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|<code>⊇</code> <code>@</code> | |<code>⊇</code> <code>@</code> | ||
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'''From''' (<code>⊇</code> or <code>@</code> and also called '''Select''', or, [[humour]]ously, ''Sane Indexing'') is a [[primitive function]] that selects multiple [[major cell]]s of its right argument using an array of [[index|indices]] given by its left. The primitive often offers additional functionality for a [[nested]] left argument, which varies from one language to another. It appears in [[SAX]] (as < | '''From''' (<code>⊇</code> or <code>@</code> and also called '''Select''', or, [[humour]]ously, ''Sane Indexing'') is a [[primitive function]] that selects multiple [[major cell]]s of its right argument using an array of [[index|indices]] given by its left. The primitive often offers additional functionality for a [[nested]] left argument, which varies from one language to another. It appears in [[SAX]] (as <syntaxhighlight lang=apl inline>@</syntaxhighlight>), [[Extended Dyalog APL]], [[dzaima/APL]], and [[Kap]] (as <syntaxhighlight lang=apl inline>⊇</syntaxhighlight>), [[J]] (as <syntaxhighlight lang=j inline>{</syntaxhighlight>), and [[BQN]] (as <code>⊏</code>). | ||
== Common usage == | == Common usage == | ||
Select is commonly used to reorder the major cells of an array. For example, the following shuffles any array into random order: | Select is commonly used to reorder the major cells of an array. For example, the following shuffles any array into random order: | ||
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/PzijNC0tJ/VR2wT7R70rHnXMeNS56FFX@6OuRVyP@qYChaEKFNQTk5JTUtPU//8HAA Try it online!]< | [https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/PzijNC0tJ/VR2wT7R70rHnXMeNS56FFX@6OuRVyP@qYChaEKFNQTk5JTUtPU//8HAA Try it online!]<syntaxhighlight lang=apl> | ||
Shuffle←?⍨∘≢⊇⊢ | Shuffle←?⍨∘≢⊇⊢ | ||
Shuffle 'abcdef' | Shuffle 'abcdef' | ||
fbdcea | fbdcea | ||
</ | </syntaxhighlight>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}} | ||
Without Select, one would have to write < | Without Select, one would have to write <syntaxhighlight lang=apl inline>Shuffle←⊢⌷⍨∘⊂?⍨∘≢</syntaxhighlight>. In this meaning, Select might be written as <syntaxhighlight lang=apl inline>⌷⍨∘⊂⍨</syntaxhighlight> or <syntaxhighlight lang=apl inline>⌷⍤0 99</syntaxhighlight> in [[Dyalog APL]] (where 99 exceeds the system's maximum array [[rank]]). | ||
In a case where the left argument is a permutation vector for the right argument, the functionality can rightfully be called ''Permute''. | In a case where the left argument is a permutation vector for the right argument, the functionality can rightfully be called ''Permute''. | ||
Select especially cleans up expressions for reordering. An ascending sort can be represented as < | Select especially cleans up expressions for reordering. An ascending sort can be represented as <syntaxhighlight lang=apl inline>⍋⊇⊢</syntaxhighlight> and "sort by" can be written as <syntaxhighlight lang=apl inline>⊇⍨∘⍋</syntaxhighlight>: | ||
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE9QTk5JTUtUVHnW1P@pd8ahjxqPebgVjBUMFEyA2/f8fAA Try it online!]< | [https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE9QTk5JTUtUVHnW1P@pd8ahjxqPebgVjBUMFEyA2/f8fAA Try it online!]<syntaxhighlight lang=apl> | ||
'abcde' ⊇⍨∘⍋ 3 1 4 1 5 | 'abcde' ⊇⍨∘⍋ 3 1 4 1 5 | ||
bdace | bdace | ||
</ | </syntaxhighlight>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}} | ||
== Extensions == | == Extensions == | ||
=== Scatter-point === | === Scatter-point === | ||
In [[A Dictionary of APL]], [[J]], and [[SAX]], a boxed left argument indicates that each [[element]] will be used independently to select a [[cell]] of the argument. The behavior on a single element is very similar to APL's [[Index (function)|Index]] function. < | In [[A Dictionary of APL]], [[J]], and [[SAX]], a boxed left argument indicates that each [[element]] will be used independently to select a [[cell]] of the argument. The behavior on a single element is very similar to APL's [[Index (function)|Index]] function. <syntaxhighlight lang=j inline>{</syntaxhighlight> has a left [[Function rank|rank]] of 0, so that results are [[mix]]ed together and those with different shapes may be padded with [[fill]]s. | ||
< | <syntaxhighlight lang=j> | ||
]a =. 4 4$(a.i.'A')}.a. | ]a =. 4 4$(a.i.'A')}.a. | ||
ABCD | ABCD | ||
| Line 37: | Line 37: | ||
