# Personalized Array Translator

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:

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