j.txt

   J:   atom,   list,  table
math: scalar, vector, matrix

Ranks #$

   i.2 3 4

 0  1  2  3
 4  5  6  7
 8  9 10 11  NB. 2 planes
             NB. 3 rows
12 13 14 15  NB. 4 columns
16 17 18 19
20 21 22 23

"0 is the same as "+ since + 0 0 0

Compositions

@: at

  [: f g                   capped fork, useful in building long trains
  (f @: g) y  =  f (g y)   monad and monad
x (f @: g) y  =  f (x g y) monad and dyad

&: appose

  (f &: g) y  =  f (g y)       monad and monad
x (f &: g) y  =  (g x) f (g y)  dyad and monad

@ atop
& compose

are used for tracking: applications of f track the applications of g

&. under

  (f &. g) y  =  g inv f g y NB. inv is ^:_1

Trains

  (f g) y  =  y f (g y) monadic hook
x (f g) y  =  x f (g y)  dyadic hook

  (f g h) y  =    (f y) g (h y)   monadic fork
x (f g h) y  =  (x f y) g (x h y)  dyadic fork

4-train   (e f g h) => hook:   (e (f g h)) NB. (verb fork)
5-train (d e f g h) => fork: (d e (f g h)) NB. (verb verb fork)

_9: to 9: - constant functions are useful because they can occur in trains

Operators: adverbs and conjunctions

Verbs

       1                 2  <- fret (negate to not include the fret)
<;._2 '-aa-bb-cc 11-22-33 '

cut, using the fret as a separator, then box the results

Puzzles

f(y) if y > 1, else y
f ^: (>&1) <=> ] ` f @. (>&1)