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{{Built-in|Tally|≢}} is a [[primitive function|primitive]] [[monadic function]] which returns the number of [[major cell]]s in its [[argument]]. The Tally of an array is also the first [[element]] of its [[shape]], or 1 if it is a [[scalar]] (since a scalar is its own major cell by convention). Tally counts the first [[axis]] rather than the last because the number of major cells is more useful in [[leading axis theory]]. | {{Built-in|Tally|≢}} or '''Count''' is a [[primitive function|primitive]] [[monadic function]] which returns the number of [[major cell]]s in its [[argument]]. The Tally of an array is also the first [[element]] of its [[shape]], or 1 if it is a [[scalar]] (since a scalar is its own major cell by convention). Tally counts the first [[axis]] rather than the last because the number of major cells is more useful in [[leading axis theory]]. | ||
== Examples == | == Examples == | ||
Tally can compute the length of a [[numeric]] [[vector]] or [[string]]. | Tally can compute the length of a [[numeric]] [[vector]] or [[string]]. | ||
< | <syntaxhighlight lang=apl> | ||
≢⍳12 | ≢⍳12 | ||
12 | 12 | ||
≢'string' | ≢'string' | ||
6 | 6 | ||
</ | </syntaxhighlight> | ||
It gives the length of the first [[axis]] in a higher-rank array. Tally applied to an array's [[shape]] gives its [[rank]]. | It gives the length of the first [[axis]] in a higher-rank array. Tally applied to an array's [[shape]] gives its [[rank]]. | ||
< | <syntaxhighlight lang=apl> | ||
≢5 4 3 2⍴1 'b' 3 'd' | ≢5 4 3 2⍴1 'b' 3 'd' | ||
5 | 5 | ||
≢⍴5 4 3 2⍴1 'b' 3 'd' | ≢⍴5 4 3 2⍴1 'b' 3 'd' | ||
4 | 4 | ||
</ | </syntaxhighlight> | ||
The Tally of a [[scalar]] is always 1. | The Tally of a [[scalar]] is always 1. | ||
< | <syntaxhighlight lang=apl> | ||
≢3.14 | ≢3.14 | ||
1 | 1 | ||
</ | </syntaxhighlight> | ||
== Description == | == Description == | ||
Tally returns the length of the first [[axis]] of its argument if it has any axes (that is, if it is not a scalar), and 1 otherwise. This can be modelled easily with [[Shape]] and [[First]]: | Tally returns the length of the first [[axis]] of its argument if it has any axes (that is, if it is not a scalar), and 1 otherwise. This can be modelled easily with [[Shape]] and [[First]]: | ||
< | <syntaxhighlight lang=apl> | ||
Tally ← {⊃(⍴⍵),1} | Tally ← {⊃(⍴⍵),1} | ||
</ | </syntaxhighlight> | ||
An alternative implementation is to count the major cells by turning each into a scalar 1 with the [[Rank operator]], then adding them up: | An alternative implementation is to count the major cells by turning each into a scalar 1 with the [[Rank operator]], then adding them up: | ||
< | <syntaxhighlight lang=apl> | ||
Tally ← +⌿ {1}⍤¯1 | Tally ← +⌿ {1}⍤¯1 | ||
</ | </syntaxhighlight> | ||
== History == | == History == | ||
Tally was introduced in [[ | Tally was introduced in [[A]] with the name "count" and symbol <syntaxhighlight lang=j inline>#</syntaxhighlight>. The same notation was carried forward to [[A+]], as well as [[J]] following [[Arthur Whitney]]'s suggestion. The primitive was present in [[NARS2000]] by 2010, with the name "Tally" and symbol <syntaxhighlight lang=apl inline>></syntaxhighlight><ref>NARS2000 Wiki. [http://wiki.nars2000.org/index.php?title=Tally&oldid=573 Tally]. Old revision: 2010-08-29.</ref>. The symbol <syntaxhighlight lang=apl inline>≢</syntaxhighlight> for Tally was introduced in [[Dyalog APL 14.0]], and quickly adopted by NARS2000. It was later added to [[GNU APL]] and has been included in many recent APLs based on Dyalog, such as [[ngn/apl]], [[dzaima/APL]], and [[APL\iv]]. | ||
Before the addition of Tally (and [[Zilde]]), there were numerous ways to get the length of a vector as a scalar:<ref>[[Roger Hui]] and [[Morten Kromberg]]. [https://dl.acm.org/doi/abs/10.1145/3386319 ''APL since 1978'']. §2.1 Tally. ACM [[HOPL]] IV. 2020-06.</ref> | |||
<syntaxhighlight lang=apl> | |||
''⍴⍴v | |||
(⍴0)⍴⍴v | |||
(⍳0)⍴⍴v | |||
(⍴v)[0] | |||
×/⍴v ⍝ shortest and obscure | |||
0⊥⍴v ⍝ shortest and obscurest | |||
</syntaxhighlight> | |||
== External links == | == External links == | ||
| Line 46: | Line 56: | ||
=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Tally.htm Dyalog] | ||
* [http://wiki.nars2000.org/index.php/Tally NARS2000] | * [http://wiki.nars2000.org/index.php/Tally NARS2000] | ||
* J [http://www.jsoftware.com/help/dictionary/d400.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/number NuVoc] | * J [http://www.jsoftware.com/help/dictionary/d400.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/number NuVoc] | ||
{{APL built-ins}} | * [https://mlochbaum.github.io/BQN/doc/shape.html BQN] (as Length) | ||
== References == | |||
<references /> | |||
{{APL built-ins}}[[Category:Primitive functions]] | |||