4d4"
      },
      "source": [
        "msg = \"A.6.1 lexp += rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x+y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "SDL = x\n",
        "mutations = [y, x-y, x*y, SDL]\n",
        "mutationNames = {\n",
        "    \"y\": \"ODL x=y\",\n",
        "    \"x - y\": \"ASRS -=\",\n",
        "    \"x*y\": \"ASRS *=\",\n",
        "    \"x\": \"SDL\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.6.1 lexp += rexp\n",
            "============================================\n",
            "x*y subsumes y\n",
            "x*y subsumes x - y\n",
            "x*y subsumes x\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f25b93f5208>"
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UfXDS0EsKbR5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 278
        },
        "outputId": "3d54f5ef-0f5a-4080-df9d-3d8966721ab5"
      },
      "source": [
        "msg = \"A.6.2 lexp -= rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x-y\n",
        "# 3) Specify a list of mutants  and mutation names\n",
        "SDL = x\n",
        "mutations = [y, x+y, x*y, SDL]\n",
        "mutationNames = {\n",
        "    \"y\": \"ODL x=y\",\n",
        "    \"x + y\": \"ASRS +=\",\n",
        "    \"x*y\": \"ASRS *=\",\n",
        "    \"x\": \"SDL\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.6.2 lexp -= rexp\n",
            "============================================\n",
            "y subsumes x + y\n",
            "y subsumes x*y\n",
            "y subsumes x\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f25b93f5ba8>"
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            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"293pt\" height=\"116pt\"\n viewBox=\"0.00 0.00 292.69 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-112 288.6932,-112 288.6932,4 -4,4\"/>\n<!-- ODL x=y -->\n<g id=\"node1\" class=\"node\">\n<title>ODL x=y</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"162.0957\" cy=\"-90\" rx=\"47.3916\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"162.0957\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">ODL x=y</text>\n</g>\n<!-- ASRS += -->\n<g id=\"node2\" class=\"node\">\n<title>ASRS +=</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"48.0957\" cy=\"-18\" rx=\"48.1917\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"48.0957\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">ASRS +=</text>\n</g>\n<!-- ODL x=y&#45;&gt;ASRS += -->\n<g id=\"edge1\" class=\"edge\">\n<title>ODL x=y&#45;&gt;ASRS +=</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M137.6399,-74.5542C121.2226,-64.1854 99.3885,-50.3955 81.391,-39.0286\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"83.2284,-36.0495 72.9045,-33.6687 79.4904,-41.9679 83.2284,-36.0495\"/>\n</g>\n<!-- ASRS *= -->\n<g id=\"node3\" class=\"node\">\n<title>ASRS *=</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"162.0957\" cy=\"-18\" rx=\"47.3916\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"162.0957\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">ASRS *=</text>\n</g>\n<!-- ODL x=y&#45;&gt;ASRS *= -->\n<g id=\"edge2\" class=\"edge\">\n<title>ODL x=y&#45;&gt;ASRS *=</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M162.0957,-71.8314C162.0957,-64.131 162.0957,-54.9743 162.0957,-46.4166\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"165.5958,-46.4132 162.0957,-36.4133 158.5958,-46.4133 165.5958,-46.4132\"/>\n</g>\n<!-- SDL -->\n<g id=\"node4\" class=\"node\">\n<title>SDL</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"256.0957\" cy=\"-18\" rx=\"28.6953\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"256.0957\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">SDL</text>\n</g>\n<!-- ODL x=y&#45;&gt;SDL -->\n<g id=\"edge3\" class=\"edge\">\n<title>ODL x=y&#45;&gt;SDL</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M183.4258,-73.6621C197.1006,-63.1877 214.9576,-49.51 229.548,-38.3345\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"231.8942,-40.9461 237.7047,-32.0867 227.6377,-35.3889 231.8942,-40.9461\"/>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yx5a0oSNK6Jt",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 278
        },
        "outputId": "a4cf17f2-8639-453e-8d07-434722f93df5"
      },
      "source": [
        "msg = \"A.6.3 lexp *= rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x*y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "SDL = x\n",
        "mutations = [y, x+y, x-y, SDL]\n",
        "mutationNames = {\n",
        "    \"y\": \"ODL x=y\",\n",
        "    \"x + y\": \"ASRS +=\",\n",
        "    \"x - y\": \"ASRS -=\",\n",
