{
  "description": "Two-step tree program with constructor at the root and apply on one branch.",
  "example": "nested_constructor_apply",
  "execution": {
    "child_nodes": [
      {
        "child_nodes": [
          {
            "child_nodes": [],
            "final_type": {
              "args": [],
              "name": "A"
            },
            "final_witness": {
              "name": "ha"
            },
            "invariants": [
              {
                "detail": "parent_ids=['g0.1.1']",
                "name": "optic_parent_interface_is_singleton",
                "passed": true
              },
              {
                "detail": "child_ids=[]",
                "name": "optic_child_ids_unique",
                "passed": true
              },
              {
                "detail": "holes=[] children=[]",
                "name": "residue_holes_match_child_interface",
                "passed": true
              },
              {
                "detail": "coupling_child_ids=[] children=[]",
                "name": "coupling_child_ids_match_interface",
                "passed": true
              },
              {
                "detail": "kind=none shared=[] edges=[]",
                "name": "coupling_kind_matches_structure",
                "passed": true
              },
              {
                "detail": "exact_children=0",
                "name": "optic_arity_matches_primitive",
                "passed": true
              },
              {
                "detail": "inferred=Atom(name='A', args=()) target=Atom(name='A', args=()) subst={}",
                "name": "optic_reassembles_parent_target",
                "passed": true
              }
            ],
            "obligation": {
              "context": [
                {
                  "name": "ha",
                  "proposition": {
                    "args": [],
                    "name": "A"
                  }
                },
                {
                  "name": "hq",
                  "proposition": {
                    "args": [],
                    "name": "Q"
                  }
                }
              ],
              "goal_id": "g0.1.1",
              "target": {
                "args": [],
                "name": "A"
              }
            },
            "optic_step": {
              "certificates": [
                "hypothesis_target_match"
              ],
              "decomposition": {
                "child_interface": {
                  "obligations": []
                },
                "coupling": {
                  "child_ids": [],
                  "dependency_edges": [],
                  "kind": "none",
                  "shared_metavars": []
                },
                "parent_interface": {
                  "obligations": [
                    {
                      "context": [
                        {
                          "name": "ha",
                          "proposition": {
                            "args": [],
                            "name": "A"
                          }
                        },
                        {
                          "name": "hq",
                          "proposition": {
                            "args": [],
                            "name": "Q"
                          }
                        }
                      ],
                      "goal_id": "g0.1.1",
                      "target": {
                        "args": [],
                        "name": "A"
                      }
                    }
                  ]
                },
                "partial_term_after": {
                  "name": "ha"
                },
                "partial_term_before": {
                  "goal_id": "g0.1.1"
                }
              },
              "residue": {
                "child_order": [],
                "template": {
                  "name": "ha"
                }
              },
              "step": {
                "hypothesis_name": "ha"
              }
            },
            "program": {
              "children": [],
              "step": {
                "hypothesis_name": "ha"
              }
            }
          }
        ],
        "final_type": {
          "args": [],
          "name": "P"
        },
        "final_witness": {
          "args": [
            {
              "name": "ha"
            }
          ],
          "rule_name": "proveP"
        },
        "invariants": [
          {
            "detail": "parent_ids=['g0.1']",
            "name": "optic_parent_interface_is_singleton",
            "passed": true
          },
          {
            "detail": "child_ids=['g0.1.1']",
            "name": "optic_child_ids_unique",
            "passed": true
          },
          {
            "detail": "holes=['g0.1.1'] children=['g0.1.1']",
            "name": "residue_holes_match_child_interface",
            "passed": true
          },
          {
            "detail": "coupling_child_ids=['g0.1.1'] children=['g0.1.1']",
            "name": "coupling_child_ids_match_interface",
            "passed": true
          },
          {
            "detail": "kind=none shared=[] edges=[]",
            "name": "coupling_kind_matches_structure",
            "passed": true
          },
          {
            "detail": "apply_children=1 expected=1",
            "name": "optic_arity_matches_primitive",
            "passed": true
          },
          {
            "detail": "inferred=Atom(name='P', args=()) target=Atom(name='P', args=()) subst={}",
            "name": "optic_reassembles_parent_target",
            "passed": true
          }
        ],
        "obligation": {
          "context": [
            {
              "name": "ha",
              "proposition": {
                "args": [],
                "name": "A"
              }
            },
            {
              "name": "hq",
              "proposition": {
                "args": [],
                "name": "Q"
              }
            }
          ],
          "goal_id": "g0.1",
          "target": {
            "args": [],
            "name": "P"
          }
        },
        "optic_step": {
          "certificates": [
            "rule_conclusion_unified"
          ],