(0 0;3 3;2 3) { a | (0 0;3 3;2 3) { a | ||
APL | APL | ||
</ | </syntaxhighlight>{{Works in|[[J]]}} | ||
In APL this extension can be defined as < | In APL this extension can be defined as <syntaxhighlight lang=apl inline>⌷⍨∘⊃⍨⍤0 ∞</syntaxhighlight> thus allowing both the above usage and "scatter point indexing":<ref>[[Richard Park]]. [https://dyalog.tv/Webinar/?v=AgYDvSF2FfU Selecting from Arrays]. [[Dyalog Webinar]]. 16 Apr 2020. (Presented in the form <syntaxhighlight lang=apl inline>((⊃⊣)⌷⊢)⍤0 99</syntaxhighlight>.)</ref> | ||
== History == | == History == | ||
From (<code>{</code>) was introduced in | From (<code>{</code>) was introduced in 1983 by [[Rationalized APL]]. This description introduced the characteristic feature of selection of multiple cells simultaneously, along with scatter-point indexing and the ability to exclude rather than include indices using a third level of boxing. It was expanded slightly in [[A Dictionary of APL]] to allow negative indices and was paired with monadic [[Catalogue]], giving the same meaning for <code>{</code> now used in [[J]]. [[Roger Hui]] expressed his support for the new definition with a presentation at [[APL87]],<ref>[[Roger Hui]]. [https://www.jsoftware.com/papers/from.htm Some Uses of <code>{</code> and <code>}</code>] at [[APL87]].</ref> and it was included in J from the earliest drafts in 1990—a limited version had even appeared in [[Arthur Whitney]]'s one-page interpreter prototype. | ||
[[SHARP APL]] followed A Dictionary of APL and used <code>{</code>, but this was later deprecated, programmers being told to use <code>@</code> instead.<ref>Soliton Associates Limited. SHARP APL for UNIX Language Guide. [https://abrudz.github.io/SAX2/SAX61.pdf#G41.16516 Deprecated Primitives: Braces]. 2000.</ref> | [[SHARP APL]] followed A Dictionary of APL and used <code>{</code>, but this was later deprecated, programmers being told to use <code>@</code> instead.<ref>Soliton Associates Limited. SHARP APL for UNIX Language Guide. [https://abrudz.github.io/SAX2/SAX61.pdf#G41.16516 Deprecated Primitives: Braces]. 2000.</ref> | ||
The name Select and glyph <code>⊇</code> were introduced by [[Extended Dyalog APL]], and subsequently adopted by [[dzaima/APL]] and [[ | The name Select and glyph <code>⊇</code> were introduced by [[Extended Dyalog APL]], and subsequently adopted by [[dzaima/APL]] and [[Kap]]. In addition to including it in Extended and the later [[Dyalog APL Vision]], [[Adám Brudzewsky]] described Select as a possible future [[Dyalog APL]] primitive in a presentation at [[Dyalog '22]].<ref>[[Adám Brudzewsky]]. [https://dyalog.tv/Dyalog22/?v=itGiA56NSl8 Filling the Core Language Gaps]. [[Dyalog '22]]. 2022-10-13.</ref> | ||
[[BQN]] uses the name Select like Extended Dyalog APL but takes the direction of the glyph <code>⊏</code>, as well as negative indexing, from J. For a nested left argument it uses a new extension: instead of viewing nesting as elaboration of each element of the left argument, it instead treats it as providing a list of left arguments to select from multiple axes of the right argument. This extension provides the functionality of APL's [[Index (function)|Index]] not by requiring the left argument as a whole to be enclosed but by requiring that each of its elements be an array. | [[BQN]] uses the name Select like Extended Dyalog APL but takes the direction of the glyph <code>⊏</code>, as well as negative indexing, from J. For a nested left argument it uses a new extension: instead of viewing nesting as elaboration of each element of the left argument, it instead treats it as providing a list of left arguments to select from multiple axes of the right argument. This extension provides the functionality of APL's [[Index (function)|Index]] not by requiring the left argument as a whole to be enclosed but by requiring that each of its elements be an array. | ||
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* [https://abrudz.github.io/SAX2/SAX61.pdf#M44.9.from SAX] | * [https://abrudz.github.io/SAX2/SAX61.pdf#M44.9.from SAX] | ||
* [https://mlochbaum.github.io/BQN/doc/select.html BQN] | * [https://mlochbaum.github.io/BQN/doc/select.html BQN] | ||
=== Publications === | |||
* [https://github.com/abrudz/primitives/blob/main/select.aplf APL model] | |||
== References == | == References == | ||
<references/> | <references/> | ||
{{APL built-ins}}[[Category:Primitive functions]] | {{APL built-ins}}[[Category:Primitive functions]] | ||