Select
⊇

Select (⊇
) (jokingly referred to as Sane Indexing) is a primitive function that allows selecting multiple major cells using indices of the cells. It is equivalent to ⌷⍨∘⊂⍨
and ⌷⍤0 ∞
, only providing a neater notation for such a fundamental concept. It was introduced in Extended Dyalog APL, and then adopted into dzaima/APL and KAP.
Common usage
Select is commonly used to reorder the major cells of an array. For example, the following shuffles any array into random order:
Shuffle←?⍨∘≢⊇⊢
Shuffle 'abcdef'
fbdcea
Without Select, one would have to write Shuffle←⊢⌷⍨∘⊂?⍨∘≢
.
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 ⊇⍨∘⍋
:
'abcde' ⊇⍨∘⍋ 3 1 4 1 5
bdace
Potential extension
Select can be defined as ⌷⍨∘⊃⍨⍤0 ∞
thus allowing both the above usage and "scatter point indexing":
1 4 3 ⊇ 4 4⍴⎕A
ABCD
MNOP
IJKL
(1 1)(4 4)(3 4) ⊇ 4 4⍴⎕A
APL