Nuvoc simplified

[David C. Salthouse]

As a student of all things Iverson, Mathematical and Debian I have had difficulty getting my head  wrapped around Nuvoc. I asked Gemini to build a more structred, though incomplete, version. I invite more experienced J users with time on their hands to point out errors and ommisions. Comments from novices welcome. 

Thanks in Advance,

Dave Salthouse

• Rank Key:

  • 0 = Atoms (Numbers)

  • 1 = Lists (Vectors)

  • _ = Everything (The whole array)

THE MONADIC BRANCH (One Argument y)

MATHEMATICS (Arithmetic)   

           - y Negate (Rank 0) | - 5 -> _5  

           % y Reciprocal (Rank 0) | % 4 -> 0.25  

            +: y Double (Rank 0) | +: 5 -> 10 

           -: y Halve (Rank 0) | -: 10 -> 5  

          *: y Square (Rank 0) | *: 3 -> 9 

          %: y Square Root (Rank 0) | %: 9 -> 3 

           ^. y Natural Log (Rank 0) | ^. 2.71 -> 1 

 

STRUCTURE (Shape) 

          $ y Shape Of (Rank _) | $ 2 3 4 -> 3 

         # y Tally (Count) (Rank _) | # 10 20 -> 2 

         , y Ravel (Flatten) (Rank _) | , i. 2 2 -> 0 1 2 3  

        |. y Reverse (Rank _) | |. 1 2 3 -> 3 2 1  

        |: y Transpose (Rank _) | Flip rows/cols  

SELECTION ( 

         {. y Head (First) (Rank _) | {. 10 20 30 -> 10  

         {: y Tail (Last) (Rank _) | {: 10 20 30 -> 30 

         }. y Behead (Drop 1) (Rank _) | }. 10 20 30 -> 20 30  

         }: y Curtail (Drop L)(Rank _) | }: 10 20 30 -> 10 20  

         ~. y Nub (Unique) (Rank _) | ~. 1 1 2 -> 1 2 

 DISCRETE MATH (Integers) 

           i. y Integers (Rank 1) | i. 5 -> 0 1 2 3 4 

           <. y Floor (Rank 0) | <. 3.14 -> 3 

           >. y Ceiling (Rank 0) | >. 3.14 -> 4 

           q: y Prime Factors (Rank 0) | q: 10 -> 2 5

DYADIC BRANCH (Two Arguments x and y)

ARITHMETIC (x combined with y) 

            x + y Plus (Rank 0 0) | 1 + 2 -> 3 

           x * y Times (Rank 0 0) | 2 * 3 -> 6 

           x % y Divide (Rank 0 0) | 1 % 2 -> 0.5 

           x ^ y Power (Rank 0 0) | 2 ^ 3 -> 8 

           x | y Residue (Mod) (Rank 0 0) | 2 | 5 -> 1 

 

STRUCTURAL (Reshaping) │ 

          x $ y Reshape (Rank 1 _) | 2 2 $ 1 -> 1 1, 1 1 

          x , y Append/Link (Rank _ _) | 1 , 2 -> 1 2 

          x # y Copy (Filter) (Rank 1 _) | 1 0 1 # 'ABC' -> 'AC'  

          x {. y Take (Rank 1 _) | 2 {. 10 20 30 -> 10 20 

LOGIC & COMPARISON 

          x = y Equal (Rank 0 0) | 1 = 1 -> 1 

          x < y Less Than (Rank 0 0) | 1 < 2 -> 1  

          x > y Greater Than (Rank 0 0) | 2 > 1 -> 1  

          x +. y GCD (OR) (Rank 0 0) | 0 +. 1 -> 1 

          x *. y LCM (AND) (Rank 0 0) | 0 *. 1 -> 0 

 SYSTEM 

           x 1!:1 y Read File (Rank 0 0) | Read y 

           x 1!:2 y Write File (Rank _ _) | Write x to y

MODIFIERS (Adverbs & Conjunctions)

• Adverbs (1 arg):

  • / Insert: Put the verb between items (+/ Sum).

  • ~ Reflex: Use y as both arguments (*~ 5 is 5 * 5).

  • \ Prefix: Apply to prefixes (+\ i.5 Running Sum).

• Conjunctions (2 args):

  • @ At: Functional Composition (f @ g).

  • & Bond: Glue an argument to a verb (double =: * & 2).

  • ^: Power: (Repeat logic).

[Richard Donovan]

Certainly seems very clear, Dave. Thumbs up from this perpetual novice!

Richard

---

From: fo...@jsoftware.com <fo...@jsoftware.com> on behalf of David C. Salthouse <d.c.sa...@gmail.com>
Sent: 30 January 2026 15:14
To: forum <fo...@jsoftware.com>
Subject: [Jforum] Nuvoc simplified

 

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[Paul Jackson]

I'm not aware of an x argument for 1!:1

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[trx2358...@yahoo.com]

I’d bet systematically checking that Gemini output is an excellent roadmap for exploring J.  Sounds like a project you yourself might like.

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