        "    \"x\": \"SDL\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.6.3 lexp *= rexp\n",
            "============================================\n",
            "y subsumes x - y\n",
            "x + y subsumes x - y\n",
            "x subsumes x - y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WfFNOrhyLULQ"
      },
      "source": [
        "**A.7 Shift operator expressions with bits:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6js88u0kLW-J"
      },
      "source": [
        "# 1) Declare variables and conditions\n",
        "x, y = BitVecs('x y', 32)\n",
        "conditions = True"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aAVw-x32Lbd4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        },
        "outputId": "8a373073-dd6e-44a9-ecd8-92401230988e"
      },
      "source": [
        "msg = \"A.7.1 lexp <<= rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x<<y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "SDL = x\n",
        "mutations = [y,SDL,x>>y]\n",
        "mutationNames = {\n",
        "    \"y\": \"ODL x=y\",\n",
        "    \"x\": \"SDL\",\n",
        "    \"x >> y\": \"ASRS >>=\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.7.1 lexp <<= rexp\n",
            "============================================\n",
            "x subsumes y\n",
            "x >> y subsumes y\n",
            "x >> y subsumes x\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TiE2yS5MN6S1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        },
        "outputId": "2b7283a9-9207-4d11-c7e3-c63d881069e9"
      },
      "source": [
        "msg = \"A.7.2 lexp >>= rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x>>y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "SDL = x\n",
        "mutations = [y,SDL,x<<y]\n",
        "mutationNames = {\n",
        "    \"y\": \"ODL x=y\",\n",
        "    \"x\": \"SDL\",\n",
        "    \"x << y\": \"ASRS <<=\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.7.2 lexp >>= rexp\n",
            "============================================\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8tKUKn-aObG-"
      },
      "source": [
        "**A.8 Assigment operator expressions with bits:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O93CwLWnOdjg"
      },
      "source": [
        "# 1) Declare variables and conditions\n",
        "x, y = BitVecs('x y', 32)\n",
        "conditions = True"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mBcV6F2TOhRA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 408
        },
        "outputId": "c54c69e9-a0dd-4fd9-e0b6-afb011b53819"
      },
      "source": [
        "msg = \"A.8.1 lexp &= rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x&y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "SDL = x\n",
        "mutations = [y,SDL,x|y,x^y]\n",
        "mutationNames = {\n",
        "    \"y\": \"ODL x=y\",\n",
        "    \"x\": \"SDL\",\n",
        "    \"x | y\": \"ASRS |=\",\n",
        "    \"x ^ y\": \"ASRS ^=\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.8.1 lexp &= rexp\n",
            "============================================\n",
            "y subsumes x | y\n",
            "x subsumes x | y\n",
            "y subsumes x ^ y\n",
            "x subsumes x ^ y\n",
            "x | y subsumes x ^ y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YnNFeyOiPPLB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        },
        "outputId": "be5e59bb-3eca-4bb7-e1b8-589becd89d07"
      },
      "source": [
        "msg = \"A.8.2 lexp |= rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x|y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "SDL = x\n",
        "mutations = [y,SDL,x&y,x^y]\n",
        "mutationNames = {\n",
        "    \"y\": \"ODL x=y\",\n",
        "    \"x\": \"SDL\",\n",
        "    \"x & y\": \"ASRS &=\",\n",
        "    \"x ^ y\": \"ASRS ^=\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.8.2 lexp |= rexp\n",
            "============================================\n",
            "y subsumes x & y\n",
            "x subsumes x & y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DM2remUVPuvB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 408
        },
        "outputId": "244edc23-73dd-434c-cf7f-3dbb5be1cc9a"
      },
      "source": [
        "msg = \"A.8.3 lexp ^= rexp\"\n",
        "print(msg)\n",
        "print('============================================')\n",
        "# 2) Specify a program\n",
        "program = x^y\n",
        "# 3) Specify a list of mutants and mutation names\n",
        "SDL = x\n",
        "mutations = [y,SDL,x|y,x&y]\n",
        "mutationNames = {\n",
        "    \"y\": \"ODL x=y\",\n",
