# 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}:: yis reserved for that purpose, planned to operate along the lines ofx 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.