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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 <syntaxhighlight lang=apl inline>f</syntaxhighlight> and <syntaxhighlight lang=apl inline>g</syntaxhighlight>, it uses <syntaxhighlight lang=apl inline>g</syntaxhighlight> [[Monadic function|monadically]] to pre-processes the right argument before applying <syntaxhighlight lang=apl inline>f</syntaxhighlight> to the given left argument and pre-processed right argument. Called [[Monadic function|monadically]] with operands <syntaxhighlight lang=apl inline>f</syntaxhighlight> and <syntaxhighlight lang=apl inline>g</syntaxhighlight>, it uses <syntaxhighlight lang=apl inline>g</syntaxhighlight> monadically to pre-processes the argument before applying <syntaxhighlight 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, <syntaxhighlight lang=apl inline>X f⍩g Y</syntaxhighlight> is equivalent to <syntaxhighlight lang=apl inline>X f g Y</syntaxhighlight>, and <syntaxhighlight lang=apl inline>f⍩g Y</syntaxhighlight> is equivalent to <syntaxhighlight lang=apl inline>Y f g Y</syntaxhighlight>. Thus, Withe can be defined as the [[dop]] <syntaxhighlight lang=apl inline>{⍺←⍵ ⋄ ⍺ ⍺⍺ ⍵⍵ ⍵}</syntaxhighlight> and is equivalent to the [[derived function]] <syntaxhighlight 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>
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 [[Kap]] as '''Compose''' (<syntaxhighlight lang=apl inline>∘</syntaxhighlight>) and 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>


== See also ==
== See also ==

Latest revision as of 06:17, 28 February 2024

⍩

Withe (⍩) is a primitive operator which forms a hook. Called dyadically with function operands f and g, it uses g monadically to pre-processes the right argument before applying f to the given left argument and pre-processed right argument. Called monadically with operands f and g, it uses g monadically to pre-processes the argument before applying f to the argument and pre-processed argument.

In usage, X f⍩g Y is equivalent to X f g Y, and f⍩g Y is equivalent to Y f g Y. Thus, Withe can be defined as the dop {⍺←⍵ ⋄ ⍺ ⍺⍺ ⍵⍵ ⍵} and is equivalent to the derived function f∘g⍨⍨.

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 Kap as Compose (∘) and 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.


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
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