        "    \"x\": \"SDL\",\n",
        "    \"x & y\": \"ASRS &=\",\n",
        "    \"x | y\": \"ASRS |=\"\n",
        "}\n",
        "# 4) Keep non equivalent mutants\n",
        "mutations = keepNonEquivalentMutants(program, mutations)\n",
        "# 5) Keep non redundant mutants\n",
        "mutations = keepNonRedundantMutants(mutations)\n",
        "# 6) Identify subsumption relations\n",
        "subsumptions = identifySubsumptions(program, mutations, conditions)\n",
        "print('============================================')\n",
        "# 7) Draw the subsumption relation graph\n",
        "createSubsumptionRelationGraph(subsumptions, mutations, mutationNames)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A.8.3 lexp ^= rexp\n",
            "============================================\n",
            "x | y subsumes y\n",
            "x | y subsumes x\n",
            "y subsumes x & y\n",
            "x subsumes x & y\n",
            "x | y subsumes x & y\n",
            "============================================\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k4w2djxpCvpG"
      },
      "source": [
        "# **Evaluating our Approach**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "09f7u9TaC8Pt"
      },
      "source": [
        "### **MuJava-M tool**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Rcjzh2GDDNK"
      },
      "source": [
        "We created a tool called Hunor to automate various steps of the study. We also developed hunor-maven-plugin to facilitate the execution of MuJava, MuJava-M, and mutation analysis in maven projects. To replicate the study or run the tools on other subjects, we provide a Docker image that contains all the tools and settings needed to run Hunor a maven project. The image is available on Docker Hub at https://hub.docker.com/r/mutationsubsumption/hunor."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oHgIBdjQDMn0"
      },
      "source": [
        "### **Our approach**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kgarF6ZNDTZr"
      },
      "source": [
        "We generate mutants for joda-time v2.10.1, commons-math v3.6.1, commons-lang v3.6, h2 v1.4.199, and javassist v3.20. The results of our study are summarized in a CSV file. The following command downloads the CSV file from GitHub."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0l0SAVYuDYwM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8172ead4-c860-4ee2-f2aa-de74939f3974"
      },
      "source": [
        "!wget -nc https://raw.githubusercontent.com/easy-software-ufal/subsumption-relations/master/Reduction%20and%20Effectiveness.csv"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2020-11-11 14:36:50--  https://raw.githubusercontent.com/easy-software-ufal/subsumption-relations/master/Reduction%20and%20Effectiveness.csv\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 151.101.0.133, 151.101.64.133, 151.101.128.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|151.101.0.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 695452 (679K) [text/plain]\n",
            "Saving to: ‘Reduction and Effectiveness.csv’\n",
            "\n",
            "Reduction and Effec 100%[===================>] 679.15K  --.-KB/s    in 0.1s    \n",
            "\n",
            "2020-11-11 14:36:51 (6.51 MB/s) - ‘Reduction and Effectiveness.csv’ saved [695452/695452]\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZEpENBx8DkHm"
      },
      "source": [
        "The field of the CSV file are the following.\n",
        "```\n",
        "id - a non-unique random identifier generated by the script.\n",
        "target - mutation target (lexp + rexp, exp, -exp, etc.)\n",
        "mutants_in_minimal - amount of mutants in the minimal set (generated by MuJava-M)\n",
        "test_suites - amount of test suites generated by EvosuiteR (each mutant in the minimal set must have one)\n",
        "assertions - amount of tests with \"asserts\" (each test suite must have one, since EvosuiterR stops when finds a test)\n",
        "mutants - amount of mutants generated by MuJava\n",
        "killed_mutants - amount of killed mutants (from the total in \"mutants\")\n",
        "not_equivalent_mutants - amount of mutants that were not classified as equivalents by TCE\n",
        "% - killed_mutants/mutants - effectiveness of MuJavaM.\n",
        "differential_success - indicates whether EvosuiteR successfully generated the test suites\n",
        "minimal - list of mutants in the minimal set\n",
        "survive - list of survived mutants \n",
        "killed - list of killed mutants\n",
        "equivalent - list of equivalent mutants classified by TCE\n",
        "class - classe onde o alvo foi encontrado.\n",