          "decomposition": {
            "child_interface": {
              "obligations": [
                {
                  "context": [
                    {
                      "name": "ha",
                      "proposition": {
                        "args": [],
                        "name": "A"
                      }
                    },
                    {
                      "name": "hq",
                      "proposition": {
                        "args": [],
                        "name": "Q"
                      }
                    }
                  ],
                  "goal_id": "g0.1.1",
                  "target": {
                    "args": [],
                    "name": "A"
                  }
                }
              ]
            },
            "coupling": {
              "child_ids": [
                "g0.1.1"
              ],
              "dependency_edges": [],
              "kind": "none",
              "shared_metavars": []
            },
            "parent_interface": {
              "obligations": [
                {
                  "context": [
                    {
                      "name": "ha",
                      "proposition": {
                        "args": [],
                        "name": "A"
                      }
                    },
                    {
                      "name": "hq",
                      "proposition": {
                        "args": [],
                        "name": "Q"
                      }
                    }
                  ],
                  "goal_id": "g0.1",
                  "target": {
                    "args": [],
                    "name": "P"
                  }
                }
              ]
            },
            "partial_term_after": {
              "args": [
                {
                  "goal_id": "g0.1.1"
                }
              ],
              "rule_name": "proveP"
            },
            "partial_term_before": {
              "goal_id": "g0.1"
            }
          },
          "residue": {
            "child_order": [
              "g0.1.1"
            ],
            "template": {
              "args": [
                {
                  "goal_id": "g0.1.1"
                }
              ],
              "rule_name": "proveP"
            }
          },
          "step": {
            "rule_name": "proveP"
          }
        },
        "program": {
          "children": [
            {
              "children": [],
              "step": {
                "hypothesis_name": "ha"
              }
            }
          ],
          "step": {
            "rule_name": "proveP"
          }
        }
      },
      {
        "child_nodes": [],
        "final_type": {
          "args": [],
          "name": "Q"
        },
        "final_witness": {
          "name": "hq"
        },
        "invariants": [
          {
            "detail": "parent_ids=['g0.2']",
            "name": "optic_parent_interface_is_singleton",
            "passed": true
          },
          {
            "detail": "child_ids=[]",
            "name": "optic_child_ids_unique",
            "passed": true
          },
          {
            "detail": "holes=[] children=[]",
            "name": "residue_holes_match_child_interface",
            "passed": true
          },
          {
            "detail": "coupling_child_ids=[] children=[]",
            "name": "coupling_child_ids_match_interface",
            "passed": true
          },
          {
            "detail": "kind=none shared=[] edges=[]",
            "name": "coupling_kind_matches_structure",
            "passed": true
          },
          {
            "detail": "exact_children=0",
            "name": "optic_arity_matches_primitive",
            "passed": true
          },
          {
            "detail": "inferred=Atom(name='Q', args=()) target=Atom(name='Q', args=()) subst={}",
            "name": "optic_reassembles_parent_target",
            "passed": true
          }
        ],
        "obligation": {
          "context": [
            {
              "name": "ha",
              "proposition": {
                "args": [],
                "name": "A"
              }
            },
            {
              "name": "hq",
              "proposition": {
                "args": [],
                "name": "Q"
              }
            }
          ],
          "goal_id": "g0.2",
          "target": {
            "args": [],
            "name": "Q"
          }
        },
        "optic_step": {
          "certificates": [
            "hypothesis_target_match"
          ],
          "decomposition": {
            "child_interface": {
              "obligations": []
            },
            "coupling": {
              "child_ids": [],
              "dependency_edges": [],
              "kind": "none",
              "shared_metavars": []
            },
            "parent_interface": {
              "obligations": [
                {
                  "context": [
                    {
                      "name": "ha",
                      "proposition": {
                        "args": [],
                        "name": "A"
                      }
                    },
                    {
                      "name": "hq",
                      "proposition": {
                        "args": [],
                        "name": "Q"
                      }
                    }
                  ],
                  "goal_id": "g0.2",
                  "target": {
                    "args": [],
                    "name": "Q"
                  }
                }
              ]
            },
            "partial_term_after": {
              "name": "hq"
            },
            "partial_term_before": {
              "goal_id": "g0.2"
            }
          },
          "residue": {
            "child_order": [],
            "template": {
              "name": "hq"
            }
          },
          "step": {
            "hypothesis_name": "hq"
          }
        },
        "program": {
          "children": [],
          "step": {
            "hypothesis_name": "hq"
          }
        }
      }
    ],
    "final_type": {
      "left": {
        "args": [],
        "name": "P"
      },
      "right": {
        "args": [],
