Personalized Array Translator: Difference between revisions

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m (Text replacement - "<source" to "<syntaxhighlight")
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! Name !! PAT statement !! Modern equivalent
! Name !! PAT statement !! Modern equivalent
|-
|-
| [[Add]] || <code>Z = X + Y</code> || <source lang=apl inline>Z ← X + Y</source>
| [[Add]] || <code>Z = X + Y</code> || <syntaxhighlight lang=apl inline>Z ← X + Y</source>
|-
|-
| [[Subtract]] || <code>Z = X - Y</code> || <source lang=apl inline>Z ← X - Y</source>
| [[Subtract]] || <code>Z = X - Y</code> || <syntaxhighlight lang=apl inline>Z ← X - Y</source>
|-
|-
| [[Multiply]] || <code>Z = X * Y</code> || <source lang=apl inline>Z ← X × Y</source>
| [[Multiply]] || <code>Z = X * Y</code> || <syntaxhighlight lang=apl inline>Z ← X × Y</source>
|-
|-
| [[Divide]] || <code>Z = X @D Y</code> || <source lang=apl inline>Z ← X ÷ Y</source>
| [[Divide]] || <code>Z = X @D Y</code> || <syntaxhighlight lang=apl inline>Z ← X ÷ Y</source>
|-
|-
| [[And]] || <code>Z = X @A Y</code> || <source lang=apl inline>Z ← X ∧ Y</source>
| [[And]] || <code>Z = X @A Y</code> || <syntaxhighlight lang=apl inline>Z ← X ∧ Y</source>
|-
|-
| [[Or]] || <code>Z = X @O Y</code> || <source lang=apl inline>Z ← X ∨ Y</source>
| [[Or]] || <code>Z = X @O Y</code> || <syntaxhighlight lang=apl inline>Z ← X ∨ Y</source>
|-
|-
| [[Constant]] Zero || <code>Z = X @000 Y</code> || <source lang=apl inline>Z ← X(=≠=)Y</source>
| [[Constant]] Zero || <code>Z = X @000 Y</code> || <syntaxhighlight lang=apl inline>Z ← X(=≠=)Y</source>
|-
|-
| [[Greater than]] || <code>Z = X @001 Y</code> || <source lang=apl inline>Z ← X > Y</source>
| [[Greater than]] || <code>Z = X @001 Y</code> || <syntaxhighlight lang=apl inline>Z ← X > Y</source>
|-
|-
| [[Equal]] || <code>Z = X @010 Y</code> || <source lang=apl inline>Z ← X = Y</source>
| [[Equal]] || <code>Z = X @010 Y</code> || <syntaxhighlight lang=apl inline>Z ← X = Y</source>
|-
|-
| [[Greater than or equal]] || <code>Z = X @011 Y</code> || <source lang=apl inline>Z ← X ≥ Y</source>
| [[Greater than or equal]] || <code>Z = X @011 Y</code> || <syntaxhighlight lang=apl inline>Z ← X ≥ Y</source>
|-
|-
| [[Less than]] || <code>Z = X @100 Y</code> || <source lang=apl inline>Z ← X < Y</source>
| [[Less than]] || <code>Z = X @100 Y</code> || <syntaxhighlight lang=apl inline>Z ← X < Y</source>
|-
|-
| [[Not equal]] || <code>Z = X @101 Y</code> || <source lang=apl inline>Z ← X ≠ Y</source>
| [[Not equal]] || <code>Z = X @101 Y</code> || <syntaxhighlight lang=apl inline>Z ← X ≠ Y</source>
|-
|-
| [[Less than or equal]] || <code>Z = X @110 Y</code> || <source lang=apl inline>Z ← X ≤ Y</source>
| [[Less than or equal]] || <code>Z = X @110 Y</code> || <syntaxhighlight lang=apl inline>Z ← X ≤ Y</source>
|-
|-
| [[Constant]] One || <code>Z = X @111 Y</code> || <source lang=apl inline>Z ← X(===)Y</source>