        "method - method where the target was found\n",
        "line - line where the target was found (MuJava generates a new source code file, which we need to check since the line may not be the same\n",
        "column - column of the mutation target\n",
        "project - project of the mutation target\n",
        "```\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "37ivHKdnDpjg"
      },
      "source": [
        "**Reading the CSV file**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BYq7gXiUDyJy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "66f2bb5d-0f2e-4342-d4f8-8e098ec60f0e"
      },
      "source": [
        "df = pandas.read_csv('Reduction and Effectiveness.csv',sep=',')\n",
        "df.tail()\n",
        "# we delete some columns\n",
        "del df['test_suites']\n",
        "del df['assertions']\n",
        "#del df['class']\n",
        "del df['method']\n",
        "del df['line']\n",
        "del df['column']\n",
        "del df['differential_success']\n",
        "del df['id']\n",
        "print(\"We have \"+str(len(df))+\" rows\")\n",
        "df.loc[df['target']=='lexp ^ rexp', 'minimal'] = 'LOR |'\n",
        "df.loc[df['target']=='exp++', 'minimal'] = 'LOI ~exp'\n",
        "df.loc[df['target']=='exp--', 'minimal'] = 'LOI ~exp'"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "We have 4137 rows\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FmYRN07bD-s6"
      },
      "source": [
        "**Defining some helper functions**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NsCqGwI9ECc2"
      },
      "source": [
        "def getElements(df, column):\n",
        "  \"\"\"\n",
        "  This function returns the set of elements present in a certain column of a dataframe.\n",
        "  \"\"\"\n",
        "  elements = []\n",
        "  for s in df[column].values:\n",
        "    s = str(s)\n",
        "    current_list_of_elements = s.split(',')\n",
        "    for element in current_list_of_elements:\n",
        "      elements.append(element)\n",
        "  elements = set(elements)\n",
        "  elements.discard(\"nan\") # we remove nan \n",
        "  return elements\n",
        "  \n",
        "def calculateNumberOfMutantsMuJava(df):\n",
        "  counter = 0\n",
        "  # go through each line of the file\n",
        "  for i in df.index: \n",
        "      line = df[df.index==i]\n",
        "      killed = getElements(line, \"killed\")\n",
        "      survive = getElements(line, \"survive\")\n",
        "      equivalent = getElements(line, \"equivalent\")\n",
        "      allMutants = killed.union(survive).union(equivalent)\n",
        "      counter = counter + len(allMutants)\n",
        "  return counter\n",
        "\n",
        "def calculateNumberOfMutantsMuJavaM(df):\n",
        "  counter = 0\n",
        "  # go through each line of the file\n",
        "  for i in df.index: \n",
        "      line = df[df.index==i]\n",
        "      minimal = getElements(line, \"minimal\")\n",
        "      counter = counter + len(minimal)\n",
        "  return counter\n",
        "\n",
        "def calculateNumberOfMutantsIntersectionEquivalentSurvived(df):\n",
        "  counter = 0\n",
        "  # go through each line of the file\n",
        "  for i in df.index: \n",
        "    line = df[df.index==i]\n",
        "    survive = getElements(line, \"survive\")\n",
        "    equivalent = getElements(line, \"equivalent\")\n",
        "    if(len(survive.intersection(equivalent))>0):\n",
        "      counter = counter + 1\n",
        "    if(len(equivalent.intersection(survive))>0):\n",
        "      counter = counter + 1\n",
        "  return counter"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o1yS8ywfEMKI"
      },
      "source": [
        "Identifying the number of occurences and mutants for the targets that have the same minimal set in the ICST and our current evaluation. The preprint of the ICST paper can be found [here.](https://www.cin.ufpe.br/~damorim/publications/guimaraes-etal-icst2020.pdf)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YCVID29xERkU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e610e2cb-d852-435a-e9c0-30b46dddcf71"
      },
      "source": [
        "# Mutations that have the same minimal set of mutants in both approaches (ICST 2020 and our approach)\n",
        "mutations = ['lexp == rexp', 'lexp != rexp', 'lexp > rexp', 'lexp >= rexp',\n",
        "            'lexp < rexp', 'lexp <= rexp', \n",
        "            'lhs <<= rhs', 'lhs >>= rhs', 'lhs &= rhs', 'lhs |= rhs', 'lhs ^= rhs',\n",
        "            'exp', '-exp', 'exp++', 'exp--','~exp','+exp','!exp',\n",
