Over: Difference between revisions

From APL Wiki
Jump to navigation Jump to search
m (Text replacement - "</source>" to "</syntaxhighlight>")
m (Text replacement - "<source" to "<syntaxhighlight")
 
Line 4: Line 4:
When the resulting function is used [[monadic]]ally, it has the same behaviour as if the [[Beside]] or [[Atop (operator)|Atop]] operator had been used:
When the resulting function is used [[monadic]]ally, it has the same behaviour as if the [[Beside]] or [[Atop (operator)|Atop]] operator had been used:
{|
{|
|<source lang=apl>  (g ⍥ h) ⍵</syntaxhighlight>|| {{←→}} ||<source lang=apl>g (h ⍵)</syntaxhighlight>
|<syntaxhighlight lang=apl>  (g ⍥ h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>g (h ⍵)</syntaxhighlight>
|}
|}
When the resulting function is used [[dyadic]]ally, both arguments are pre-processed:
When the resulting function is used [[dyadic]]ally, both arguments are pre-processed:
{|
{|
|<source lang=apl>⍺ (g ⍥ h) ⍵</syntaxhighlight>|| {{←→}} ||<source lang=apl>(h ⍺) g (h ⍵)</syntaxhighlight>
|<syntaxhighlight lang=apl>⍺ (g ⍥ h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>(h ⍺) g (h ⍵)</syntaxhighlight>
|}
|}


== Examples ==
== Examples ==
<source lang=apl>
<syntaxhighlight lang=apl>
       x←3 1 2
       x←3 1 2
       y←4 6 5
       y←4 6 5
Line 24: Line 24:
== Close composition ==
== Close composition ==


In [[SHARP APL]] and [[J]], Over is implemented as a [[close composition]], meaning that (using SHARP syntax) <source lang=apl inline>f⍤g</syntaxhighlight> has the overall [[function rank]] of <source lang=apl inline>g</syntaxhighlight>. J uses <code>&</code> for the close form and <code>&:</code> for the rankless form that appears in modern APLs.
In [[SHARP APL]] and [[J]], Over is implemented as a [[close composition]], meaning that (using SHARP syntax) <syntaxhighlight lang=apl inline>f⍤g</syntaxhighlight> has the overall [[function rank]] of <syntaxhighlight lang=apl inline>g</syntaxhighlight>. J uses <code>&</code> for the close form and <code>&:</code> for the rankless form that appears in modern APLs.


== History ==
== History ==


[[Ken Iverson]] defined Over in 1978 as part of [[Operators and Functions]],<ref>[[Ken Iverson]]. [https://www.jsoftware.com/papers/opfns.htm ''Operators and Functions''], §8 Composition and Duality. IBM Research Report #RC7091. 1978-04-26.</ref> with the glyph <source lang=apl inline>¨</syntaxhighlight>. He called it Composition, as there was no [[Atop operator]]. It was added to [[SHARP APL]] as a [[close composition]] with glyph <source lang=apl inline>⍤</syntaxhighlight> and name "on", with a limited implementation in 1981<ref>[https://www.jsoftware.com/papers/satn41.htm "Composition and Enclosure"]. SATN-41, 1981-06-20.</ref> followed by a full implementation in 1983 with the introduction of [[function rank]].<ref>[https://www.jsoftware.com/papers/satn45.htm "Language Extensions of May 1983"]. SATN-45, 1983-05-02.</ref>
[[Ken Iverson]] defined Over in 1978 as part of [[Operators and Functions]],<ref>[[Ken Iverson]]. [https://www.jsoftware.com/papers/opfns.htm ''Operators and Functions''], §8 Composition and Duality. IBM Research Report #RC7091. 1978-04-26.</ref> with the glyph <syntaxhighlight lang=apl inline>¨</syntaxhighlight>. He called it Composition, as there was no [[Atop operator]]. It was added to [[SHARP APL]] as a [[close composition]] with glyph <syntaxhighlight lang=apl inline>⍤</syntaxhighlight> and name "on", with a limited implementation in 1981<ref>[https://www.jsoftware.com/papers/satn41.htm "Composition and Enclosure"]. SATN-41, 1981-06-20.</ref> followed by a full implementation in 1983 with the introduction of [[function rank]].<ref>[https://www.jsoftware.com/papers/satn45.htm "Language Extensions of May 1983"]. SATN-45, 1983-05-02.</ref>


The glyph <source lang=apl inline>⍥</syntaxhighlight> appeared in [[NARS2000]], with name "Composition", by 2011.<ref>[http://wiki.nars2000.org/index.php?title=Composition Composition]. [[NARS2000]] Wiki.</ref> The name "Over" was used in [[Dyalog APL 18.0]], suggested by [[Adám Brudzewsky]].<ref>Adam Brudzewsky. Chat message {{m|42021088}}. [[APL Orchard]]. 31 Dec 2017.</ref>
The glyph <syntaxhighlight lang=apl inline>⍥</syntaxhighlight> appeared in [[NARS2000]], with name "Composition", by 2011.<ref>[http://wiki.nars2000.org/index.php?title=Composition Composition]. [[NARS2000]] Wiki.</ref> The name "Over" was used in [[Dyalog APL 18.0]], suggested by [[Adám Brudzewsky]].<ref>Adam Brudzewsky. Chat message {{m|42021088}}. [[APL Orchard]]. 31 Dec 2017.</ref>


== External links ==
== External links ==

Latest revision as of 22:13, 10 September 2022

Over () is a primitive dyadic operator which takes two function operands and produces a derived function which pre-processes the argument(s) using the monadic right operand, before applying the left operand on/between the result(s).

Explanation

When the resulting function is used monadically, it has the same behaviour as if the Beside or Atop operator had been used:

  (g  h) 
g (h )

When the resulting function is used dyadically, both arguments are pre-processed:

 (g  h) 
(h ) g (h )

Examples

      x3 1 2
      y4 6 5
      x +(/) y ⍝ add the max of x and max of y
9
      ⍝ same as
      (/x)+⌈/y
9

Close composition

In SHARP APL and J, Over is implemented as a close composition, meaning that (using SHARP syntax) fg has the overall function rank of g. J uses & for the close form and &: for the rankless form that appears in modern APLs.

History

Ken Iverson defined Over in 1978 as part of Operators and Functions,[1] with the glyph ¨. He called it Composition, as there was no Atop operator. It was added to SHARP APL as a close composition with glyph and name "on", with a limited implementation in 1981[2] followed by a full implementation in 1983 with the introduction of function rank.[3]

The glyph appeared in NARS2000, with name "Composition", by 2011.[4] The name "Over" was used in Dyalog APL 18.0, suggested by Adám Brudzewsky.[5]

External links

Lessons

Documentation

References

  1. Ken Iverson. Operators and Functions, §8 Composition and Duality. IBM Research Report #RC7091. 1978-04-26.
  2. "Composition and Enclosure". SATN-41, 1981-06-20.
  3. "Language Extensions of May 1983". SATN-45, 1983-05-02.
  4. Composition. NARS2000 Wiki.
  5. Adam Brudzewsky. Chat message 42021088. APL Orchard. 31 Dec 2017.
APL built-ins [edit]
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
Operators SearchReplace