Is it possible to build arrays of verbs? I've tried this:
f =: >:
f2 =: f f
There's no syntax error but f2 is clearly not an array of verbs. For instance
f2 yields f f
$ f2 yields $ f2
0 { f2 yields 0 { f2
2 3 $ f behaves in a similar way.
I'd also like to know if verbs can be activated by the name.
Edited
Instead of f2 =: f f, which is a composition, let's have
f =: >:
f2 =: 2 1 $ f
f2 yields 2 1 $ f
$ f2 yields $ f2
0 { f2 yields 0 { f2
It seems that f2 represents the sequence 2 1 $ f, while in the case of an atom, e.g. 2 1 $ 7, the right side is a vector.
A collection of functions is called a gerund in J and is formed using the tick "`":
g =: +`-`f
┌─┬─┬─┐
│+│-│f│
└─┴─┴─┘
You can use @. to apply the appropriate verb using its index:
4 2 3 (g @. 0) 1 5 6
5 7 9
4 2 3 (g @. 1) 1 5 6
3 _3 _3
4 2 3 (g @. 2) 1 5 6
1 0 0
NB. defining a 2x2 gerund:
k =: 2 2 $ +`-`*`%
┌─┬─┐
│+│-│
├─┼─┤
│*│%│
└─┴─┘
1 (((<0 0) { k) @. 0) 2
3
1 (((<0 1) { k) @. 0) 2
_1
1 (((<1 0) { k) @. 0) 2
2
1 (((<1 1) { k) @. 0) 2
0.5
The index can also be a new verb that depends on the arguments or a list of indices.