{
  "task": {
    "id": "case_15",
    "name": "double_minus_index",
    "summary": "Returns each token multiplied by two and subtracted by its index.",
    "examples": [
      {
        "input": [
          "BOS",
          2,
          4,
          3,
          2
        ],
        "output": [
          "BOS",
          4,
          7,
          4,
          1
        ]
      },
      {
        "input": [
          "BOS",
          4,
          1,
          3,
          1
        ],
        "output": [
          "BOS",
          8,
          1,
          4,
          -1
        ]
      },
      {
        "input": [
          "BOS",
          3,
          4,
          2,
          4
        ],
        "output": [
          "BOS",
          6,
          7,
          2,
          5
        ]
      },
      {
        "input": [
          "BOS",
          3,
          4,
          0,
          3
        ],
        "output": [
          "BOS",
          6,
          7,
          -2,
          3
        ]
      },
      {
        "input": [
          "BOS",
          4,
          1,
          2,
          2
        ],
        "output": [
          "BOS",
          8,
          1,
          2,
          1
        ]
      }
    ],
    "is_categorical": true
  },
  "program": "values, *sops = sops; for sop in sops: values = rasp.SequenceMap(lambda x, y: (*x, y) if isinstance(x, tuple) else (x, y), values, sop); return rasp.Map(lambda args: f(*args), values)",
  "components": [
    {
      "id": "L0_MLP",
      "hook": "blocks.0.mlp.hook_post",
      "role": {
        "tag": "COMBINER",
        "note": "Builds an intermediate representation that packages multiple per-position inputs together so they can be processed as a single combined object downstream."
      },
      "rasp_vars": [
        "values_tuple_stage_1"
      ],
      "labels": [
        "sequence_map_3"
      ]
    },
    {
      "id": "L1_MLP",
      "hook": "blocks.1.mlp.hook_post",
      "role": {
        "tag": "COMBINER",
        "note": "Extends the combined per-position representation by incorporating the position index, forming the final set of arguments needed for the arithmetic step."
      },
      "rasp_vars": [
        "values_tuple_stage_2"
      ],
      "labels": [
        "sequence_map_2"
      ]
    },
    {
      "id": "L2_MLP",
      "hook": "blocks.2.mlp.hook_post",
      "role": {
        "tag": "MAPPER",
        "note": "Computes the final per-position arithmetic from the bundled arguments (equivalent to doubling the token value and subtracting the index)."
      },
      "rasp_vars": [
        "output"
      ],
      "labels": [
        "map_1"
      ]
    }
  ]
}