Commute: Difference between revisions

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{{Built-in|Commute|⍨}} is a [[monadic operator]] that takes a [[dyadic function]] as operand and modifies how the argument(s) of its derived functions are used. If the derived function is used monadically, the argument is also used as left argument. This usage is also known as '''Self''' or, more informally, '''Selfie'''. If the derived function is used dyadically, the arguments are swapped. This usage is also known as '''Swap'''. The [[glyph]] is also used for [[Constant]].
{{Built-in|Commute|⍨}}, or <syntaxhighlight lang=apl inline>⊂</syntaxhighlight> in [[SHARP APL]], is a [[monadic operator]] that takes a [[dyadic function]] as operand and modifies how the argument(s) of its derived functions are used. If the derived function is used monadically, the argument is also used as left argument. This usage is also known as '''Self''' or, more informally, '''Selfie'''. If the derived function is used dyadically, the arguments are swapped. This usage is also known as '''Swap'''. The [[glyph]] is also used for [[Constant]].


== Examples ==
== Examples ==


This decrements from the vector:
This decrements from the vector:
<source lang=apl>
<syntaxhighlight lang=apl>
       1 -⍨ 1 2 3
       1 -⍨ 1 2 3
0 1 2
0 1 2
Line 10: Line 10:
{{Works in|[[Dyalog APL]], [[dzaima/APL]], [[NARS2000]]}}
{{Works in|[[Dyalog APL]], [[dzaima/APL]], [[NARS2000]]}}
Double:
Double:
<source lang=apl>
<syntaxhighlight lang=apl>
       +⍨1 2 3
       +⍨1 2 3
2 4 6
2 4 6
Line 16: Line 16:
{{Works in|[[Dyalog APL]], [[dzaima/APL]], [[NARS2000]]}}
{{Works in|[[Dyalog APL]], [[dzaima/APL]], [[NARS2000]]}}


[[Commute]] can be used to emulate a monadic <source lang=apl inline>f g h</syntaxhighlight> [[Fork]] when combined with [[Compose]] (note the following code is not workable APL, but a series of evaluations):
[[Commute]] can be used to emulate a monadic <syntaxhighlight lang=apl inline>f g h</syntaxhighlight> [[Fork]] when combined with [[Compose]] (note the following code is not workable APL, but a series of evaluations):
<source lang=apl>
<syntaxhighlight lang=apl>
g⍨∘f⍨∘h⍨ x   
g⍨∘f⍨∘h⍨ x   
x g⍨∘f⍨∘h x ⍝ the last ⍨ is being used monadically, i.e. Selfie
x g⍨∘f⍨∘h x ⍝ the last ⍨ is being used monadically, i.e. Selfie
Line 28: Line 28:
== History ==
== History ==


The Commute operator was defined in [[Operators and Functions]] in 1978, and taken up by [[NARS]] as a result. [[Dyalog]], influenced by NARS, included the operator early on. While it didn't appear in [[SHARP APL]], it was included in [[J]] as "Reflex/Passive" (<source lang=j inline>~</syntaxhighlight>).
The Commute operator was defined with glyph <syntaxhighlight lang=apl inline>⍨</syntaxhighlight> in [[Operators and Functions]] in 1978, and taken up by [[NARS]] as a result. [[Dyalog]], influenced by NARS, included the operator early on. [[SHARP APL]] later added the operator with glyph <syntaxhighlight lang=apl inline>⊂</syntaxhighlight>, and it was included in [[J]] as "Reflex/Passive" (<syntaxhighlight lang=j inline>~</syntaxhighlight>). The [[ISO/IEC 13751:2001]] standard included the operator as defined in NARS, although it was unsupported by mainstream dialects such as [[APLX]] and [[APL+Win]] at the time,<ref>F.H.D. van Batenburg. [http://archive.vector.org.uk/art10000930 Conformity of APL Implementations to the ISO APL Standard]. [[Vector journal]] Volume 21, No.3. 2005-05.</ref> and remains unsupported by [[APL2]].


== External links ==
== External links ==
Line 41: Line 41:
* [https://mlochbaum.github.io/BQN/doc/swap.html BQN]
* [https://mlochbaum.github.io/BQN/doc/swap.html BQN]


== References ==
<references/>
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]

Latest revision as of 16:56, 16 March 2024

⍨

Commute (⍨), or ⊂ in SHARP APL, is a monadic operator that takes a dyadic function as operand and modifies how the argument(s) of its derived functions are used. If the derived function is used monadically, the argument is also used as left argument. This usage is also known as Self or, more informally, Selfie. If the derived function is used dyadically, the arguments are swapped. This usage is also known as Swap. The glyph is also used for Constant.

Examples

This decrements from the vector: 

      1 -⍨ 1 2 3
0 1 2
Works in: Dyalog APL, dzaima/APL, NARS2000

Double: 

      +⍨1 2 3
2 4 6
Works in: Dyalog APL, dzaima/APL, NARS2000

Commute can be used to emulate a monadic f g h Fork when combined with Compose (note the following code is not workable APL, but a series of evaluations): 

g⍨∘f⍨∘h⍨ x   
x g⍨∘f⍨∘h x ⍝ the last ⍨ is being used monadically, i.e. Selfie
x g⍨∘f⍨ h x
(h x) g⍨∘f x ⍝ the last ⍨ is being used dyadically, i.e. Swap
(h x) g⍨ (f x) 
(f x) g (h x) ⍝ the last ⍨ is being used dyadically, i.e. Swap

History

The Commute operator was defined with glyph ⍨ in Operators and Functions in 1978, and taken up by NARS as a result. Dyalog, influenced by NARS, included the operator early on. SHARP APL later added the operator with glyph ⊂, and it was included in J as "Reflex/Passive" (~). The ISO/IEC 13751:2001 standard included the operator as defined in NARS, although it was unsupported by mainstream dialects such as APLX and APL+Win at the time,[1] and remains unsupported by APL2.

External links

Lessons

Documentation

References

  1. ↑ F.H.D. van Batenburg. Conformity of APL Implementations to the ISO APL Standard. Vector journal Volume 21, No.3. 2005-05.
APL built-ins [edit]
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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
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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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