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...e [[comparison tolerance]] and [[close composition]] operators including [[Under]]. ...taxhighlight lang=apl inline><</syntaxhighlight> || || See [[#Structural|Structural]] || 0 0 || [[Less Than]]

...then undoing the pre-processing.<ref>[https://mlochbaum.github.io/BQN/help/under.html BQN: Circle Jot (⌾)]</ref> In [[SHARP APL]] and [[J]], Under is implemented as a [[close composition]], meaning that (using SHARP syntax

.... They can also be combined with an array-oriented [[operator]] to perform structural manipulations on arrays. Identity functions are a central feature of [[taci === Structural manipulation ===

...ype of the original array elements was smaller (in bits) than a pointer, [[structural function]]s on the array will be slower. Even if the original type was larg

...n" or subdivide it further. Two prominent subcategories of functions are [[structural function]]s, which rearrange elements of the argument or its subarrays with

...ed with <syntaxhighlight lang=apl inline>u</syntaxhighlight>. [[Structural Under]] allows the assignment to be performed in a functional style, with no temp ((~u)\a) ⊣⍢(u∘/) (u\b) ⍝ Structural Under

...For many operations, such as [[scalar function]] [[reduction]]s and most [[structural function]]s, these extensions are equivalent. Reversing along the first axi

...itself until it is long enough. An implementation using indices instead of structural manipulation is also possible:

...xhighlight lang=apl inline>F⍢G</syntaxhighlight> ||colspan=2| [[Structural under]]

...ral agencies). These systems were unique in that they not only presented a structural view of the material, but a chronological view as well. Becker's second rec

...Instead we can insert the glider into a matrix of zeros using [[structural Under]]:

Under the direction of [[Roger Hui]], who had been hired by [[Dyalog Ltd.]] in 20 ...rformance.htm performance improvements] were made in [[structural function|structural]] and selective functions such as [[Transpose]], [[Catenate]], [[Take]], [[

...]], as well as other primitives characteristic of BQN such as [[structural Under]], [[Classify]], and a [[Transpose]] that rotates the axes of its argument | <code>⍜</code> || [[Under]] || Dyadic modifier || Apply a function under another

The J source code was made open under the GPL in March 2011.<ref>[[Eric Iverson]]. [http://www.jsoftware.com/pipe ...|| 1990-10-22 || [[Rank operator|Rank]] with a function right operand, [[Under]]

...|16.0]], it is used for Boolean [[Compress]] and [[Expand]], and several [[structural function]]s on Boolean arrays.

* '''An On-Line Proof Checker Operating under APL/360, with Applications for Computer-Aided Instruction in Logic, Mathema * '''Speech synthesis under APL'''. Donald B. Rueter. [https://doi.org/10.1145/800269.810855].