Avoiding a repeated verb name in a train

Question

Consider a dyadic verb g, defined in terms of a dyadic verb f:

g=. [ f&.|: f

Is it possible to rewrite g so that the f term appears only once, but the behavior is unchanged?

UPDATE: Local Context

This question came up as part of my solution to this problem, which "expanding" a matrix in both directions like so:

Original Matrix

1 2 3
4 5 6
7 8 9

Expanded Matrix

1 1 1 1 2 3 3 3 3
1 1 1 1 2 3 3 3 3
1 1 1 1 2 3 3 3 3
1 1 1 1 2 3 3 3 3
4 4 4 4 5 6 6 6 6
7 7 7 7 8 9 9 9 9
7 7 7 7 8 9 9 9 9
7 7 7 7 8 9 9 9 9
7 7 7 7 8 9 9 9 9

My solution was to expand the matrix rows first using:

f=. ([ # ,:@{.@]) , ] , [ # ,:@{:@]

And then to apply that same solution under the transpose to expand the columns of the already row-expanded matrix:

3 ([ f&.|: f) m

And I noticed that it wasn't possible to write my solution with making the temporary verb f, or repeating its definition inline...

Try it online!

Credits

Bob is right in the general case. If you give us more details and context on your specific case, there might be a local solution. – Subscapular

@DanBron Thanks. I've updated the post. – Credits

Answer 1

Knowing the context helps. You can also approach this using (|:@f)^:(+: x) y. A tacit (and golfed) solution would be 0&(|:{.,],{:)~+:.

   (>: i. 3 3) (0&(|:{.,],{:)~+:) 2
1 1 1 2 3 3 3
1 1 1 2 3 3 3
1 1 1 2 3 3 3
4 4 4 5 6 6 6
7 7 7 8 9 9 9
7 7 7 8 9 9 9
7 7 7 8 9 9 9

Barrens

that golfed solution is beautiful, but i can't figure out how you mapped the power ^: solution down to it. It parses like this, which would mean that it's equivalent to 4 (0&(|:{.,],{:)) m, but since 0 is already bonded as the left arg to the verb on its right, I don't see where the 4 comes into play or how it produces the final result. – Credits

@Credits Let m be the matrix and n be the number of times that matrix is expanded. A breakdown for it is m (0&(|:{.,],{:)~+:) n to m 0&(|:{.,],{:)~ (+: n) to (+: n) 0&(|:{.,],{:) m to (0&(|:{.,],{:))^:(+: n) m – Barrens

makes sense until the very last step: what rule is being applied there? – Credits

@Credits It's another rule for bond & where a noun is bonded to a dyad, and then called dyadically. For example, x m&f y becomes m&f^:x y – Barrens

ah, ok that makes sense i think genuinely didn't know about that one, or had at least thoroughly forgotten it. great solution. you should post it. – Credits

Answer 2

I don't think it is possible. The right tine is going to be the result of x f y and the left tine is x The middle tine will transpose and apply f to the arguments and then transpose the result back. If you take the right f out then there is not a way to have x f y and if the middle f is removed then you do not have f applied to the transpose.

My guess is that you are looking for a primitive that will accomplish the same result with only one mention of f, but I don't know of one.

Knowing the J community someone will prove me wrong!

Carollcarolle