| [[Constant]] One || <code>Z = X @111 Y</code> || <syntaxhighlight lang=apl inline>Z ← X(===)Y</source>
|-
|-
| "Ceiling" ([[Maximum]]) || <code>Z = X @C Y</code> || <source lang=apl inline>Z ← X ⌈ Y</source>
| "Ceiling" ([[Maximum]]) || <code>Z = X @C Y</code> || <syntaxhighlight lang=apl inline>Z ← X ⌈ Y</source>
|-
|-
| "Floor" ([[Minimum]]) || <code>Z = X @F Y</code> || <source lang=apl inline>Z ← X ⌊ Y</source>
| "Floor" ([[Minimum]]) || <code>Z = X @F Y</code> || <syntaxhighlight lang=apl inline>Z ← X ⌊ Y</source>
|-
|-
| [[Exponential]] || <code>Z = X @E Y</code> || <source lang=apl inline>Z ← X * Y</source>
| [[Exponential]] || <code>Z = X @E Y</code> || <syntaxhighlight lang=apl inline>Z ← X * Y</source>
|-
|-
| [[Assignment]] || <code>Z = X</code> || <source lang=apl inline>Z ← X</source>
| [[Assignment]] || <code>Z = X</code> || <syntaxhighlight lang=apl inline>Z ← X</source>
|-
|-
| [[Not]] || <code>Z = @N X</code> || <source lang=apl inline>Z ← ~ X</source>
| [[Not]] || <code>Z = @N X</code> || <syntaxhighlight lang=apl inline>Z ← ~ X</source>
|-
|-
| [[Absolute value]] || <code>Z = @A X</code> || <source lang=apl inline>Z ← | X</source>
| [[Absolute value]] || <code>Z = @A X</code> || <syntaxhighlight lang=apl inline>Z ← | X</source>
|-
|-
| [[Circular|Sine]] || <code>Z = @S X</code> || <source lang=apl inline>Z ← 1 ○ X</source>
| [[Circular|Sine]] || <code>Z = @S X</code> || <syntaxhighlight lang=apl inline>Z ← 1 ○ X</source>
|-
|-
| [[Circular|Cosine]] || <code>Z = @C X</code> || <source lang=apl inline>Z ← 2 ○ X</source>
| [[Circular|Cosine]] || <code>Z = @C X</code> || <syntaxhighlight lang=apl inline>Z ← 2 ○ X</source>
|-
|-
| [[Log]] (base 10) || <code>Z = @L X</code> || <source lang=apl inline>Z ← 10 ⍟ X</source>
| [[Log]] (base 10) || <code>Z = @L X</code> || <syntaxhighlight lang=apl inline>Z ← 10 ⍟ X</source>
|-
|-
| [[Round up]] || <code>Z = @U X</code> || <source lang=apl inline>Z ← ⌈ X</source>
| [[Round up]] || <code>Z = @U X</code> || <syntaxhighlight lang=apl inline>Z ← ⌈ X</source>
|-
|-
| [[Round down]] || <code>Z = @D X</code> || <source lang=apl inline>Z ← ⌊ X</source>
| [[Round down]] || <code>Z = @D X</code> || <syntaxhighlight lang=apl inline>Z ← ⌊ X</source>
|-
|-
| [[Matrix]] [[Transpose]] || <code>Z = @T X</code> || <source lang=apl inline>Z ← ⍉ X</source>
| [[Matrix]] [[Transpose]] || <code>Z = @T X</code> || <syntaxhighlight lang=apl inline>Z ← ⍉ X</source>
|-
|-
| [[Reduction]]* || <code>Z = @U X</code> || <source lang=apl inline>Z ← +/ X</source>
| [[Reduction]]* || <code>Z = @U X</code> || <syntaxhighlight lang=apl inline>Z ← +/ X</source>
|-
|-
| [[Base]] || <code>Z = X @B Y</code> || <source lang=apl inline>Z ← X ⊥ Y</source>
| [[Base]] || <code>Z = X @B Y</code> || <syntaxhighlight lang=apl inline>Z ← X ⊥ Y</source>
|-
|-
| [[Residue]] || <code>Z = X @W Y</code> || <source lang=apl inline>Z ← X | Y</source>
| [[Residue]] || <code>Z = X @W Y</code> || <syntaxhighlight lang=apl inline>Z ← X | Y</source>
|-
|-
