Withe: Difference between revisions

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{{Built-in|Withe|⍩}} is a [[primitive operator]] which forms a [[hook]]. Called [[Dyadic function|dyadically]] with function operands <source lang=apl inline>f</source> and <source lang=apl inline>g</source>, it uses <source lang=apl inline>g</source> [[Monadic function|monadically]] to pre-processes the right argument before applying <source lang=apl inline>f</source> to the given left argument and pre-processed right argument. Called [[Monadic function|monadically]] with operands <source lang=apl inline>f</source> and <source lang=apl inline>g</source>, it uses <source lang=apl inline>g</source> monadically to pre-processes the argument before applying <source lang=apl inline>f</source> to the argument and pre-processed argument.
{{Built-in|Withe|⍩}} is a [[primitive operator]] which forms a [[hook]]. Called [[Dyadic function|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> [[Monadic function|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 [[Monadic function|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</source> is equivalent to <source lang=apl inline>X f g Y</source>, and <source lang=apl inline>f⍩g Y</source> is equivalent to <source lang=apl inline>Y f g Y</source>. Thus, Withe can be defined as the [[dop]] <source lang=apl inline>{⍺←⍵ ⋄ ⍺ ⍺⍺ ⍵⍵ ⍵}</source> and is equivalent to the [[derived function]] <source lang=apl inline>f∘g⍨⍨</source>.
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]],<ref>[[Ken Iverson]]. [[A Dictionary of APL]]. [https://www.jsoftware.com/papers/APLDictionary1.htm#withe Withe]. [[APL Quote Quad]], Volume 18, Number 1, 1987-09.</ref> but substituted by the 2-[[train]] in [[J]] after the proposal in [[Ken Iverson|Iverson]] and [[Eugene McDonnell|McDonnell]]'s paper ''Phrasal Forms''.<ref>[[Ken Iverson]] and [[Eugene McDonnell]]. [http://www.jsoftware.com/papers/fork.htm Phrasal forms] at [[APL89]].</ref> It is present in [[BQN]] as '''After''' (<code>⟜</code>).<ref>[[Marshall Lochbaum]]. ''Tutorial: Combinators''. [https://mlochbaum.github.io/BQN/tutorial/combinator.html#before-and-after Before and After]. Accessed 2021-09-01.</ref>
Withe first appeared in [[A Dictionary of APL]],<ref>[[Ken Iverson]]. [[A Dictionary of APL]]. [https://www.jsoftware.com/papers/APLDictionary1.htm#withe Withe]. [[APL Quote Quad]], Volume 18, Number 1, 1987-09.</ref> but substituted by the 2-[[train]] in [[J]] after the proposal in [[Ken Iverson|Iverson]] and [[Eugene McDonnell|McDonnell]]'s paper ''Phrasal Forms''.<ref>[[Ken Iverson]] and [[Eugene McDonnell]]. [http://www.jsoftware.com/papers/fork.htm Phrasal forms] at [[APL89]].</ref> It is present in [[BQN]] as '''After''' (<code>⟜</code>).<ref>[[Marshall Lochbaum]]. ''Tutorial: Combinators''. [https://mlochbaum.github.io/BQN/tutorial/combinator.html#before-and-after Before and After]. Accessed 2021-09-01.</ref>

Revision as of 10:50, 11 September 2022

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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