Best strategies for reading J code

Question

I've been using J for a few months now, and I find that reading unfamiliar code (e.g. that I didn't write myself) is one of the most challenging aspects of the language, particularly when it's in tacit. After a while, I came up with this strategy:

1) Copy the code segment into a word document

2) Take each operator from (1) and place it on a separate line, so that it reads vertically

3) Replace each operator with its verbal description in the Vocabulary page

4) Do a rough translation from J syntax into English grammar

5) Use the translation to identify conceptually related components and separate them with line breaks

6) Write a description of what each component from (5) is supposed to do, in plain English prose

7) Write a description of what the whole program is supposed to do, based on (6)

8) Write an explanation of why the code from (1) can be said to represent the design concept from (7).

Although I learn a lot from this process, I find it to be rather arduous and time-consuming -- especially if someone designed their program using a concept I never encountered before. So I wonder: do other people in the J community have favorite ways to figure out obscure code? If so, what are the advantages and disadvantages of these methods?

EDIT:

An example of the sort of code I would need to break down is the following:

binconv =: +/@ ((|.@(2^i.@#@])) * ]) @ ((3&#.)^:_1)

I wrote this one myself, so I happen to know that it takes a numerical input, reinterprets it as a ternary array and interprets the result as the representation of a number in base-2 with at most one duplication. (e.g., binconv 5 = (3^1)+2*(3^0) -> 1 2 -> (2^1)+2*(2^0) = 4.) But if I had stumbled upon it without any prior history or documentation, figuring out that this is what it does would be a nontrivial exercise.

Answer 1

Just wanted to add to Jordan's Answer : if you don't have box display turned on, you can format things this way explicitly with 5!:2

   f =. <.@-:@#{/:~
   5!:2 < 'f'
┌───────────────┬─┬──────┐
│┌─────────┬─┬─┐│{│┌──┬─┐│
││┌──┬─┬──┐│@│#││ ││/:│~││
│││<.│@│-:││ │ ││ │└──┴─┘│
││└──┴─┴──┘│ │ ││ │      │
│└─────────┴─┴─┘│ │      │
└───────────────┴─┴──────┘

There's also a tree display:

   5!:4 <'f'
              ┌─ <.
        ┌─ @ ─┴─ -:
  ┌─ @ ─┴─ #       
──┼─ {             
  └─ ~ ─── /:     

See the vocabulary page for 5!: Representation and also 9!: Global Parameters for changing the default.

Also, for what it's worth, my own approach to reading J has been to retype the expression by hand, building it up from right to left, and looking up the pieces as I go, and using identity functions to form temporary trains when I need to.

So for example:

   /:~ i.5
0 1 2 3 4
   NB. That didn't tell me anything
   /:~ 'hello'
ehllo
   NB. Okay, so it sorts. Let's try it as a train:
   [ { /:~ 'hello'
┌─────┐
│ehllo│
└─────┘
   NB. Whoops. I meant a train:
   ([ { /:~) 'hello'
|domain error
|       ([{/:~)'hello'
   NB. Not helpful, but the dictionary says
   NB. "{" ("From") wants a number on the left.
   (0: { /:~) 'hello'
e
   (1: { /:~) 'hello'
h
   NB. Okay, it's selecting an item from the sorted list.
   NB. So f is taking the ( <. @ -: @ # )th item, whatever that means...
   <. -: # 'hello'
2
   NB. ??!?....No idea. Let's look up the words in the dictionary.
   NB. Okay, so it's the floor (<.) of half (-:) the length (#)
   NB. So the whole phrase selects an item halfway through the list.
   NB. Let's test to make sure.
   f 'radar' NB. should return 'd'
d
   NB. Yay!

addendum:

   NB. just to be clear:
   f 'drara' NB. should also return 'd' because it sorts first
d

Answer 2

Try breaking the verb up into its components first, and then see what they do. And rather than always referring to the vocab, you could simply try out a component on data to see what it does, and see if you can figure it out. To see the structure of the verb, it helps to know what parts of speech you're looking at, and how to identify basic constructions like forks (and of course, in larger tacit constructions, separate by parentheses). Simply typing the verb into the ijx window and pressing enter will break down the structure too, and probably help.

Consider the following simple example: <.@-:@#{/:~

I know that <. -: # { and /: are all verbs, ~ is an adverb, and @ is a conjunction (see the parts of speech link in the vocab). Therefore I can see that this is a fork structure with left verb <.@-:@# , right verb /:~ , and dyad { . This takes some practice to see, but there is an easier way, let J show you the structure by typing it into the ijx window and pressing enter:

   <.@-:@#{/:~
+---------------+-+------+
|+---------+-+-+|{|+--+-+|
||+--+-+--+|@|#|| ||/:|~||
|||<.|@|-:|| | || |+--+-+|
||+--+-+--+| | || |      |
|+---------+-+-+| |      |
+---------------+-+------+

Here you can see the structure of the verb (or, you will be able to after you get used to looking at these). Then, if you can't identify the pieces, play with them to see what they do.

   10?20
15 10 18 7 17 12 19 16 4 2
   /:~ 10?20
1 4 6 7 8 10 11 15 17 19
   <.@-:@# 10?20
5

You can break them down further and experiment as needed to figure them out (this little example is a median verb).

J packs a lot of code into a few characters and big tacit verbs can look very intimidating, even to experienced users. Experimenting will be quicker than your documenting method, and you can really learn a lot about J by trying to break down large complex verbs. I think I'd recommend focusing on trying to see the grammatical structure and then figure out the pieces, building it up step by step (since that's how you'll eventually be writing tacit verbs).