        "            'lexp & rexp','lexp | rexp','lexp ^ rexp',\n",
        "            'lexp && rexp','lexp || rexp']          \n",
        "indexes = []       \n",
        "result = pandas.DataFrame(columns=df.columns) \n",
        "\n",
        "for i in df.index: \n",
        "    line = df[df.index==i]    \n",
        "    t = line['target'].values\n",
        "    if(t[0] in mutations):\n",
        "      if(t[0] == 'lexp == rexp'):\n",
        "        minimal = getElements(line, 'minimal')\n",
        "        if(minimal == {'ROR >=', 'ROR false', 'ROR <='}):\n",
        "          result = result.append(line)\n",
        "      elif(t[0] == 'lexp != rexp'): \n",
        "        minimal = getElements(line, 'minimal')\n",
        "        if(minimal == {'ROR >', 'ROR true', 'ROR <'}):\n",
        "          result = result.append(line)\n",
        "      elif(t[0] == 'exp'): \n",
        "        minimal = getElements(line,'minimal')\n",
        "        if(minimal == {'AOIU -exp'}):\n",
        "          result = result.append(line)          \n",
        "      else:\n",
        "        result = result.append(line)\n",
        "\n",
        "print(\"We have \"+ str(len(result)) +\" occurences of mutation targets\")\n",
        "print(\"We have \"+ str(calculateNumberOfMutantsMuJava(result)) +\" mutants generated by MuJava in our evaluation\")\n",
        "print(\"We have \"+ str(calculateNumberOfMutantsMuJavaM(result)) +\" mutants generated by MuJava-M in our evaluation\")\n",
        "print(\"We have \"+ str(len(getElements(result, \"target\"))) +\" different targets in our evaluation\")\n",
        "getElements(result, \"target\")\n",
        "\n",
        "df = result\n",
        "\n",
        "projects = df['project'].unique()\n",
        "print('We evaluate the following large real open source projects: '+str(projects))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "We have 1403 occurences of mutation targets\n",
            "We have 6898 mutants generated by MuJava in our evaluation\n",
            "We have 1850 mutants generated by MuJava-M in our evaluation\n",
            "We have 18 different targets in our evaluation\n",
            "We evaluate the following large real open source projects: ['h2' 'joda-time' 'commons-math' 'javassist' 'commons-lang']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pEa2DiDQEWNN"
      },
      "source": [
        "Identifying the number of classes, and mutants generated by MuJava and MuJava-M in each project"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m9Jo0nM6EXK-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "86a79a99-8f39-4a37-f19e-1e4b84fc9d4e"
      },
      "source": [
        "numberOfClasses = 0\n",
        "numberOfMutantsMuJava = 0\n",
        "numberOfMutantsMuJavaM = 0\n",
        "\n",
        "for p in projects:\n",
        "  rows = df[df['project']==str(p)]\n",
        "  classes = len(rows[\"class\"].unique())\n",
        "  numberOfClasses = numberOfClasses + classes\n",
        "  mujava = calculateNumberOfMutantsMuJava(rows)\n",
        "  numberOfMutantsMuJava = numberOfMutantsMuJava + mujava\n",
        "  mujavam = calculateNumberOfMutantsMuJavaM(rows)\n",
        "  numberOfMutantsMuJavaM = numberOfMutantsMuJavaM + mujavam\n",
        "  print(\"Project \"+str(p)+\": #classes: \"+str(classes)+\"; #mutants generated by MuJava: \"+\n",
        "        str(mujava)+\"; #mutants generated by MuJavaM: \"+str(mujavam))\n",
        "  \n",
        "print(\"We evaluate in total:\" + \n",
        "      \"\\n#classes: \" + str(numberOfClasses) +\n",
        "      \"\\n#mutants generated by MuJava: \" + str(numberOfMutantsMuJava) + \n",
        "      \"\\n#mutants generated by MuJavaM: \" + str(numberOfMutantsMuJavaM))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Project h2: #classes: 11; #mutants generated by MuJava: 231; #mutants generated by MuJavaM: 63\n",
            "Project joda-time: #classes: 38; #mutants generated by MuJava: 2755; #mutants generated by MuJavaM: 666\n",
            "Project commons-math: #classes: 34; #mutants generated by MuJava: 1282; #mutants generated by MuJavaM: 368\n",
            "Project javassist: #classes: 20; #mutants generated by MuJava: 893; #mutants generated by MuJavaM: 216\n",
            "Project commons-lang: #classes: 22; #mutants generated by MuJava: 1737; #mutants generated by MuJavaM: 537\n",
            "We evaluate in total:\n",
            "#classes: 125\n",
            "#mutants generated by MuJava: 6898\n",
            "#mutants generated by MuJavaM: 1850\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uUQvX3u3Eh4w"
      },
      "source": [
