{
  "task": {
    "id": "case_113",
    "name": "invert_if_sorted",
    "summary": "Inverts the sequence if it is sorted in ascending order, otherwise leaves it unchanged.",
    "examples": [
      {
        "input": [
          "BOS",
          6,
          19,
          28,
          14,
          10,
          7,
          28,
          20,
          6
        ],
        "output": [
          "BOS",
          6.0,
          19.0,
          28.0,
          14.0,
          10.0,
          7.0,
          28.0,
          20.0,
          6.0
        ]
      },
      {
        "input": [
          "BOS",
          25,
          18,
          22,
          10,
          10,
          23,
          20,
          3,
          7
        ],
        "output": [
          "BOS",
          25.0,
          18.0,
          22.0,
          10.0,
          10.0,
          23.0,
          20.0,
          3.0,
          7.0
        ]
      },
      {
        "input": [
          "BOS",
          24,
          16,
          26,
          26,
          9,
          27,
          27,
          15,
          14
        ],
        "output": [
          "BOS",
          24.0,
          16.0,
          26.0,
          26.0,
          9.0,
          27.0,
          27.0,
          15.0,
          14.0
        ]
      },
      {
        "input": [
          "BOS",
          1,
          27,
          20,
          0,
          11,
          25,
          21,
          28,
          11
        ],
        "output": [
          "BOS",
          1.0,
          27.0,
          20.0,
          0.0,
          11.0,
          25.0,
          21.0,
          28.0,
          11.0
        ]
      },
      {
        "input": [
          "BOS",
          23,
          2,
          21,
          20,
          1,
          23,
          11,
          29,
          5
        ],
        "output": [
          "BOS",
          23.0,
          2.0,
          21.0,
          20.0,
          1.0,
          23.0,
          11.0,
          29.0,
          5.0
        ]
      }
    ],
    "is_categorical": true
  },
  "program": "shifter = rasp.Select(rasp.indices, rasp.indices, lambda x, y: x == y - 1 or (x == 0 and y == 0))\nshifted = rasp.Aggregate(shifter, rasp.tokens)\nchecks = rasp.SequenceMap(lambda x, y: 1 if x <= y else 0, shifted, rasp.tokens)\nzero_selector = rasp.Select(checks, rasp.Map(lambda x: 0, rasp.indices), rasp.Comparison.EQ)\ninvert_decider = rasp.Map(lambda x: 1 if x > 0 else -1, rasp.SelectorWidth(zero_selector))\navg_idx = rasp.Map(lambda x: x / 2 - 0.5, rasp.SelectorWidth(rasp.Select(rasp.indices, rasp.indices, rasp.Comparison.TRUE)))\ndiff_to_avg_idx = rasp.SequenceMap(lambda x, y: x - y, rasp.indices, avg_idx)\ninverter = rasp.SequenceMap(lambda x, y: x + y, avg_idx, rasp.SequenceMap(lambda x, y: x * y, invert_decider, diff_to_avg_idx))\ninvert_selector = rasp.Select(inverter, rasp.indices, rasp.Comparison.EQ)\nreturn rasp.Aggregate(invert_selector, rasp.tokens)",
  "components": [
    {
      "id": "L0H0_ATTN",
      "hook": "blocks.0.attn.hook_result[0]",
      "role": {
        "tag": "AGGREGATOR",
        "note": "Counts the number of non-increasing steps in the sequence by attending over positions where the sortedness check fails"
      },
      "rasp_vars": [
        "shifter"
      ],
      "labels": [
        "selector_width_6_selector_width_attn_output"
      ]
    },
    {
      "id": "L0H1_ATTN",
      "hook": "blocks.0.attn.hook_result[1]",
      "role": {
        "tag": "ROUTER",
        "note": "Produces the shifted token stream that aligns each token with its predecessor."
      },
      "rasp_vars": [
        "shifted"
      ],
      "labels": [
        "aggregate_14"
      ]
    },
    {
      "id": "L0_MLP",
      "hook": "blocks.0.mlp.hook_post",
      "role": {
        "tag": "MAPPER",
        "note": "Converts the attention-derived selector-width signal into sortedness evidence used by the global invert/keep decision."
      },
      "rasp_vars": [
        "checks",
        "zero_selector"
      ],
      "labels": [
        "selector_width_6",
        "selector_width_6_selector_width_attn_output",
        "map_13"
      ]
    },
    {
      "id": "L1_MLP",
      "hook": "blocks.1.mlp.hook_post",
      "role": {
        "tag": "COMBINER",
        "note": "Converts the sortedness evidence into a single invert/keep control signal for the rest of the circuit."
      },
      "rasp_vars": [
        "checks",
        "invert_decider"
      ],
      "labels": [
        "map_4",
        "sequence_map_12"
      ]
    },
    {
      "id": "L2H0_ATTN",
      "hook": "blocks.2.attn.hook_result[0]",
      "role": {
        "tag": "AGGREGATOR",
        "note": "Provides the sequence-length-style signal that is later turned into a center index reference for inversion."
      },
      "rasp_vars": [
        "length_helper"
      ],
      "labels": [
        "selector_width_10_selector_width_attn_output"
      ]
    },
    {
      "id": "L2_MLP",
      "hook": "blocks.2.mlp.hook_post",
      "role": {
        "tag": "COMBINER",
        "note": "Turns the length/position information into a center reference and a per-position offset-from-center signal used for inversion arithmetic."
      },
      "rasp_vars": [
        "avg_idx",
        "diff_to_avg_idx"
      ],
      "labels": [
        "selector_width_10",
        "selector_width_10_selector_width_attn_output",
        "sequence_map_8"
      ]
    },
    {
      "id": "L3_MLP",
      "hook": "blocks.3.mlp.hook_post",
      "role": {
        "tag": "MAPPER",
        "note": "Prepares an intermediate numeric signal for building the inverted index mapping."
      },
      "rasp_vars": [
        "inversion_prep"
      ],
      "labels": [
        "map_7"
      ]
    },
    {
      "id": "L4_MLP",
      "hook": "blocks.4.mlp.hook_post",
      "role": {
        "tag": "COMBINER",
        "note": "Combines the center reference, per-position offset, and the invert/keep control to produce the target source index for each position."
      },
      "rasp_vars": [
        "inverter"
      ],
      "labels": [
        "sequence_map_5"
      ]
    },
    {
      "id": "L5_MLP",
      "hook": "blocks.5.mlp.hook_post",
      "role": {
        "tag": "COMBINER",
        "note": "Finalizes the per-position index routing plan that will be used to either invert the sequence or leave it unchanged."
      },
      "rasp_vars": [
        "invert_selector"
      ],
      "labels": [
        "sequence_map_3"
      ]
    },
    {
      "id": "L6H0_ATTN",
      "hook": "blocks.6.attn.hook_result[0]",
      "role": {
        "tag": "ROUTER",
        "note": "Executes the final token movement: each position copies from its computed source index, yielding either the inverted or original sequence."
      },
      "rasp_vars": [
        "output"
      ],
      "labels": [
        "aggregate_1"
      ]
    }
  ]
}