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:''In the [[APL2]] family and many related dialects, <syntaxhighlight lang=apl inline>⊂</syntaxhighlight> indicates [[Partition]].'' | |||
{{Built-in|Partitioned Enclose|⊂}} is a [[dyadic function]] which splits its right argument into differently sized pieces as determined by the left argument. It was introduced by [[NARS]] and appears in [[Dyalog APL]] and some newer dialects influenced by it. | |||
== Description == | |||
In the simplest case, and on a vector right argument, the corresponding element in the left argument indicates where '''divisions''' begin: | In the simplest case, and on a vector right argument, the corresponding element in the left argument indicates where '''divisions''' begin: | ||
< | <syntaxhighlight lang=apl> | ||
1 0 1 0 0 0 0⊂'HiEarth' | 1 0 1 0 0 0 0⊂'HiEarth' | ||
┌──┬─────┐ | ┌──┬─────┐ | ||
│Hi│Earth│ | │Hi│Earth│ | ||
└──┴─────┘ | └──┴─────┘ | ||
</ | </syntaxhighlight> | ||
{{Works in|[[Dyalog APL]]}} | {{Works in|[[Dyalog APL]], [[Extended Dyalog APL]]}} | ||
=== Non-Boolean left argument === | |||
< | Older dialects restrict the left argument to provide only the above functionality. However, the left argument can be interpreted as a count of how many partitions begin with a particular position: | ||
<syntaxhighlight lang=apl> | |||
2 0 3 0 0 0 0⊂'HiEarth' | 2 0 3 0 0 0 0⊂'HiEarth' | ||
┌┬──┬┬┬─────┐ | ┌┬──┬┬┬─────┐ | ||
││Hi│││Earth│ | ││Hi│││Earth│ | ||
└┴──┴┴┴─────┘ | └┴──┴┴┴─────┘ | ||
</ | </syntaxhighlight> | ||
Additional trailing empty divisions are | === Short left argument === | ||
< | The dialects that support this extension also allow omission of trailing zeros, which is useful if the partitioning vector is generated by [[indices#Inverse|where's inverse]]: | ||
<syntaxhighlight lang=apl> | |||
⍸⍣¯1⊢1 1 3 3 3 | |||
2 0 3 | |||
2 0 3⊂'HiEarth' | |||
┌┬──┬┬┬─────┐ | |||
││Hi│││Earth│ | |||
└┴──┴┴┴─────┘ | |||
</syntaxhighlight> | |||
=== Long left argument === | |||
Additional trailing empty divisions are created by adding an additional division count corresponding to the position beyond the end of the right argument: | |||
<syntaxhighlight lang=apl> | |||
1 0 1 0 0 0 0 1⊂'HiEarth' | 1 0 1 0 0 0 0 1⊂'HiEarth' | ||
┌──┬─────┬┐ | ┌──┬─────┬┐ | ||
│Hi│Earth││ | │Hi│Earth││ | ||
└──┴─────┴┘ | └──┴─────┴┘ | ||
</ | </syntaxhighlight> | ||
== Split into lengths == | |||
The above extensions allow a simple definition of a split-into-lengths function: | |||
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/qLdP/VHf1GBXvZRHbROqNQxtH3UufNS7S/NRx/JHvWvAnC1AvhVQEVABkJWSVqJg8Ki7BSKQkllcABSshQgAjdEAUuHB6uquZal5JerqGurqwanFxZn5eQFFmSABBXX1FHV1zUddi4EKnSOBvLS8YqCA@v/ggpzMEpAjHvVuVXjU1fSod4XCo94dj3oXH1pvqKAdowCkHrVNNtQB2ff/v7GCsYKJAliTgrpHfrljUWpkfqm9OgA Try it online!] | [https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/qLdP/VHf1GBXvZRHbROqNQxtH3UufNS7S/NRx/JHvWvAnC1AvhVQEVABkJWSVqJg8Ki7BSKQkllcABSshQgAjdEAUuHB6uquZal5JerqGurqwanFxZn5eQFFmSABBXX1FHV1zUddi4EKnSOBvLS8YqCA@v/ggpzMEpAjHvVuVXjU1fSod4XCo94dj3oXH1pvqKAdowCkHrVNNtQB2ff/v7GCsYKJAliTgrpHfrljUWpkfqm9OgA Try it online!] | ||
< | <syntaxhighlight lang=apl> | ||
Split←{⍵ ⊂⍨ ⍸⍣¯1 +\ ¯1↓1,⍺} | Split←{⍵ ⊂⍨ ⍸⍣¯1 +\ ¯1↓1,⍺} | ||
3 3 4 Split 'HowAreYou?' | 3 3 4 Split 'HowAreYou?' | ||
| Line 32: | Line 48: | ||
│How│Are│You?│ | │How│Are│You?│ | ||
└───┴───┴────┘ | └───┴───┴────┘ | ||
</ | </syntaxhighlight> | ||
{{ | |||
== Extension support == | |||
The following table shows which of the extensions to <syntaxhighlight lang=apl inline>⍺</syntaxhighlight> introduced by [[Dyalog APL 18.0]] are supported in various dialects. [[dzaima/APL]] doesn't support extended lengths but instead requires a short <syntaxhighlight lang=apl inline>⍺</syntaxhighlight>, assuming the first value is 1. This means it can't drop elements as the original Partitioned Enclose typically does, but also means it can't produce leading or trailing empty partitions. | |||
{| class=wikitable | |||
! Languages !! Non-boolean !! Left argument length | |||
|- | |||
| [[NARS]] || {{No}} || <syntaxhighlight lang=apl inline>=≢⍵</syntaxhighlight> | |||
|- | |||
| [[Dyalog APL]], [[April]] || {{Yes}} || <syntaxhighlight lang=apl inline>≤1+≢⍵</syntaxhighlight> | |||
|- | |||
| [[dzaima/APL]] || {{Yes}} || <syntaxhighlight lang=apl inline>=¯1+≢⍵</syntaxhighlight> (first entry assumed 1) | |||
|- | |||
| [[Kap]] (<syntaxhighlight lang=apl inline>⊆</syntaxhighlight>) || {{Yes}} || <syntaxhighlight lang=apl inline>=≢⍵</syntaxhighlight> | |||
|} | |||
== See also == | |||
* [[Partition]] | |||
* [[Cut (K)]] | |||
* [[Partition representations]] | |||
==External links== | ==External links== | ||
===Tutorials=== | ===Tutorials=== | ||