Identity: Difference between revisions

:''This page is about the class of primitive functions. For the result of an empty reduction, see [[Identity element]].''

An '''Identity function''', or '''tack function''', is one of the three [[primitive function]]s which returns one of its [[argument]]s with no modification:

Identity functions (Identity in particular) may be used like elements of [[APL syntax|syntax]] to break up [[stranding]], or to force a [[shy]] result to be shown. They can also be combined with an array-oriented [[operator]] to perform structural manipulations on arrays. Identity functions are a central feature of [[tacit programming]], in which functions and operators rather than names are used to direct the flow of arguments. The pairing of both Left and Right with monadic Identity makes it easier to design [[ambivalent]] functions which usefully work with one or two arguments.

The [[monadic]] Identity function simply returns its [[argument]].

       ⊢ 'argument'

argument

       ⊢pi←3.14

3.14

Left and Right return the left and right arguments, respectively, when called [[dyad]]ically.

       'left' ⊣ 'right'

left

       'left' ⊢ 'right'

right

== Uses ==

As the left [[operand]] to [[Beside]], Right makes the resulting [[derived function]] ignore its left argument (so the result is produced by a [[monadic]] invocation of the right operand, on the right argument). The same pattern can be produced by using Right as the right operand to [[Atop]].

       2 ⊢∘- 7

¯7

       2 -⍤⊢ 7

¯7

In both cases the derived function, when called monadically, simply acts on the right argument, as there is no left argument to ignore.

       ⊢∘- 7

¯7

       -⍤⊢ 7

¯7

The mirror image—using only the left argument while ignoring the right—is attained by using [[Atop]] (either the operator, or a 2-train) with Left as the right operand.

       2 -⍤⊣ 7

¯2

       -⍤⊣ 2

¯2

       ' ' (≠⊆⊢) 'split on spaces'

┌─────┬──┬──────┐

│split│on│spaces│

└─────┴──┴──────┘

=== Structural manipulation ===

       ⊢A ← 3 4⍴⍳12

1  2  3  4

       ⊢⌿ A  ⍝ Last column

9 10 11 12

A [[Scan]] using Left extends the first element along each axis to the whole axis, while retaining the argument's shape. This is because a scan reduces on [[prefix]]es, and the first element of a prefix is the first element of the entire array. On the other hand, Right Scan doesn't change the argument, since the last element from each prefix gives the entire array.

       ⊣\ 'vector'

vvvvvv

       ⊢\ 'vector'

vector

Right [[Each]] checks the arguments for [[conformability]] and returns the right argument, possibly applying [[scalar extension]] or [[singleton extension]]; Left Each does the same for the left argument.

       A ⊢¨ 0  ⍝ Extends the right argument

0 0 0 0

       A⊢¨1 2 3

       ∧

The [[outer product]] with Left adds the axes from the right argument to the left argument, while the outer product with Right adds the axes from the left argument to the right argument. In each case the resulting array is constant along any of the added axes. In the case of Right outer product, the result is composed of [[cell]]s matching the right argument, and can also be obtained by [[Reshape|reshaping]] the right argument.

       'left' ∘.⊣ ⍳6

llllll

1 2 3 4 5 6

1 2 3 4 5 6

== External links ==

* Dyalog: [https://help.dyalog.com/17.1/Content/Language/Symbols/Left%20Tack.htm Left Tack], [https://help.dyalog.com/17.1/Content/Language/Symbols/Right%20Tack.htm Right Tack]

* APLX: [http://microapl.com/apl_help/ch_020_020_754.htm Left], [http://microapl.com/apl_help/ch_020_020_756.htm Right], [http://microapl.com/apl_help/ch_020_020_755.htm Pass]

{{APL built-ins}}[[Category:Primitive functions]]