Atop (operator)

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Atop () is a primitive dyadic operator which takes two function operands and produces a derived function which uses the left operand monadically to post-processes the result of the ambivalent right operand.

Explanation

When the resulting function is used monadically, it has the same behaviour as if the Atop 2-train or any of the Beside or Over operators had been used:

  (g  h) 
g (h )

When the resulting function is used dyadically, the result is post-processed:

 (g  h) 
g ( h )

Examples

      x3 1 2
      y4 6 5
      x - y ⍝ the negation of the max of x y
¯4 ¯6 ¯5
      ⍝ same as
      -xy
¯4 ¯6 ¯5

Close composition

In SHARP APL and J, Atop 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

Atop was defined as subordinate to Over in Ken Iverson's 1978 paper Operators and Functions: that is, the derived function f¨g works as an Atop if f is strictly monadic or (in the dyadic case) g is strictly dyadic. 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" (initially "over"), with a limited implementation in 1981[1] followed by a full implementation in 1983 with the introduction of function rank.[2] The name "Atop" was introduced by J (which uses "At" for its non-close form). The glyph was chosen for Dyalog APL 18.0, shared with the Rank operator.

External links

Lessons

Documentation

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  1. "Composition and Enclosure". SATN-41, 1981-06-20.
  2. "Language Extensions of May 1983". SATN-45, 1983-05-02.