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{{Built-in|Over|<nowiki>⍥</nowiki>}} is a [[dyadic operator]] which takes two [[function]]s and produce a [[function]] (<source lang=apl inline>⍥</source>).
{{Built-in|Over|⍥}} is a [[primitive operator|primitive]] [[dyadic operator]] which takes two [[function]] [[operand]]s 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 ==
== Explanation ==
When the resulting function is used [[monadic]]ally, it is the same as [[Atop]].
When the resulting function is used [[monadic]]ally, it has the same behaviour as if the [[Beside]] or [[Atop operator]] had been used:
{|
{|
|<source lang=apl>  (g ⍥ h) ⍵</source>|| {{←→}} ||<source lang=apl>g (h ⍵)</source>
|<source lang=apl>  (g ⍥ h) ⍵</source>|| {{←→}} ||<source lang=apl>g (h ⍵)</source>
|}
|}
When the resulting function is used [[dyadic]]ally, then it forms an [[Over]] expression (which is the true purpose of this operator).
When the resulting function is used [[dyadic]]ally, both arguments are pre-processed:
{|
{|
|<source lang=apl>⍺ (g ⍥ h) ⍵</source>|| {{←→}} ||<source lang=apl>(h ⍺) g (h ⍵)</source>
|<source lang=apl>⍺ (g ⍥ h) ⍵</source>|| {{←→}} ||<source lang=apl>(h ⍺) g (h ⍵)</source>
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== Examples ==
== Examples ==
<source lang=apl>
<source lang=apl>
       x←1 2 3
       x←3 1 2
       y←4 5 6
       y←4 6 5
    x +⍥(⌈/) y ⍝ add the max of x and max of y
      x +⍥(⌈/) y ⍝ add the max of x and max of y
9
9
       ⍝ same as
       ⍝ same as
Line 21: Line 21:
9
9
</source>
</source>
== External links ==
=== Lessons ===
* [https://chat.stackexchange.com/rooms/52405/conversation/lesson-47-atop--and-over-#55084108 APL Cultivation]
=== Documentation ===
* [https://help.dyalog.com/latest/#Language/Primitive%20Operators/Over.htm Dyalog]
* J [https://www.jsoftware.com/help/dictionary/d632.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/ampco NuVoc]
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]

Revision as of 21:50, 9 September 2021

⍥

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

      x←3 1 2
      y←4 6 5
      x +⍥(⌈/) y ⍝ add the max of x and max of y
9
      ⍝ same as
      (⌈/x)+⌈/y
9

External links

Lessons

Documentation

APL built-ins [edit]
Primitives (Timeline) Functions
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
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
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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