Vocabulary/curlylfcoco
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{:: y Map
Rank Infinity -- operates on x and y as a whole -- WHY IS THIS IMPORTANT?
A map of the boxed noun y
i.e. a noun having the same box structure as y but with each leaf replaced by the path to that leaf.
- A leaf is a noun that is unboxed.
This includes one that is empty, i.e. has no contents. - A path is a boxed noun whose leaves are integers.
It describes a sequence of selections and unboxings that points to a given (nested) box of a boxed noun.
A valid path can serve as x in Fetch (x {:: y) to fetch the contents of its target box.
boxxopen_z_ NB. a standard library (stdlib) verb with an interesting structure
<^:(L. < *@#)
] y=: 5!:2<'boxxopen_z_' NB. a sample boxed noun describing its structure
+-+--+--------------+
|<|^:|+--+-+-------+|
| | ||L.|<|+-+-+-+||
| | || | ||*|@|#|||
| | || | |+-+-+-+||
| | |+--+-+-------+|
+-+--+--------------+
{:: y NB. replaces each LEAF of y by its PATH
+---+---+---------------------------------------+
|+-+|+-+|+-----+-----+-------------------------+|
||0|||1|||+-+-+|+-+-+|+-------+-------+-------+||
|+-+|+-+|||2|0|||2|1|||+-+-+-+|+-+-+-+|+-+-+-+|||
| | ||+-+-+|+-+-+|||2|2|0|||2|2|1|||2|2|2||||
| | || | ||+-+-+-+|+-+-+-+|+-+-+-+|||
| | || | |+-------+-------+-------+||
| | |+-----+-----+-------------------------+|
+---+---+---------------------------------------+
] x=: 2;2;1 NB. the PATH corresponding to the LEAF: '@'
+-+-+-+
|2|2|1|
+-+-+-+
x {:: y NB. Use the PATH (x) to extract the LEAF: '@'
@
Oddities
1. {:: y does not produce a path for a leaf that contains an empty array of boxes.
x {:: y Fetch
Rank 1 _ -- operates on lists of x and the entirety of y -- WHY IS THIS IMPORTANT?
A list of the contents of selected boxes in a boxed noun: y
Each sub-path of x gets replaced by its target box.
If x points to a single box, the result is the contents of that box
]y =. 1 2;3 4;5 6 7
+---+---+-----+
|1 2|3 4|5 6 7|
+---+---+-----+
1 {:: y
3 4
] y=: 5!:2<'boxxopen'
+-+--+--------------+
|<|^:|+--+-+-------+|
| | ||L.|<|+-+-+-+||
| | || | ||*|@|#|||
| | || | |+-+-+-+||
| | |+--+-+-------+|
+-+--+--------------+
2 {:: y
+--+-+-------+
|L.|<|+-+-+-+|
| | ||*|@|#||
| | |+-+-+-+|
+--+-+-------+
(2;0) {::y
L.
(2;2) {::y
+-+-+-+
|*|@|#|
+-+-+-+
(2;2;1) {::y
@
(0,:1) {::y NB. the result has the tally (#) of x (i.e. 2)
<
^:
When x and y are unboxed, (x {:: y) performs simple indexing into y
5 6 {:: i. 10 10 NB. Fetch row 5 column 6
56
(<5 6) { i. 10 10 NB. This is the other way to do that
56
(x {:: y) fetches portions of a boxed structure. There is no corresponding primitive to modify a portion of a boxed structure. x m}:: y is reserved for that purpose, planned to operate along the lines of x m} y, but it is unimplemented. If you want to modify internal portions of a multilevel boxed noun, look at utilities for amending boxed structures.
