While playing around with J (link), I found that you can create a sequence of shape N0 N1 ... NK with i. taking a list as its parameters. Since i. creates a range 0 .. RHS and >: increments each value in a range, i. >: i. RHS creates a non-empty range. We can use , to flatten it and +/ to summate it. Given an RHS, this looks like:
+/ , i. >: i. RHS
One can trivially convert this to a tacit expression using an extended monadic fork and capping the left branch [:.
[: +/ [: , [: i. [: >: i.
However, I find this rather bulky and that it could be more concise. How might I make it more so?
I have found a more concise solution that I would also like feedback on. Observing that the last members in each of the lists (before being summated) is (n-1)!. Since , flattens the list, we can emulate this with i., and since the endpoint is not included, we have another solution:
+/ i. ! RHS
Converting this to a tacit expression in the same way as above yields:
[: +/ [: i. !
However, I do not know of a better method for converting a monadic sequence of operations to a tacit verb.
Moving some verbs into variables:
sum =: +/
cap =: [:
cap sum cap i. !
How can this code be improved?
Some example input/outputs (work for both functions).
sum =: +/
cap =: [:
sp =: cap sum cap i. !
max =: 8
(2 , max) $ (i.max) , (sp"0 i.max)
0 1 2 3 4 5 6 7
0 0 1 15 276 7140 258840 12698280
The first row is input to sp, and the second row is its output.
@instead of[:? \$\endgroup\$[:or@(which usually requires parens) -- neither ideal. It's frustrating because the non-tacit right to left eval gives you a beautiful succinct pipeline by default:+/ , i. >: i. 4equals([: +/ [: , [: i. [: >: i.) 4, the former being much prettier obv. What one wants is to say "save this as a tacit verb, but then execute it as if not tacit". Alas.... \$\endgroup\$