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Catalogue | { 1 0 _ | From

`{y` forms a catalogue from the atoms of its argument, its shape being the chain of the shapes of the opened items of`y` .`` The common shape of the boxed results is`$y` .`` For example:
       { 'ht';'ao';'gtw'
    +---+---+---+
    |hag|hat|haw|
    +---+---+---+
    |hog|hot|how|
    +---+---+---+
    +---+---+---+
    |tag|tat|taw|
    +---+---+---+
    |tog|tot|tow|
    +---+---+---+
The Cartesian product is readily defined in terms of`{` ,`` thus:
       CP=: {@(,&<)
       0 1 CP 2 3 4
    +---+---+---+
    |0 2|0 3|0 4|
    +---+---+---+
    |1 2|1 3|1 4|
    +---+---+---+
|  | If`x` is an integer in the range from`-n=: #y` to`n-1` ,`` then`x{y` selects item`n|x` from `y` .`` Thus:
       2 0 _1 _3 { 'abcdefg'
    cage

       t=:3 4$'abcdefghijkl'
       1{t
    efgh
More generally,`>x` may be a list whose successive elements are (possibly) boxed arrays that specify selection along successive axes of`y` . Finally, if any`r=:>j{>x` used in the selection is itself boxed, selection is made by the indices along that axis that do not occur in`>r` . Note that the result in the very last dyadic example, that is,`(<<<_1){m` ,`` is all except the last item.

       t=: 3 4 $ 'abcdefghijkl'
       t; (1{t); (2 1{t); (1{"1 t); ((,1){"1 t); (2 1{"1 t)
    +----+----+----+---+-+--+
    |abcd|efgh|ijkl|bfj|b|cb|
    |efgh|    |efgh|   |f|gf|
    |ijkl|    |    |   |j|kj|
    +----+----+----+---+-+--+

       t; (2 0{t); ((<2 0){t); ((2 0;1 3){t); ((<2 0;1 3){t)
    +----+----+-+--+--+
    |abcd|ijkl|i|ih|jl|
    |efgh|abcd| |  |bd|
    |ijkl|    | |  |  |
    +----+----+-+--+--+

       (_1{m); (_1{"2 m); (_1{"1 m); (<<<_1){m=:i.2 3 4
    +-----------+-----------+--------+---------+
    |12 13 14 15| 8  9 10 11| 3  7 11|0 1  2  3|
    |16 17 18 19|20 21 22 23|15 19 23|4 5  6  7|
    |20 21 22 23|           |        |8 9 10 11|
    +-----------+-----------+--------+---------+

>> << Ndx Usr Pri Phr Dic Rel Voc !: wd Help Dictionary