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Cut | m;.n u;.n _ 1/2 _ | Cut

`u;.0 y` applies`u` to`y` after reversing`y` along each axis; it is equivalent to`(0 _1 */$y) u;.0 y` .
The fret `0{y` (the leading item of`y`)`` marks the start of an interval of items of`y` ;`` the phrase`u;.1 y` applies`u` to each such interval. The phrase`u;._1 y` differs only in that frets are excluded from the result. In`u;.2` and`u;._2` the fret is the last item, and marks the ends of intervals.
The monads`u;.3` and`u;._3` apply`u` to tesselation by "maximal cubes", that is, they are defined by their dyadic cases using the left argument`($$y)$<./$y` .
`m;.n y` applies successive verbs from the gerund`m` to the cuts of`y` ,`` extending`m` cyclically as required.

`x u;.0 y` applies`u` to a rectangle or cuboid of`y` with one vertex at the point in`y` indexed by`v=:0{x` ,`` and with the opposite vertex determined as follows: the dimension is`|1{x` ,`` but the rectangle extends back from`v` along any axis`j` for which the index`j{v` is negative. Finally, the order of the selected items is reversed along each axis`k` for which`k{1{x` is negative. If`x` is a vector, it is treated as the matrix`0,:x` .
The frets in the dyadic cases`1` ,`_1` ,`2` ,`` and`_2` are determined by the`1`s`` in boolean vector`x` ;`` an empty vector`x` and non-zero`#y` indicates the entire of`y` .`` In general, boolean vector`>j{x` specifies how axis`j` is to be cut.
`u;.3` and`u;._3` yield (possibly overlapping) tesselations.`x u;._3 y` applies`u` to each complete rectangle of size`|1{x` beginning at integer multiples of (each item of) the movement vector`0{x` ,`` with an infinite size being replaced by the signed length of the corresponding axis. As in`u;.0` ,`` reversal occurs along each axis for which the size`1{x` is negative. The case of a list`x` is equivalent to`1,:x` ,`` and therefore provides a complete tesselation of size`x` .`` The case`u;.3` differs in that shards of length less than`|1{x` are included.
`x m;.n y` applies successive verbs from the gerund`m` to the cuts of`y` ,`` extending`m` cyclically as required.
The 0- and 3-cuts have a left rank of 2; the 1- and 2-cuts have a left rank of 1.

       y=: 'worlds on worlds '
       (<;.2 y) ; ($;._2 y) ; (3 5$i.10) ; (+/ ;.1 (3 5$i.10))
    +---------------------+-+---------+-----------+
    |+-------+---+-------+|6|0 1 2 3 4|5 7 9 11 13|
    ||worlds |on |worlds ||2|5 6 7 8 9|0 1 2  3  4|
    |+-------+---+-------+|6|0 1 2 3 4|           |
    +---------------------+-+---------+-----------+

       1 0 1 0 0 <;.1 i.5 7
    +--------------------+
    |0 1 2  3  4  5  6   |
    |7 8 9 10 11 12 13   |
    +--------------------+
    |14 15 16 17 18 19 20|
    |21 22 23 24 25 26 27|
    |28 29 30 31 32 33 34|
    +--------------------+
       ('';1 0 0 0 1 0 1) <;.1 i.5 7
    +-----------+-----+--+
    | 0  1  2  3| 4  5| 6|
    | 7  8  9 10|11 12|13|
    |14 15 16 17|18 19|20|
    |21 22 23 24|25 26|27|
    |28 29 30 31|32 33|34|
    +-----------+-----+--+
       (1 0 1 0 0;1 0 0 0 1 0 1) <;.1 i.5 7
    +-----------+-----+--+
    |0 1 2  3   | 4  5| 6|
    |7 8 9 10   |11 12|13|
    +-----------+-----+--+
    |14 15 16 17|18 19|20|
    |21 22 23 24|25 26|27|
    |28 29 30 31|32 33|34|
    +-----------+-----+--+

       x=:1 _2,:_2 3 [ z=: i. 5 5
       x ; (x ];.0 z) ; z
    +-----+--------+--------------+
    | 1 _2|11 12 13| 0  1  2  3  4|
    |_2  3| 6  7  8| 5  6  7  8  9|
    |     |        |10 11 12 13 14|
    |     |        |15 16 17 18 19|
    |     |        |20 21 22 23 24|
    +-----+--------+--------------+

       (y=: a. {~ (a. i. 'a') + i. 4 4);(a=: 1 1 ,: 2 2)
    +----+---+
    |abcd|1 1|
    |efgh|2 2|
    |ijkl|   |
    |mnop|   |
    +----+---+

       (<;.3 y) ; ((($$y)$<./$y)<;.3 y) ; (a <;.3 y) ; <(a <;._3 y)
    +---------------+---------------+------------+----------+
    |+----+---+--+-+|+----+---+--+-+|+--+--+--+-+|+--+--+--+|
    ||abcd|bcd|cd|d|||abcd|bcd|cd|d|||ab|bc|cd|d|||ab|bc|cd||
    ||efgh|fgh|gh|h|||efgh|fgh|gh|h|||ef|fg|gh|h|||ef|fg|gh||
    ||ijkl|jkl|kl|l|||ijkl|jkl|kl|l||+--+--+--+-+|+--+--+--+|
    ||mnop|nop|op|p|||mnop|nop|op|p|||ef|fg|gh|h|||ef|fg|gh||
    |+----+---+--+-+|+----+---+--+-+||ij|jk|kl|l|||ij|jk|kl||
    ||efgh|fgh|gh|h|||efgh|fgh|gh|h||+--+--+--+-+|+--+--+--+|
    ||ijkl|jkl|kl|l|||ijkl|jkl|kl|l|||ij|jk|kl|l|||ij|jk|kl||
    ||mnop|nop|op|p|||mnop|nop|op|p|||mn|no|op|p|||mn|no|op||
    |+----+---+--+-+|+----+---+--+-+|+--+--+--+-+|+--+--+--+|
    ||ijkl|jkl|kl|l|||ijkl|jkl|kl|l|||mn|no|op|p||          |
    ||mnop|nop|op|p|||mnop|nop|op|p||+--+--+--+-+|          |
    |+----+---+--+-+|+----+---+--+-+|            |          |
    ||mnop|nop|op|p|||mnop|nop|op|p||            |          |
    |+----+---+--+-+|+----+---+--+-+|            |          |
    +---------------+---------------+------------+----------+

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