        "Identifying the number of occurrences for each target"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NTK5MustEizj",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7b8df065-e50a-4af3-dad0-564cffdf4ff6"
      },
      "source": [
        "targets = getElements(df,\"target\")\n",
        "def listTargetsOccurrences(df):\n",
        "  for t in targets:\n",
        "    dfTargets = df[df['target']==t]\n",
        "    projects = dfTargets['project'].unique()\n",
        "    if len(dfTargets) > 0:\n",
        "      print(\"Target: \"+t+\" Occurrences: \"+str(len(dfTargets))+\" Projects: \"+str(len(projects)))\n",
        "      \n",
        "listTargetsOccurrences(df)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Target: lexp > rexp Occurrences: 19 Projects: 4\n",
            "Target: lexp == rexp Occurrences: 34 Projects: 2\n",
            "Target: lexp & rexp Occurrences: 33 Projects: 2\n",
            "Target: lexp | rexp Occurrences: 6 Projects: 1\n",
            "Target: lexp || rexp Occurrences: 25 Projects: 4\n",
            "Target: lexp < rexp Occurrences: 35 Projects: 4\n",
            "Target: ~exp Occurrences: 13 Projects: 2\n",
            "Target: -exp Occurrences: 38 Projects: 4\n",
            "Target: exp++ Occurrences: 4 Projects: 3\n",
            "Target: exp-- Occurrences: 4 Projects: 2\n",
            "Target: lexp != rexp Occurrences: 14 Projects: 4\n",
            "Target: lexp <= rexp Occurrences: 16 Projects: 3\n",
            "Target: lexp ^ rexp Occurrences: 6 Projects: 1\n",
            "Target: exp Occurrences: 1089 Projects: 5\n",
            "Target: lhs ^= rhs Occurrences: 1 Projects: 1\n",
            "Target: !exp Occurrences: 27 Projects: 4\n",
            "Target: lexp && rexp Occurrences: 13 Projects: 2\n",
            "Target: lexp >= rexp Occurrences: 26 Projects: 4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OZQ5QfBzEqfN"
      },
      "source": [
        "Identifying the reduction and effectiveness of our approach for each target"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n1PtK108Eria",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5d410f0b-c51b-4237-9fde-ad34fec2e2b7"
      },
      "source": [
        "def getReductionAndEffectivenessOurApproach(df):\n",
        "  mapOurApproachMinimal = {}\n",
        "  mapBaselineMinimal = {}\n",
        "  mapAllMutants = {}\n",
        "  for i in df.index: \n",
        "      line = df[df.index==i]\n",
        "      target = str(line['target'].values)\n",
        "      killed = getElements(line, \"killed\")\n",
        "      survive = getElements(line, \"survive\")\n",
        "      equivalent = getElements(line, \"equivalent\")\n",
        "      ourMinimal = getElements(line, \"minimal\")\n",
        "      baselineMinimal = ourMinimal.union(survive)-equivalent\n",
        "      allMutants = killed.union(survive)-equivalent\n",
        "      mapOurApproachMinimal[target] = mapOurApproachMinimal.get(target, 0) + len(ourMinimal)\n",
        "      mapBaselineMinimal[target] = mapBaselineMinimal.get(target, 0) + len(baselineMinimal)\n",
        "      mapAllMutants[target] = mapAllMutants.get(target, 0) + len(allMutants)\n",
        "  print(mapOurApproachMinimal)\n",
        "  print(mapBaselineMinimal)\n",
        "  print(mapAllMutants)  \n",
        "  keys = mapOurApproachMinimal.keys()\n",
        "  effectiveness = 0\n",
        "  reduction = 0\n",
        "  for k in keys:\n",
        "    effectiveness = mapOurApproachMinimal.get(k, 0)/mapBaselineMinimal.get(k, 0)\n",
        "    reduction = mapOurApproachMinimal.get(k, 0)/mapAllMutants.get(k, 0)\n",
        "    print(\"Target: \"+str(k)+\" Reduction: \"+str(1-reduction)+\" Effectiveness: \"+str(effectiveness))\n",
        "\n",
        "getReductionAndEffectivenessOurApproach(df)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{\"['exp']\": 1089, \"['lexp > rexp']\": 57, \"['lexp || rexp']\": 100, \"['lexp >= rexp']\": 78, \"['!exp']\": 27, \"['lexp != rexp']\": 42, \"['-exp']\": 38, \"['lexp == rexp']\": 102, \"['lexp < rexp']\": 105, \"['lexp && rexp']\": 52, \"['lexp <= rexp']\": 48, \"['exp++']\": 4, \"['lexp ^ rexp']\": 6, \"['~exp']\": 13, \"['exp--']\": 4, \"['lexp & rexp']\": 66, \"['lexp | rexp']\": 18, \"['lhs ^= rhs']\": 1}\n",
            "{\"['exp']\": 2307, \"['lexp > rexp']\": 57, \"['lexp || rexp']\": 100, \"['lexp >= rexp']\": 78, \"['!exp']\": 27, \"['lexp != rexp']\": 42, \"['-exp']\": 41, \"['lexp == rexp']\": 102, \"['lexp < rexp']\": 105, \"['lexp && rexp']\": 52, \"['lexp <= rexp']\": 48, \"['exp++']\": 4, \"['lexp ^ rexp']\": 6, \"['~exp']\": 13, \"['exp--']\": 6, \"['lexp & rexp']\": 66, \"['lexp | rexp']\": 18, \"['lhs ^= rhs']\": 2}\n",