Common Uses
1. To select and open a single box from a list of boxes
]a =: 'zero';'one';'two';'three'
+----+---+---+-----+
|zero|one|two|three|
+----+---+---+-----+
2 {:: a
two
For this purpose x {:: y is faster than the equivalent > x { y
2. To select from a deep structure
]a =: 'zero';'one';('two point zero';'two point one';'two point two');'three'
+----+---+--------------------------------------------+-----+
|zero|one|+--------------+-------------+-------------+|three|
| | ||two point zero|two point one|two point two|| |
| | |+--------------+-------------+-------------+| |
+----+---+--------------------------------------------+-----+
(2;1) {:: a
two point one
(< < 1 3 _1) {:: a
+---+-----+-----+
|one|three|three|
+---+-----+-----+
(2 ; < < 1 2) {:: a
+-------------+-------------+
|two point one|two point two|
+-------------+-------------+
3. To perform multidimensional indexing, when x is unboxed.
This is equivalent to >^:('' -.@-: $) (<x) { y
- select from y using x
- if the result is not an atom, open it.
2 1 3 {:: i. 10 10 10 NB. coordinates for each axis
213
2 1 {:: i. 10 10 10 NB. omitted trailing axes are taken in full
210 211 212 213 214 215 216 217 218 219
1 2 {:: i. 3 4 NB. selection of an atom
6
1 2 {:: <"0 i. 3 4 NB. if the atom is boxed, it is opened
6
1 2 {:: i. 3 4 5 NB. selection of multiple atoms
30 31 32 33 34
1 2 {:: <"0 i. 3 4 5 NB. they are not opened
+--+--+--+--+--+
|30|31|32|33|34|
+--+--+--+--+--+
4. To select a subarray from a boxed array
]A =: 'abcde' ; 10 + i. 2 4
+-----+-----------+
|abcde|10 11 12 13|
| |14 15 16 17|
+-----+-----------+
(0 ; << 1 2 3) {:: A NB. selection of a subvector
bcd
(0 ; <<< 1 2 3) {:: A NB. additional boxing excludes indices
ae
(1 ; 0 1) {:: A NB. selection of a scalar from subarray
11
(1 ; < 0 ; 1) {:: A NB. the same as above
11
(1 ; < 0 1 ; 1 2) {:: A NB. selection of a submatrix
11 12
15 16
More Information
The path is defined by its effect on x {:: y .
The path is a list of boxes which are processed one by one, as follows:
- If x is empty or unboxed, it is put into a single box before the following is executed; that is, unboxed or empty x is processed as <x.
- selectedy =: y initializes the noun being searched
- Then, for each box of x:
]a =: 'zero';'one';('two point zero';'two point one');'three'
+----+---+------------------------------+-----+
|zero|one|+--------------+-------------+|three|
| | ||two point zero|two point one|| |
| | |+--------------+-------------+| |
+----+---+------------------------------+-----+
(<0) {:: a NB. 0 means: item 0 along the first axis
zero
(<,0) {:: a NB. ...means the same thing
zero
(<<0) {:: a NB. ...means the same thing
zero
(<<,0) {:: a NB. ...now it is a list of items (length 1), therefore not unboxed
+----+
|zero|
+----+
$ (<<,0) {:: a
1
The same rules apply when going down into the structure
((<2),(<<0)) {:: a
two point zero
((<2),(<,0)) {:: a
two point zero
((<2),(<<,0)) {:: a
+--------------+
|two point zero|
+--------------+
((<2),(<<0 1)) {:: a
+--------------+-------------+
|two point zero|two point one|
+--------------+-------------+
(;) is often used to build x.
Remember:
- x;y always boxes x
- x;y boxes y only if not already boxed
(2;,0) {:: a
two point zero
(2;<,0) {:: a
two point zero
(2;<<,0) {:: a
+--------------+
|two point zero|
+--------------+
Details
1. If x is unboxed, it is first boxed before being used as the path.
] z=: 0 1 {:: i. 2 3
1
assert z -: (<0 1) {:: i. 2 3
Exception: If x is an atom, it is used as the selector directly. The only difference this makes is that it causes (0 {:: atom) to give a result of (> atom) rather than an error.
2. If any selection other than the last selects an array, J signals rank error .
((<<0 1),(<'')) {:: a NB. Can't follow more than one selection path
|rank error
((<<0 1)) {:: a NB. But may end with multiple leaves
+----+---+
|zero|one|
+----+---+
Oddities
1. The definition of fetch in the J Dictionary does not conform to the behavior of x{::y as described above.