From

⊇ @

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 @), Extended Dyalog APL, dzaima/APL, and Kap (as ⊇), J (as {), 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!

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

Works in: dzaima/APL, Extended Dyalog APL

Without Select, one would have to write Shuffle←⊢⌷⍨∘⊂?⍨∘≢. In this meaning, Select might be written as ⌷⍨∘⊂⍨ or ⌷⍤0 99 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 ⍋⊇⊢ and "sort by" can be written as ⊇⍨∘⍋:

Try it online!

      'abcde' ⊇⍨∘⍋ 3 1 4 1 5
bdace

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. { has a left rank of 0, so that results are mixed together and those with different shapes may be padded with fills.

   ]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

Works in: J

In APL this extension can be defined as ⌷⍨∘⊃⍨⍤0 ∞ thus allowing both the above usage and "scatter point indexing":

History

From ({) 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 { now used in J. Roger Hui expressed his support for the new definition with a presentation at APL87, 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.

The name Select and glyph ⊇ 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.

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

• Index (function)
• Bracket indexing
• Pick

External links

Documentation

• J: Dictionary, Nuvoc
• SAX
• BQN

Publications

• APL model