{
  "task": {
    "id": "case_45",
    "name": "double_first_half",
    "summary": "Doubles the first half of the sequence",
    "examples": [
      {
        "input": [
          "BOS",
          2,
          4,
          2,
          6,
          4,
          8,
          6,
          1,
          3
        ],
        "output": [
          "BOS",
          4,
          8,
          4,
          12,
          8,
          8,
          6,
          1,
          3
        ]
      },
      {
        "input": [
          "BOS",
          4,
          1,
          7,
          5,
          1,
          4,
          0,
          9,
          5
        ],
        "output": [
          "BOS",
          8,
          2,
          14,
          10,
          2,
          4,
          0,
          9,
          5
        ]
      },
      {
        "input": [
          "BOS",
          10,
          10,
          7,
          4,
          3,
          7,
          7,
          2,
          5
        ],
        "output": [
          "BOS",
          20,
          20,
          14,
          8,
          6,
          7,
          7,
          2,
          5
        ]
      },
      {
        "input": [
          "BOS",
          8,
          0,
          10,
          10,
          9,
          2,
          6,
          3,
          8
        ],
        "output": [
          "BOS",
          16,
          0,
          20,
          20,
          18,
          2,
          6,
          3,
          8
        ]
      },
      {
        "input": [
          "BOS",
          6,
          3,
          10,
          7,
          4,
          6,
          9,
          2,
          6
        ],
        "output": [
          "BOS",
          12,
          6,
          20,
          14,
          8,
          6,
          9,
          2,
          6
        ]
      }
    ],
    "is_categorical": true
  },
  "program": "length = rasp.SelectorWidth(rasp.Select(rasp.tokens, rasp.tokens, rasp.Comparison.TRUE)).named(\"length\")\nfirst_half_selector = rasp.SequenceMap(lambda idx, length: 1 if idx < length / 2 else 0, rasp.indices, length).named(\"first_half_selector\")\ndouble_first_half = rasp.SequenceMap(lambda x, sel: x * (1 + sel), rasp.tokens, first_half_selector).named(\"double_first_half\")\nreturn double_first_half",
  "components": [
    {
      "id": "L0H0_ATTN",
      "hook": "blocks.0.attn.hook_result[0]",
      "role": {
        "tag": "AGGREGATOR",
        "note": "Produces a sequence-length signal by counting tokens via the attention output width."
      },
      "rasp_vars": [
        "length_helper"
      ],
      "labels": [
        "length_3_selector_width_attn_output"
      ]
    },
    {
      "id": "L0_MLP",
      "hook": "blocks.0.mlp.hook_post",
      "role": {
        "tag": "MAPPER",
        "note": "Computes the sequence length feature used to split the sequence into halves."
      },
      "rasp_vars": [
        "length"
      ],
      "labels": [
        "length_3",
        "length_3_selector_width_attn_output"
      ]
    },
    {
      "id": "L1_MLP",
      "hook": "blocks.1.mlp.hook_post",
      "role": {
        "tag": "COMBINER",
        "note": "Builds a per-position mask indicating whether the position is in the first half."
      },
      "rasp_vars": [
        "first_half_selector"
      ],
      "labels": [
        "first_half_selector_2"
      ]
    },
    {
      "id": "L2_MLP",
      "hook": "blocks.2.mlp.hook_post",
      "role": {
        "tag": "COMBINER",
        "note": "Conditionally doubles elements in the first half using the first-half mask."
      },
      "rasp_vars": [
        "double_first_half"
      ],
      "labels": [
        "double_first_half_1"
      ]
    }
  ]
}