        "name": "Q"
      }
    },
    "final_witness": {
      "left": {
        "args": [
          {
            "name": "ha"
          }
        ],
        "rule_name": "proveP"
      },
      "right": {
        "name": "hq"
      }
    },
    "invariants": [
      {
        "detail": "parent_ids=['g0']",
        "name": "optic_parent_interface_is_singleton",
        "passed": true
      },
      {
        "detail": "child_ids=['g0.1', 'g0.2']",
        "name": "optic_child_ids_unique",
        "passed": true
      },
      {
        "detail": "holes=['g0.1', 'g0.2'] children=['g0.1', 'g0.2']",
        "name": "residue_holes_match_child_interface",
        "passed": true
      },
      {
        "detail": "coupling_child_ids=['g0.1', 'g0.2'] children=['g0.1', 'g0.2']",
        "name": "coupling_child_ids_match_interface",
        "passed": true
      },
      {
        "detail": "kind=independent shared=[] edges=[]",
        "name": "coupling_kind_matches_structure",
        "passed": true
      },
      {
        "detail": "constructor_children=2",
        "name": "optic_arity_matches_primitive",
        "passed": true
      },
      {
        "detail": "inferred=And(left=Atom(name='P', args=()), right=Atom(name='Q', args=())) target=And(left=Atom(name='P', args=()), right=Atom(name='Q', args=())) subst={}",
        "name": "optic_reassembles_parent_target",
        "passed": true
      }
    ],
    "obligation": {
      "context": [
        {
          "name": "ha",
          "proposition": {
            "args": [],
            "name": "A"
          }
        },
        {
          "name": "hq",
          "proposition": {
            "args": [],
            "name": "Q"
          }
        }
      ],
      "goal_id": "g0",
      "target": {
        "left": {
          "args": [],
          "name": "P"
        },
        "right": {
          "args": [],
          "name": "Q"
        }
      }
    },
    "optic_step": {
      "certificates": [
        "conjunction_split"
      ],
      "decomposition": {
        "child_interface": {
          "obligations": [
            {
              "context": [
                {
                  "name": "ha",
                  "proposition": {
                    "args": [],
                    "name": "A"
                  }
                },
                {
                  "name": "hq",
                  "proposition": {
                    "args": [],
                    "name": "Q"
                  }
                }
              ],
              "goal_id": "g0.1",
              "target": {
                "args": [],
                "name": "P"
              }
            },
            {
              "context": [
                {
                  "name": "ha",
                  "proposition": {
                    "args": [],
                    "name": "A"
                  }
                },
                {
                  "name": "hq",
                  "proposition": {
                    "args": [],
                    "name": "Q"
                  }
                }
              ],
              "goal_id": "g0.2",
              "target": {
                "args": [],
                "name": "Q"
              }
            }
          ]
        },
        "coupling": {
          "child_ids": [
            "g0.1",
            "g0.2"
          ],
          "dependency_edges": [],
          "kind": "independent",
          "shared_metavars": []
        },
        "parent_interface": {
          "obligations": [
            {
              "context": [
                {
                  "name": "ha",
                  "proposition": {
                    "args": [],
                    "name": "A"
                  }
                },
                {
                  "name": "hq",
                  "proposition": {
                    "args": [],
                    "name": "Q"
                  }
                }
              ],
              "goal_id": "g0",
              "target": {
                "left": {
                  "args": [],
                  "name": "P"
                },
                "right": {
                  "args": [],
                  "name": "Q"
                }
              }
            }
          ]
        },
        "partial_term_after": {
          "left": {
            "goal_id": "g0.1"
          },
          "right": {
            "goal_id": "g0.2"
          }
        },
        "partial_term_before": {
          "goal_id": "g0"
        }
      },
      "residue": {
        "child_order": [
          "g0.1",
          "g0.2"
        ],
        "template": {
          "left": {
            "goal_id": "g0.1"
          },
          "right": {
            "goal_id": "g0.2"
          }
        }
      },
      "step": {}
    },
    "program": {
      "children": [
        {
          "children": [
            {
              "children": [],
              "step": {
                "hypothesis_name": "ha"
              }
            }
          ],
          "step": {
            "rule_name": "proveP"
          }
        },
        {
          "children": [],
          "step": {
            "hypothesis_name": "hq"
          }
        }
      ],
      "step": {}
    }
  },
  "program": {
    "children": [
      {
        "children": [
          {
            "children": [],
            "step": {
              "hypothesis_name": "ha"
            }
          }
        ],
        "step": {
          "rule_name": "proveP"
        }
      },
      {
        "children": [],
        "step": {
          "hypothesis_name": "hq"
        }
      }
    ],
    "step": {}
  },
  "root": {
    "context": [
      {
        "name": "ha",
        "proposition": {
          "args": [],
          "name": "A"
        }
      },
      {
        "name": "hq",
        "proposition": {
          "args": [],
          "name": "Q"
        }
      }
    ],
    "goal_id": "g0",
    "target": {
      "left": {
        "args": [],
        "name": "P"
      },
      "right": {
        "args": [],
        "name": "Q"
      }
    }
  },
  "rules": [
    {
      "conclusion": {
        "args": [],
        "name": "P"
      },
      "name": "proveP",
      "premises": [
        {
          "args": [],
          "name": "A"
        }
      ]
    }
  ]
}