The tetration is an operation defined as an iterated exponentiation (e.g 2^^4 = 2^(2^(2^2)) = 65536)
I'm learning the J programming language and want to experiment with the ^: (power of verb) function . Specifically, I want to use it to tacitly compute the tetration of two numbers. I want to do this tacitly in order to better understand modifier trains in J.
So far, I've only been able to write this code: ^/@# . It creates a list of x copies of y and inserts ^ between the items, effectively producing y^^x. However, I don't want that solution, because it doesn't let x be infinite, and it also doesn't use the ^: function. I haven't been able to make any further progress. Can anyone help me?
The tetration is an operation defined as an iterated exponentiation (e.g 2^^4 = 2^(2^(2^2)) = 65536)
I'm learning the J programming language and want to experiment with the ^: (power of verb) function . Specifically, I want to use it to tacitly compute the tetration of two numbers. I want to do this tacitly in order to better understand modifier trains in J.
So far, I've only been able to write this code: ^/@# . It creates a list of x copies of y and inserts ^ between the items, effectively producing y^^x. However, I don't want that solution, because it doesn't let x be infinite, and it also doesn't use the ^: function. I haven't been able to make any further progress. Can anyone help me?
First of all, in my opinion, your solution is the idiomatic way to go for this. It is the natural way to express a right fold.
Then, there is the new-ish Fold (F:) which you could use like 1 ] F:: (2&^) 4 == init ] F:: operator times.
To use only the Power of verb (and assuming you mean general iterated exponential, not just the hyper-4) you simply repeat your operator n times:
(2&^)>:4 ] 1
65536
NB. or simply
2 ^^:4 ] 1
The problem here is that you "waste" your input y to the standard initial value of 1. This makes a tacit formulation a bit cumbersome. However, because the initial value and the operator use the same constant, we can compress the expression to:
(^^:3 ])~ 2
To make repetition-count tacit, you need to make it dynamic, so you need all your inputs (base and count) into x or y and verbs that will feed them appropriately to ^:. For example you could:
(u^:h)~ 2 4
where u and h providing (y u y == 2&^) and (y h y == 4) with whatever tacit forms you prefer:
u =: (0{[) ^ (0{])
h =: <:@(1 { ])
(u^:h)~ 2 4
65536
(u^:h)~ 1.5 3
2.1062