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Frame agreement (view source)

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=== Model ===
=== Model ===
In dialects that do not feature frame prefix agreement, it can nevertheless be utilised by the introduction of an explicit operator:
In dialects that do not feature frame prefix agreement, it can nevertheless be utilised by the introduction of an explicit operator:


<syntaxhighlight lang=apl>
<syntaxhighlight lang=apl>
       _FA_←{
       _FA_←{
           assert←{0≡⍵:'no common frame prefix' ⎕SIGNAL 4 ⋄ ⍵}
           assert←{0≡⍵:'error: no common frame prefix' ⎕SIGNAL 4 ⋄ ⍵}
           r←1↓⌽3⍴⌽⍵⍵ ⋄ pp←≢¨p←⍴¨⍺⍵              ⍝ dyadic ranks, array ranks
           r←1↓⌽3⍴⌽⍵⍵ ⋄ ar←≢¨p←⍴¨⍺⍵      ⍝ dyadic ranks, array ranks, shapes
           c←r{⍺≥0:⍺⌊⍵ ⋄ ⍵≤∣⍺:0⌈⍺+⍵ ⋄ ⍺+⍵}¨pp    ⍝ cell ranks
           c←r{⍺>0:⍺⌊⍵ ⋄ 0⌈⍺+⍵}¨ar      ⍝ cell ranks
           fl fr←(-c)↓¨p                         ⍝ frames                       
           fl fr←(-c)↓¨p                 ⍝ left and right frames                       
           s←fl{⍺<⍥≢⍵:⍺ ⋄ ⍵}fr                   ⍝ shorter frame
           s←fl{⍺<⍥≢⍵:⍺ ⋄ ⍵}fr           ⍝ shorter frame
           k←{⍬≡⍵:99 ⋄ -≢⍵}s                     ⍝ relative rank
           k←{⍬≡⍵:99 ⋄ -≢⍵}s             ⍝ relative rank
           assert ⍺∧⍥(s≡(≢s)↑⍴)⍵:                 ⍝ do frames agree?
           assert ⍺∧⍥(s≡(≢s)↑⍴)⍵:       ⍝ do frames agree?
           ⍺ ⍺⍺⍤c⍤k⊢⍵
           ⍺ ⍺⍺⍤c⍤k⊢⍵
       }
       }
      ⎕IO←0
      x←⍳2
      y←2 3 2⍴⍳12
       x+_FA_ 0 1⊢y
       x+_FA_ 0 1⊢y
  0  1
  0  1
Line 152: Line 148:
</syntaxhighlight>
</syntaxhighlight>
{{Works in|[[Dyalog APL]]}}
{{Works in|[[Dyalog APL]]}}
The <syntaxhighlight lang=apl inline>c←r{⍺≥0:⍺⌊⍵ ⋄ ⍵≤∣⍺:0⌈⍺+⍵ ⋄ ⍺+⍵}¨pp    ⍝ cell ranks</syntaxhighlight> line of <syntaxhighlight lang=apl inline>_FA_</syntaxhighlight> addresses various asymmetries in computing cell rank. The table below shows the cell ranks corresponding to pairs of operand and argument ranks.
{|class=wikitable
! operand rank          !!        argument rank          !! cell rank
|-
| <syntaxhighlight lang=apl inline>¯5</syntaxhighlight>    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>0</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>¯3</syntaxhighlight>    || <syntaxhighlight lang=apl inline>5</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>2</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>¯3</syntaxhighlight>    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>0</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>3</syntaxhighlight>    || <syntaxhighlight lang=apl inline>5</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>5</syntaxhighlight>    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>3</syntaxhighlight>    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>
|}
The next table demonstrates the relations (in tacit code) among the operand ranks and corresponding argument ranks, given what the cell rank should be.
{|class=wikitable
! operand rank (o)    !!    relation between o and a    !!      argument rank (a)    !!    resultant cell rank
|-
| <syntaxhighlight lang=apl inline>¯5</syntaxhighlight>    ||    <syntaxhighlight lang=apl inline>0⌈+</syntaxhighlight>    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>0</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>¯3</syntaxhighlight>    ||      <syntaxhighlight lang=apl inline>+</syntaxhighlight>    || <syntaxhighlight lang=apl inline>5</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>2</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>¯3</syntaxhighlight>    ||      <syntaxhighlight lang=apl inline>+</syntaxhighlight>    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>0</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>3</syntaxhighlight>    ||      <syntaxhighlight lang=apl inline>⌊</syntaxhighlight>    || <syntaxhighlight lang=apl inline>5</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>5</syntaxhighlight>    ||      <syntaxhighlight lang=apl inline>⌊</syntaxhighlight>    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>
|-
| <syntaxhighlight lang=apl inline>3</syntaxhighlight>    ||      <syntaxhighlight lang=apl inline>⌊</syntaxhighlight>    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>                    || <syntaxhighlight lang=apl inline>3</syntaxhighlight>
|-
|}
[[Category:Leading axis theory]][[Category:Function characteristics]][[Category:Conformability]]{{APL features}}
[[Category:Leading axis theory]][[Category:Function characteristics]][[Category:Conformability]]{{APL features}}
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