Vocabulary/AmendingBoxedStructures
Amending Boxed Structures
J has no primitive verb for making a change deep inside a boxed structure. Some user-written conjunctions and verbs to do so are collected here.
applyintree
u applyintree n applies the verb u to the contents of the cell whose path is n.
Examples of applyintree
]y =. (;: 'An array with'), < (;: 'Interesting contents') ; 1 2 3
+--+-----+----+------------------------------+
|An|array|with|+----------------------+-----+|
| | | ||+-----------+--------+|1 2 3||
| | | |||Interesting|contents|| ||
| | | ||+-----------+--------+| ||
| | | |+----------------------+-----+|
+--+-----+----+------------------------------+
{. applyintree 2 y
+--+-----+-+------------------------------+
|An|array|w|+----------------------+-----+|
| | | ||+-----------+--------+|1 2 3||
| | | |||Interesting|contents|| ||
| | | ||+-----------+--------+| ||
| | | |+----------------------+-----+|
+--+-----+-+------------------------------+
{. was applied to the contents of the cell with index 2.
{. applyintree (3;0;1) y
+--+-----+----+-----------------------+
|An|array|with|+---------------+-----+|
| | | ||+-----------+-+|1 2 3||
| | | |||Interesting|c|| ||
| | | ||+-----------+-+| ||
| | | |+---------------+-----+|
+--+-----+----+-----------------------+
{. was applied to the contents of the cell with path (3;0;1). This path means: start with the overall array, and take item 3 and open it; then take item 0 of those contents, and open that; then take item 1 and open that. The verb u is applied to the final contents.
2 + applyintree (3;1) y +--+-----+----+------------------------------+ |An|array|with|+----------------------+-----+| | | | ||+-----------+--------+|3 4 5|| | | | |||Interesting|contents|| || | | | ||+-----------+--------+| || | | | |+----------------------+-----+| +--+-----+----+------------------------------+
In the dyadic form, the x argument is passed down unchanged until u is executed.
10 20 + applyintree (3;1;(<<1 2)) y +--+-----+----+--------------------------------+ |An|array|with|+----------------------+-------+| | | | ||+-----------+--------+|1 12 23|| | | | |||Interesting|contents|| || | | | ||+-----------+--------+| || | | | |+----------------------+-------+| +--+-----+----+--------------------------------+
Each box in a path follows the rules for left arguments of From (x { y). Here, the double-boxed selector picks 2 values from the last box. 10 20 is added to the pair.
The selection does not have to go all the way to the leaves of the boxed array:
2 3 ({. each) applyintree (3;0) y
+--+-----+----+----------------+
|An|array|with|+--------+-----+|
| | | ||+--+---+|1 2 3||
| | | |||In|con|| ||
| | | ||+--+---+| ||
| | | |+--------+-----+|
+--+-----+----+----------------+
The selection stopped at the two-element list of boxes, to which u was applied.
Definition of applyintree
NB. Conjunction. Apply u at the cell indicated by n
applyintree =: 2 : 0
if. #n do. ((u applyintree (}.n)) L:_1 ({.n){y) ({.n)} y else. u y end.
:
if. #n do. (x u applyintree (}.n) L:_ _1 ({.n){y) ({.n)} y else. x u y end.
)
More modern version with correct support for multidimensional boxing arrays (trees). No support of matching partial value of leaf (double boxing in path).
applyintree =: 2 : 0
i =. >^:((1=#)@>) {. n
(u`(u applyintree (}.n))@.(1<#n)&.:> i{y) i} y
:
i =. >^:((1=#)@>) {. n
((x&u)`(x&(u applyintree (}.n)))@.(1<#n)&.:> i{y) i} y
)
Restriction
The shape of the selected portion of y may not change.
10 , applyintree (3;1;1) y
|rank error
| (x u applyintree(}.n)L:_ _1({.n){y) ({.n)}y
The problem is that the modified value replaces the original in the array. Here, we are trying to replace an atom with a list.
Remember, though, that a box is always an atom, so a box can be replaced even if its contents change shape:
10 , applyintree (3;1) y +--+-----+----+---------------------------------+ |An|array|with|+----------------------+--------+| | | | ||+-----------+--------+|10 1 2 3|| | | | |||Interesting|contents|| || | | | ||+-----------+--------+| || | | | |+----------------------+--------+| +--+-----+----+---------------------------------+