            "{\"['exp']\": 4501, \"['lexp > rexp']\": 152, \"['lexp || rexp']\": 225, \"['lexp >= rexp']\": 208, \"['!exp']\": 54, \"['lexp != rexp']\": 112, \"['-exp']\": 92, \"['lexp == rexp']\": 272, \"['lexp < rexp']\": 280, \"['lexp && rexp']\": 117, \"['lexp <= rexp']\": 127, \"['exp++']\": 14, \"['lexp ^ rexp']\": 36, \"['~exp']\": 31, \"['exp--']\": 24, \"['lexp & rexp']\": 185, \"['lexp | rexp']\": 30, \"['lhs ^= rhs']\": 3}\n",
            "Target: ['exp'] Reduction: 0.7580537658298157 Effectiveness: 0.4720416124837451\n",
            "Target: ['lexp > rexp'] Reduction: 0.625 Effectiveness: 1.0\n",
            "Target: ['lexp || rexp'] Reduction: 0.5555555555555556 Effectiveness: 1.0\n",
            "Target: ['lexp >= rexp'] Reduction: 0.625 Effectiveness: 1.0\n",
            "Target: ['!exp'] Reduction: 0.5 Effectiveness: 1.0\n",
            "Target: ['lexp != rexp'] Reduction: 0.625 Effectiveness: 1.0\n",
            "Target: ['-exp'] Reduction: 0.5869565217391304 Effectiveness: 0.926829268292683\n",
            "Target: ['lexp == rexp'] Reduction: 0.625 Effectiveness: 1.0\n",
            "Target: ['lexp < rexp'] Reduction: 0.625 Effectiveness: 1.0\n",
            "Target: ['lexp && rexp'] Reduction: 0.5555555555555556 Effectiveness: 1.0\n",
            "Target: ['lexp <= rexp'] Reduction: 0.6220472440944882 Effectiveness: 1.0\n",
            "Target: ['exp++'] Reduction: 0.7142857142857143 Effectiveness: 1.0\n",
            "Target: ['lexp ^ rexp'] Reduction: 0.8333333333333334 Effectiveness: 1.0\n",
            "Target: ['~exp'] Reduction: 0.5806451612903225 Effectiveness: 1.0\n",
            "Target: ['exp--'] Reduction: 0.8333333333333334 Effectiveness: 0.6666666666666666\n",
            "Target: ['lexp & rexp'] Reduction: 0.6432432432432432 Effectiveness: 1.0\n",
            "Target: ['lexp | rexp'] Reduction: 0.4 Effectiveness: 1.0\n",
            "Target: ['lhs ^= rhs'] Reduction: 0.6666666666666667 Effectiveness: 0.5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FL5pr-NUFEw4"
      },
      "source": [
        "### **Comparison with random sampling**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oh3-Ea8TFMsI"
      },
      "source": [
        "Defining some functions to calculate the effectiveness of the random sampling approach"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Sbrj2suWFIzw"
      },
      "source": [
        "# Defining some constants\n",
        "MEAN = 0\n",
        "MEDIAN = 1\n",
        "\n",
        "def generateRandomList(quantity, interval):\n",
        "  randomList = []\n",
        "  counter = 0\n",
        "  while counter < quantity:\n",
        "    value = rd.randint(1, interval)\n",
        "    if(value in randomList):\n",
        "      continue\n",
        "    else:\n",
        "      randomList.append(value)\n",
        "      counter = counter + 1\n",
        "  return randomList\n",
        "\n",
        "def calculateSuccessOfRandom(baseline, random):\n",
        "  counter = 0\n",
        "  for elem in random:\n",
        "    if(elem in baseline):\n",
        "      counter = counter + 1\n",
        "  return counter\n",
        "\n",
        "def calculateEffectivenessOfRandom(quantityMutantsBaseline, quantityMutantsTotal, percentualRandom, iterations, measureType):  \n",
        "  # create a list with the baseline mutants\n",
        "  baseline = generateRandomList(quantityMutantsBaseline, quantityMutantsTotal)\n",
        "  quantityRandomElements = math.ceil(percentualRandom * quantityMutantsTotal) \n",
        "  successOfRandom = list()\n",
        "\n",
        "  for x in range(iterations):\n",
        "    randomList = generateRandomList(quantityRandomElements, quantityMutantsTotal)\n",
        "    currentSuccessOfRandom = calculateSuccessOfRandom(baseline, randomList)\n",
        "    successOfRandom.append(currentSuccessOfRandom)\n",
        "\n",
        "  if measureType == MEAN:\n",
        "    return sum(successOfRandom)/(quantityMutantsBaseline * iterations)\n",
        "  if measureType == MEDIAN:\n",
        "    successOfRandom.sort()\n",
        "    return successOfRandom[int(iterations/2)]/quantityMutantsBaseline\n",
        "\n",
        "def calculateEffectivenessOfRandomAll(df, percentualRandom, measureType, iterations):\n",
        "  counter = 0\n",
        "  successOfRandom = list()\n",
        "\n",
        "  # go through each line of the file\n",
        "  for i in df.index: \n",
        "      line = df[df.index==i]\n",
        "      killed = getElements(line, \"killed\")\n",
        "      survive = getElements(line, \"survive\")\n",
        "      equivalent = getElements(line, \"equivalent\")\n",
