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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 <source lang=apl inline>@</source>), [[Extended Dyalog APL]], [[dzaima/APL]], and [[KAP]] (as <source lang=apl inline>⊇</source>), [[J]] (as <source lang=j inline>{</source>), and [[BQN]] (as <code>⊏</code>).
'''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>@</source>), [[Extended Dyalog APL]], [[dzaima/APL]], and [[KAP]] (as <syntaxhighlight lang=apl inline>⊇</source>), [[J]] (as <syntaxhighlight lang=j inline>{</source>), 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!]<source lang=apl>
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/PzijNC0tJ/VR2wT7R70rHnXMeNS56FFX@6OuRVyP@qYChaEKFNQTk5JTUtPU//8HAA Try it online!]<syntaxhighlight lang=apl>
       Shuffle←?⍨∘≢⊇⊢
       Shuffle←?⍨∘≢⊇⊢
       Shuffle 'abcdef'
       Shuffle 'abcdef'
fbdcea
fbdcea
</source>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}
</source>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}
Without Select, one would have to write <source lang=apl inline>Shuffle←⊢⌷⍨∘⊂?⍨∘≢</source>. In this meaning, Select might be written as <source lang=apl inline>⌷⍨∘⊂⍨</source> or <source lang=apl inline>⌷⍤0 99</source> in [[Dyalog APL]] (where 99 exceeds the system's maximum array [[rank]]).
Without Select, one would have to write <syntaxhighlight lang=apl inline>Shuffle←⊢⌷⍨∘⊂?⍨∘≢</source>. In this meaning, Select might be written as <syntaxhighlight lang=apl inline>⌷⍨∘⊂⍨</source> or <syntaxhighlight lang=apl inline>⌷⍤0 99</source> 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 <source lang=apl inline>⍋⊇⊢</source> and "sort by" can be written as <source lang=apl inline>⊇⍨∘⍋</source>:
Select especially cleans up expressions for reordering. An ascending sort can be represented as <syntaxhighlight lang=apl inline>⍋⊇⊢</source> and "sort by" can be written as <syntaxhighlight lang=apl inline>⊇⍨∘⍋</source>:


[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE9QTk5JTUtUVHnW1P@pd8ahjxqPebgVjBUMFEyA2/f8fAA Try it online!]<source lang=apl>
[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
Line 24: Line 24:
== 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. <source lang=j inline>{</source> 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.
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>{</source> 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.
<source lang=j>
<syntaxhighlight lang=j>
   ]a =. 4 4$(a.i.'A')}.a.
   ]a =. 4 4$(a.i.'A')}.a.
ABCD
ABCD
Line 38: Line 38:
APL
APL
</source>{{Works in|[[J]]}}
</source>{{Works in|[[J]]}}
In APL this extension can be defined as <source lang=apl inline>⌷⍨∘⊃⍨⍤0 ∞</source> 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 <source lang=apl inline>((⊃⊣)⌷⊢)⍤0 99</source>.)</ref>
In APL this extension can be defined as <syntaxhighlight lang=apl inline>⌷⍨∘⊃⍨⍤0 ∞</source> 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</source>.)</ref>


== History ==
== History ==

Revision as of 20:57, 10 September 2022

⊇ @

From (⊇ or @ and also called Select, or, humourously, Sane Indexing) is a primitive function that selects multiple major cells of its right argument using an array of 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>@</source>), Extended Dyalog APL, dzaima/APL, and KAP (as <syntaxhighlight lang=apl inline>⊇</source>), J (as <syntaxhighlight lang=j inline>{</source>), and BQN (as ⊏).

Common usage

Select is commonly used to reorder the major cells of an array. For example, the following shuffles any array into random order: Try it online!<syntaxhighlight lang=apl> 

     Shuffle←?⍨∘≢⊇⊢
     Shuffle 'abcdef'

fbdcea

</source>

Works in: dzaima/APL, Extended Dyalog APL

Without Select, one would have to write <syntaxhighlight lang=apl inline>Shuffle←⊢⌷⍨∘⊂?⍨∘≢</source>. In this meaning, Select might be written as <syntaxhighlight lang=apl inline>⌷⍨∘⊂⍨</source> or <syntaxhighlight lang=apl inline>⌷⍤0 99</source> 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.

Select especially cleans up expressions for reordering. An ascending sort can be represented as <syntaxhighlight lang=apl inline>⍋⊇⊢</source> and "sort by" can be written as <syntaxhighlight lang=apl inline>⊇⍨∘⍋</source>:

Try it online!<syntaxhighlight lang=apl> 

     'abcde' ⊇⍨∘⍋ 3 1 4 1 5

bdace

</source>

Works in: dzaima/APL, Extended Dyalog APL

Extensions

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. <syntaxhighlight lang=j inline>{</source> has a left rank of 0, so that results are mixed together and those with different shapes may be padded with fills. <syntaxhighlight lang=j> 

  ]a =. 4 4$(a.i.'A')}.a.

ABCD EFGH IJKL MNOP 

  0 3 2 { a

ABCD MNOP IJKL 

  (0 0;3 3;2 3) { a

APL

</source>

Works in: J

In APL this extension can be defined as <syntaxhighlight lang=apl inline>⌷⍨∘⊃⍨⍤0 ∞</source> thus allowing both the above usage and "scatter point indexing":[1]

History

From ({) was introduced in 1986 by A Dictionary of APL, with the same meaning now used in J. This description introduced the characteristic feature of selection of multiple cells simultaneously, as well as the pairing with monadic Catalogue, scatter-point indexing, negative indices, and the ability to exclude rather than include indices using a third level of boxing. Roger Hui expressed his support for the new definition with a presentation at the next APL conference[2], 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 {, but this was later deprecated, programmers being told to use @ instead.[3]

The name Select and glyph ⊇ were introduced by Extended Dyalog APL, and subsequently adopted by dzaima/APL and KAP.

BQN uses the name Select like Extended Dyalog APL but takes the direction of the glyph ⊏, 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 not by requiring the left argument as a whole to be enclosed but by requiring that each of its elements be an array.

See also

External links

Documentation

References

  1. ↑ Richard Park. Selecting from Arrays. Dyalog Webinar. 16 Apr 2020. (Presented in the form <syntaxhighlight lang=apl inline>((⊃⊣)⌷⊢)⍤0 99</source>.)
  2. ↑ Roger Hui. Some Uses of { and } at APL87.
  3. ↑ Soliton Associates Limited. SHARP APL for UNIX Language Guide. Deprecated Primitives: Braces. 2000.
APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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