Over: Difference between revisions

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In [[SHARP APL]] and [[J]], Over is implemented as a [[close composition]], meaning that (using SHARP syntax) <source lang=apl inline>f⍤g</source> has the overall [[function rank]] of <source lang=apl inline>g</source>. 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) <source lang=apl inline>f⍤g</source> has the overall [[function rank]] of <source lang=apl inline>g</source>. J uses <code>&</code> for the close form and <code>&:</code> for the rankless form that appears in modern APLs.
== 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>¨</source>. 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>⍤</source> and name "upon", 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>⍥</source> 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>[https://chat.stackexchange.com/transcript/message/42021088#42021088]</ref>


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

Revision as of 02:29, 26 April 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

      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

Close composition

In SHARP APL and J, Over is implemented as a close composition, meaning that (using SHARP syntax) f⍤g 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 "upon", 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

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
  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. ↑ [1]
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