{
  "task": {
    "id": "case_124",
    "name": "check_all_equal",
    "summary": "Check if all elements in a list are equal.",
    "examples": [
      {
        "input": [
          "BOS",
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3
        ],
        "output": [
          "BOS",
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ]
      },
      {
        "input": [
          "BOS",
          9,
          4,
          0,
          2,
          5,
          3,
          7,
          10,
          8
        ],
        "output": [
          "BOS",
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
        ]
      },
      {
        "input": [
          "BOS",
          2,
          1,
          8,
          9,
          4,
          3,
          0,
          6,
          5
        ],
        "output": [
          "BOS",
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
        ]
      },
      {
        "input": [
          "BOS",
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
        ],
        "output": [
          "BOS",
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ]
      },
      {
        "input": [
          "BOS",
          3,
          8,
          0,
          10,
          5,
          6,
          4,
          7,
          9
        ],
        "output": [
          "BOS",
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
        ]
      }
    ],
    "is_categorical": true
  },
  "program": "unequal_selector = rasp.Select(rasp.tokens, rasp.tokens, lambda x, y: x != y)\nchecks = rasp.SelectorWidth(unequal_selector)\nzero_selector = rasp.Select(checks, rasp.Map(lambda x: 0, rasp.indices), rasp.Comparison.EQ)\nreturn rasp.Map(lambda x: 1 if x > 0 else 0, rasp.SelectorWidth(zero_selector))",
  "components": [
    {
      "id": "L0H0_ATTN",
      "hook": "blocks.0.attn.hook_result[0]",
      "role": {
        "tag": "AGGREGATOR",
        "note": "Aggregates positions holding tokens unequal to the current token into a per-position mismatch count."
      },
      "rasp_vars": [
        "unequal_selector"
      ],
      "labels": [
        "selector_width_4_selector_width_attn_output"
      ]
    },
    {
      "id": "L0_MLP",
      "hook": "blocks.0.mlp.hook_post",
      "role": {
        "tag": "MAPPER",
        "note": "Turns the mismatch signal into a per-position mismatch count and prepares it for the global decision."
      },
      "rasp_vars": [
        "checks"
      ],
      "labels": [
        "selector_width_4",
        "map_5",
        "selector_width_4_selector_width_attn_output"
      ]
    },
    {
      "id": "L1H0_ATTN",
      "hook": "blocks.1.attn.hook_result[0]",
      "role": {
        "tag": "AGGREGATOR",
        "note": "Aggregates positions where the mismatch count is zero, producing a per-position count of zero-mismatch occurrences."
      },
      "rasp_vars": [
        "zero_selector"
      ],
      "labels": [
        "selector_width_2_selector_width_attn_output"
      ]
    },
    {
      "id": "L1_MLP",
      "hook": "blocks.1.mlp.hook_post",
      "role": {
        "tag": "MAPPER",
        "note": "Converts the zero-mismatch mask into a scalar-like summary signal that can be read out."
      },
      "rasp_vars": [
        "all_equal_signal"
      ],
      "labels": [
        "selector_width_2",
        "selector_width_2_selector_width_attn_output"
      ]
    },
    {
      "id": "L2_MLP",
      "hook": "blocks.2.mlp.hook_post",
      "role": {
        "tag": "INDICATOR",
        "note": "Outputs the final binary decision: 1 if all elements are equal, otherwise 0."
      },
      "rasp_vars": [
        "all_equal"
      ],
      "labels": [
        "map_1"
      ]
    }
  ]
}