foldList adverb in J

Question

In response to the question of FoldList like primitive in J, I wanted to create an adverb fold so that x u fold y is to fold y with verb u and inital value x:

    fold =: 2 : 0
z =.x
for_item. y do. z =. z u item end.
z
)

But I got error when trying it out:

   1 (+fold) 1 2 3
|value error: x
|   z=.    x

what's wrong here? thanks.

Answer 1

Just a couple small things.

First, the numeric code for an adverb is 1. The 2 : 0 you have is defining a conjunction, not an adverb. The way it stands now, J is expecting two direct arguments to fold, and you've only provided one (the +; the two numeric arrays are indirect, not direct, arguments). However, that's not what J is complaining about here, because the other issue is actually tripping it up first. I'll get to that in a second, but nevertheless the first thing you need to do is define fold as an adverb [1].

The more immediate issue that J is complaining about is that it doesn't know what you mean by x. Why? For the same reason that it would if you replaced 2 : 0 (or conjunction define) -- or even, more pertinently, adverb define -- with verb define. Because explicit verbs (direct or derived) are monadic by default and have no x argument (hence mentioning x is a value error). If you want to define a dyadic verb, you must ask for it explicitly.

Now, defining a dyadic verb directly is straightforward: instead of saying verb define, you simply say dyad define. But deriving a dyadic verb from a modifier (adverb or conjunction) is a little less obvious. You must use the special colon syntax which allows you to separate the monadic and dyadic valences of explicit definitions. This syntax applies to all explicit definitions, including verbs, adverbs, and conjunctions, but for adverbs and conjunctions it is the only way to derive an explicit verb.

Bottom line:

fold =: adverb define
  NB. Note solitary colon on next line. Everything after that is dyadic.
:
  z =.x
  for_item. y do. z =. z u item end.
  z
)

[1]: You may find using the standard covers for nameclasses easier to remember (and read later), as in adverb define and conjunction define (for one-liners, you can use def in place of define).