Withe

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Withe () is a primitive operator which forms a hook. Called dyadically with function operands <source lang=apl inline>f</syntaxhighlight> and <source lang=apl inline>g</syntaxhighlight>, it uses <source lang=apl inline>g</syntaxhighlight> monadically to pre-processes the right argument before applying <source lang=apl inline>f</syntaxhighlight> to the given left argument and pre-processed right argument. Called monadically with operands <source lang=apl inline>f</syntaxhighlight> and <source lang=apl inline>g</syntaxhighlight>, it uses <source lang=apl inline>g</syntaxhighlight> monadically to pre-processes the argument before applying <source lang=apl inline>f</syntaxhighlight> to the argument and pre-processed argument.

In usage, <source lang=apl inline>X f⍩g Y</syntaxhighlight> is equivalent to <source lang=apl inline>X f g Y</syntaxhighlight>, and <source lang=apl inline>f⍩g Y</syntaxhighlight> is equivalent to <source lang=apl inline>Y f g Y</syntaxhighlight>. Thus, Withe can be defined as the dop <source lang=apl inline>{⍺←⍵ ⋄ ⍺ ⍺⍺ ⍵⍵ ⍵}</syntaxhighlight> and is equivalent to the derived function <source lang=apl inline>f∘g⍨⍨</syntaxhighlight>.

Withe first appeared in A Dictionary of APL,[1] but substituted by the 2-train in J after the proposal in Iverson and McDonnell's paper Phrasal Forms.[2] It is present in BQN as After ().[3]

See also

References

  1. Ken Iverson. A Dictionary of APL. Withe. APL Quote Quad, Volume 18, Number 1, 1987-09.
  2. Ken Iverson and Eugene McDonnell. Phrasal forms at APL89.
  3. Marshall Lochbaum. Tutorial: Combinators. Before and After. Accessed 2021-09-01.


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