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

      x←3 1 2
      y←4 6 5
      x -⍤⌈ y ⍝ the negation of the max of x y
¯4 ¯6 ¯5
      ⍝ same as
      -x⌈y
¯4 ¯6 ¯5

Close composition

In SHARP APL and J, Atop 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

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 (the combined operator ¨ was called Composition). 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

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