| [[Compression]] || <code>Z = U / X</code> || <source lang=apl inline>Z ← U / X</source>
| [[Compression]] || <code>Z = U / X</code> || <syntaxhighlight lang=apl inline>Z ← U / X</source>
|-
|-
| Post <code>Z</code> with <code>X</code> controlled by <code>U</code> || <code>Z = U @P X</code> ||
| Post <code>Z</code> with <code>X</code> controlled by <code>U</code> || <code>Z = U @P X</code> ||
|-
|-
| [[Reshape|Dimension array]] || <code>@D X , C , R</code> || <source lang=apl inline>X ← R C ⍴ X</source> or <source lang=apl inline>X ⍴⍨← R C</source>  
| [[Reshape|Dimension array]] || <code>@D X , C , R</code> || <syntaxhighlight lang=apl inline>X ← R C ⍴ X</source> or <syntaxhighlight lang=apl inline>X ⍴⍨← R C</source>  
|-
|-
| [[Catenate|Juxtaposition]] || <code>Z = X , X</code> || <source lang=apl inline>Z ← X , X</source>  
| [[Catenate|Juxtaposition]] || <code>Z = X , X</code> || <syntaxhighlight lang=apl inline>Z ← X , X</source>  
|-
|-
| Left [[rotate]] || <code>Z = K @L X</code> || <source lang=apl inline>Z ← K ⌽ X</source>  
| Left [[rotate]] || <code>Z = K @L X</code> || <syntaxhighlight lang=apl inline>Z ← K ⌽ X</source>  
|-
|-
| Right [[rotate]] || <code>Z = K @R X</code> || <source lang=apl inline>Z ← (-K) ⌽ X</source>  
| Right [[rotate]] || <code>Z = K @R X</code> || <syntaxhighlight lang=apl inline>Z ← (-K) ⌽ X</source>  
|-
|-
| Compare and [[branch]] || <code>X @C Y, A, B, C</code> ||
| Compare and [[branch]] || <code>X @C Y, A, B, C</code> ||
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| Update <code>X</code>, compare and branch || <code>@U X , Y , A , B , C</code> ||
| Update <code>X</code>, compare and branch || <code>@U X , Y , A , B , C</code> ||
|-
|-
| [[Range|Interval]] || <code>Z = @I I , J</code> || <source lang=apl inline>Z ← I … J</source>
| [[Range|Interval]] || <code>Z = @I I , J</code> || <syntaxhighlight lang=apl inline>Z ← I … J</source>
|-
|-
| Mid-selection array || <code>Z = @M I , J</code> ||
| Mid-selection array || <code>Z = @M I , J</code> ||
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| Get data (cards) || <code>@G X</code> ||
| Get data (cards) || <code>@G X</code> ||
|-
|-
| Type data || <code>@T X</code> || <source lang=apl inline>⎕ ← X</source>
| Type data || <code>@T X</code> || <syntaxhighlight lang=apl inline>⎕ ← X</source>
|-
|-
| Transform floating–alphanumeric || <code>Z = @X Y</code> || <source lang=apl inline>Z ← ⎕UCS Y</source> or <source lang=apl inline>Z ← ⎕AF X</source>
| Transform floating–alphanumeric || <code>Z = @X Y</code> || <syntaxhighlight lang=apl inline>Z ← ⎕UCS Y</source> or <syntaxhighlight lang=apl inline>Z ← ⎕AF X</source>
|-
|-
| Accept data from typewriter || <code>@A X</code> || <source lang=apl inline>X ← ⍞</source>
| Accept data from typewriter || <code>@A X</code> || <syntaxhighlight lang=apl inline>X ← ⍞</source>
|-
|-
| Type heading message and proceed || <code>@H any heading</code> ||
| Type heading message and proceed || <code>@H any heading</code> ||

