Beside: Difference between revisions

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(f∘g⍨ is Withe)
 
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{{Built-in|Beside|∘}}, '''Compose''' or '''After''' is a [[primitive operator]]. It shares the glyph <source lang=apl inline>∘</source> with [[Bind]]. 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 applies <source lang=apl inline>f</source> to the result of applying <source lang=apl inline>g</source> to the argument.
{{Built-in|Beside|∘}}, '''Compose''' or '''After''' is a [[primitive operator]]. It shares the glyph [[Jot]] (<syntaxhighlight lang=apl inline>∘</syntaxhighlight>) with [[Bind]]. Called [[Dyadic function|dyadically]] with function [[operand]]s <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 applies <syntaxhighlight lang=apl inline>f</syntaxhighlight> to the result of applying <syntaxhighlight lang=apl inline>g</syntaxhighlight> to the 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>f g Y</source>. Thus, beside can be defined as the [[dop]] <source lang=apl inline>{⍺←⊢ ⋄ ⍺ ⍺⍺ ⍵⍵ ⍵}</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>f g Y</syntaxhighlight>. Thus, beside can be defined as the [[dop]] <syntaxhighlight lang=apl inline>{⍺←⊢ ⋄ ⍺ ⍺⍺ ⍵⍵ ⍵}</syntaxhighlight>.


== Examples ==
== Examples ==
When used [[monadic]]ally, <source lang=apl inline>f∘g</source> behaves the same as an [[atop]]:
When used [[monadic]]ally, <syntaxhighlight lang=apl inline>f∘g</syntaxhighlight> behaves the same as an [[atop]]:


<source lang=apl>
<syntaxhighlight lang=apl>
       -∘÷ 2  
       -∘÷ 2  
¯0.5
¯0.5
Line 12: Line 12:
       -(÷2)
       -(÷2)
¯0.5
¯0.5
</source>
</syntaxhighlight>


When used [[dyadic]]ally, <source lang=apl inline>f∘g</source> forms a dyadic [[hook]]:
When used [[dyadic]]ally, <syntaxhighlight lang=apl inline>f∘g</syntaxhighlight> forms a dyadic [[hook]]:


<source lang=apl>
<syntaxhighlight lang=apl>
       'oy'≡∘⌽'yo'
       'oy'≡∘⌽'yo'
1
1
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       'oy'≡⌽'yo'
       'oy'≡⌽'yo'
1
1
</source>
</syntaxhighlight>


When used monadically with [[Commute]], <source lang=apl inline>f∘g</source> forms a monadic [[hook]]:
When used monadically with [[Commute]], <syntaxhighlight lang=apl inline>f∘g</syntaxhighlight> forms a monadic [[hook]]:
<source lang=apl>
<syntaxhighlight lang=apl>
       ≡∘⌽⍨'UwU'
       ≡∘⌽⍨'UwU'
1
1
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       'UwU'≡⌽'UwU'
       'UwU'≡⌽'UwU'
1
1
</source>
</syntaxhighlight>
This is equivalent to the dyadic behaviour of [[Withe]] <syntaxhighlight lang=apl inline>f⍩g</syntaxhighlight>.


== External links ==
== External links ==

Latest revision as of 06:20, 28 February 2024

∘

Beside (∘), Compose or After is a primitive operator. It shares the glyph Jot (∘) with Bind. 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 applies f to the result of applying g to the argument.

In usage, X f∘g Y is equivalent to X f g Y, and f∘g Y is equivalent to f g Y. Thus, beside can be defined as the dop {⍺←⊢ ⋄ ⍺ ⍺⍺ ⍵⍵ ⍵}.

Examples

When used monadically, f∘g behaves the same as an atop: 

      -∘÷ 2 
¯0.5
      ⍝ same as
      -(÷2)
¯0.5

When used dyadically, f∘g forms a dyadic hook: 

      'oy'≡∘⌽'yo'
1
      ⍝ same as
      'oy'≡⌽'yo'
1

When used monadically with Commute, f∘g forms a monadic hook: 

      ≡∘⌽⍨'UwU'
1
      ⍝ same as this, because operators are left-associative, unlike functions which are right-associative
      (≡∘⌽)⍨'UwU'
1
      ⍝ same as
      'UwU'≡⌽'UwU'
1

This is equivalent to the dyadic behaviour of Withe f⍩g.

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
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