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 Map {::  _ 1 _ Fetch

 {::y has the same boxing as y and its elements are the paths to each leaf (each open array). x{::y fetches a subarray of y according to path x ; the selection at each level is based on { and, except at the last level, must result in an atom.

Map and Fetch can be modeled as follows:
```   cat  =: { @: (i.&.>) @: \$
mapp =: 4 : 'if. L. y do. (<"0 x,&.><"0 cat y) mapp&.> y else. >x end.'
map  =: a:&mapp
fetch=: >@({&>/)@(<"0@|.@[ , <@]) " 1 _
```
The following phrases illustrate the use of Map and Fetch:
```   ] y=: 1 2 3;4 5;i.4 5
+-----+---+--------------+
|1 2 3|4 5| 0  1  2  3  4|
|     |   | 5  6  7  8  9|
|     |   |10 11 12 13 14|
|     |   |15 16 17 18 19|
+-----+---+--------------+
```
 (2;_1 _1){::y The number 19 (_1;3 4) {::y The number 19 {::y Paths to each open array {::cat L: 0 y Paths to each open scalar
```   ] t=: 5!:2 <'fetch'         An array with an interesting structure
+------------------------------------------------------+-+---+
|+-----------------+-+--------------------------------+|"|1 _|
||+-+-+-----------+|@|+--------------------+-+-------+|| |   |
|||>|@|+-------+-+|| ||+--------------+-+-+|,|+-+-+-+||| |   |
||| | ||+-+-+-+|/||| |||+-------+-+--+|@|[|| ||<|@|]|||| |   |
||| | |||{|&|>|| ||| ||||+-+-+-+|@||.|| | || |+-+-+-+||| |   |
||| | ||+-+-+-+| ||| |||||<|"|0|| |  || | || |       ||| |   |
||| | |+-------+-+|| ||||+-+-+-+| |  || | || |       ||| |   |
||+-+-+-----------+| |||+-------+-+--+| | || |       ||| |   |
||                 | ||+--------------+-+-+| |       ||| |   |
||                 | |+--------------------+-+-------+|| |   |
|+-----------------+-+--------------------------------+| |   |
+------------------------------------------------------+-+---+
```
 (0;2;0;0;0){:: t Fetch the subarray corresp. to <"0 in t (0;2;0;0;0;_1){:: t Fetch the 0 in that t ,&< L: 0 1 {:: t Label each leaf with its path < S: 0 t The boxed leaves of t < S: 1 {:: t The boxed paths of t t ,&< S: 0 1 {:: t A 2-column table of leaves and paths # 0: S: 0 t The number of leaves in t

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