Revision as of 21:27, 10 September 2022


The Personalized Array Translator (PAT) was an early experimental system create by Dr. Herbert Hellerman of the IBM System Research Institute. It was the first implementation of Iverson Notation as a programming language, preceding even IVSYS/7090. Ken Iverson used the PAT system in his early work with students in the local secondary school, and had a profound influence on Iverson's notation, as can be seen in his book Elementary Functions An Algorithmic Treatment.

In lieu of most proper APL glyphs, PAT used letters prefixed by the @ symbol. Comparison functions were denoted by @ followed by three digits 0 or 1, indicating whether the function would return 1 or 0 if the left argument would be less than, equal to, or greater than the right argument, respectively. The language only allowed application of one function per statement, with the result being assigned. Valid statements were:[1]

Name PAT statement Modern equivalent
Add Z = X + Y <syntaxhighlight lang=apl inline>Z ← X + Y</source>
Subtract Z = X - Y <syntaxhighlight lang=apl inline>Z ← X - Y</source>
Multiply Z = X * Y <syntaxhighlight lang=apl inline>Z ← X × Y</source>
Divide Z = X @D Y <syntaxhighlight lang=apl inline>Z ← X ÷ Y</source>
And Z = X @A Y <syntaxhighlight lang=apl inline>Z ← X ∧ Y</source>
Or Z = X @O Y <syntaxhighlight lang=apl inline>Z ← X ∨ Y</source>
Constant Zero Z = X @000 Y <syntaxhighlight lang=apl inline>Z ← X(=≠=)Y</source>
Greater than Z = X @001 Y <syntaxhighlight lang=apl inline>Z ← X > Y</source>
Equal Z = X @010 Y <syntaxhighlight lang=apl inline>Z ← X = Y</source>
Greater than or equal Z = X @011 Y <syntaxhighlight lang=apl inline>Z ← X ≥ Y</source>
Less than Z = X @100 Y <syntaxhighlight lang=apl inline>Z ← X < Y</source>
Not equal Z = X @101 Y <syntaxhighlight lang=apl inline>Z ← X ≠ Y</source>
Less than or equal Z = X @110 Y <syntaxhighlight lang=apl inline>Z ← X ≤ Y</source>
Constant One Z = X @111 Y <syntaxhighlight lang=apl inline>Z ← X(===)Y</source>
"Ceiling" (Maximum) Z = X @C Y <syntaxhighlight lang=apl inline>Z ← X ⌈ Y</source>
"Floor" (Minimum) Z = X @F Y <syntaxhighlight lang=apl inline>Z ← X ⌊ Y</source>
Exponential Z = X @E Y <syntaxhighlight lang=apl inline>Z ← X * Y</source>
Assignment Z = X <syntaxhighlight lang=apl inline>Z ← X</source>
Not Z = @N X <syntaxhighlight lang=apl inline>Z ← ~ X</source>
Absolute value Z = @A X X</source>
Sine Z = @S X <syntaxhighlight lang=apl inline>Z ← 1 ○ X</source>
Cosine Z = @C X <syntaxhighlight lang=apl inline>Z ← 2 ○ X</source>
Log (base 10) Z = @L X <syntaxhighlight lang=apl inline>Z ← 10 ⍟ X</source>
Round up Z = @U X <syntaxhighlight lang=apl inline>Z ← ⌈ X</source>
Round down Z = @D X <syntaxhighlight lang=apl inline>Z ← ⌊ X</source>
Matrix Transpose Z = @T X <syntaxhighlight lang=apl inline>Z ← ⍉ X</source>
Reduction* Z = @U X <syntaxhighlight lang=apl inline>Z ← +/ X</source>
Base Z = X @B Y <syntaxhighlight lang=apl inline>Z ← X ⊥ Y</source>
Residue Z = X @W Y Y</source>
Compression Z = U / X <syntaxhighlight lang=apl inline>Z ← U / X</source>
Post Z with X controlled by U Z = U @P X
Dimension array @D X , C , R <syntaxhighlight lang=apl inline>X ← R C ⍴ X</source> or <syntaxhighlight lang=apl inline>X ⍴⍨← R C</source>
Juxtaposition Z = X , X <syntaxhighlight lang=apl inline>Z ← X , X</source>
Left rotate Z = K @L X <syntaxhighlight lang=apl inline>Z ← K ⌽ X</source>
Right rotate Z = K @R X <syntaxhighlight lang=apl inline>Z ← (-K) ⌽ X</source>
Compare and branch X @C Y, A, B, C
Update X, compare and branch @U X , Y , A , B , C
Interval Z = @I I , J <syntaxhighlight lang=apl inline>Z ← I … J</source>
Mid-selection array Z = @M I , J
Get data (cards) @G X
Type data @T X <syntaxhighlight lang=apl inline>⎕ ← X</source>
Transform floating–alphanumeric Z = @X Y <syntaxhighlight lang=apl inline>Z ← ⎕UCS Y</source> or <syntaxhighlight lang=apl inline>Z ← ⎕AF X</source>
Accept data from typewriter @A X <syntaxhighlight lang=apl inline>X ← ⍞</source>
Type heading message and proceed @H any heading
Type message, return to monitor @M any message
  • Any scalar dyadic function may replace + in a reduction statement.

References

  1. ↑ Hellerman, H. Experimental personalized array translator system. Communications of the ACM. July 1964. [[wikipedia:doi|]]: https://doi.org/10.1145/364520.364573
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