        "      minimal = getElements(line, \"minimal\")\n",
        "      baseline = minimal.union(survive)-equivalent\n",
        "      allMutants = killed.union(survive)-equivalent\n",
        "      currentSuccessOfRandom = calculateEffectivenessOfRandom(len(baseline), len(allMutants), percentualRandom, iterations, measureType)\n",
        "      successOfRandom.append(currentSuccessOfRandom)\n",
        "      counter = counter + 1\n",
        "\n",
        "  if measureType == MEAN:\n",
        "    return sum(successOfRandom)/counter\n",
        "  if measureType == MEDIAN:\n",
        "    successOfRandom.sort()\n",
        "    return successOfRandom[int(counter/2)]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oIL2lrvcFXhq"
      },
      "source": [
        "Defining some functions to caculate the effectiveness of our approach"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MS49lrzHFYg-"
      },
      "source": [
        "def calculateSamplingRateSubsumptionRelations(df):\n",
        "  total = 0\n",
        "  minimalCount = 0\n",
        "  # go through each line of the file\n",
        "  for i in df.index: \n",
        "      line = df[df.index==i]\n",
        "      killed = getElements(line, \"killed\")\n",
        "      survive = getElements(line, \"survive\")\n",
        "      equivalent = getElements(line, \"equivalent\")\n",
        "      minimal = getElements(line, \"minimal\")\n",
        "      allMutants = killed.union(survive)-equivalent\n",
        "      minimalCount = minimalCount + len(minimal)\n",
        "      total = total + len(allMutants)\n",
        "  return minimalCount/total\n",
        "\n",
        "def calculateEffectivenessOfOurApproachAll(df):\n",
        "  counter = 0\n",
        "  successOfOurApproach = 0\n",
        "\n",
        "  # go through each line of the file\n",
        "  for i in df.index: \n",
        "      line = df[df.index==i]\n",
        "      killed = getElements(line, \"killed\")\n",
        "      survive = getElements(line, \"survive\")\n",
        "      equivalent = getElements(line, \"equivalent\")\n",
        "      minimal = getElements(line, \"minimal\")\n",
        "      baseline = minimal.union(survive)-equivalent\n",
        "      allMutants = killed.union(survive)-equivalent\n",
        "      currentSuccessOfOurApproach = len(minimal)/len(baseline)\n",
        "      successOfOurApproach = successOfOurApproach + currentSuccessOfOurApproach\n",
        "      counter = counter + 1\n",
        "\n",
        "  return successOfOurApproach/counter"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2GIrgqIaFgRo"
      },
      "source": [
        "Calculating the effectiveness of both approaches"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "quKAoVKoFhNg",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "02634c86-1ae7-4ea8-abfd-0a1c287dc64b"
      },
      "source": [
        "#measureType = MEAN # mean of success in the X iterations in each line\n",
        "measureType = MEDIAN # median of success in the X iterations in each line\n",
        "sample = 10 # number of considered sampling rates\n",
        "iterationsInEachLine = 100 # number of runnings in each line\n",
        "values = []\n",
        "x = []\n",
        "\n",
        "for i in range(sample):\n",
        "  xval = i/sample\n",
        "  x.append(xval)\n",
        "  effectiveness = calculateEffectivenessOfRandomAll(df, xval, measureType, iterationsInEachLine)\n",
        "  values.append(effectiveness)\n",
        "\n",
        "ourApproachEff = calculateEffectivenessOfOurApproachAll(df)\n",
        "ourApproachSamp = calculateSamplingRateSubsumptionRelations(df)\n",
        "print(\"Our approach has a sampling rate of \"+str(ourApproachSamp)+\n",
        "      \" and an effectiveness of \"+str(ourApproachEff))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Our approach has a sampling rate of 0.28624477796688846 and an effectiveness of 0.759265858873844\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iwAZluVxFn1B"
      },
      "source": [
        "Creating a figure to compare our approach to the random sampling approach"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QIAiBIBMFo9Y",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "9818c7e8-c12b-48ac-86ad-2cb3d61c25dc"
      },
      "source": [
        "plt.plot(x, values)\n",
        "plt.xlabel('random sampling')\n",
        "plt.ylabel('effectiveness')\n",
        "plt.plot(ourApproachSamp,ourApproachEff,'ro') \n",
        "plt.text(ourApproachSamp,ourApproachEff,'Our approach',horizontalalignment='right')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}