first you are using + monadially here.

A conjunction (most of them) becomes a verb after it has 2 arguments bound to 
it.  So,

f =: +^:10

is a dyadic (or monadic verb, but monadic + is not that interesting)

 5 (+^:10) 0 
50 

 5 (+^:10) 2 
52 


A way to double 10 times, that looks a bit similar but is a monadic adverb

 10 (+:^:)   2 
2048 


A dyadic adverb needs 2 parameters on the right

f =. +^:

5 (10 f)   2 
52 




----- Original Message -----
From: Jon Hough <[email protected]>
To: "[email protected]" <[email protected]>
Cc: 
Sent: Sunday, August 2, 2015 11:26 AM
Subject: [Jprogramming] Understanding ^:

I'm attempting some functions that use verb power (^:) , but I'm a little lost 
when it comes to the concept of what is getting iterated.
For example, in pseudo code: 
function f(y){
a = y; //cache initial value 

counter = 10;
while(counter-->0){
y = y + a;
}
return y;}
In the above code, y was initially cached for later use. Trying this in tacit J 
I did:
f =: +]^:10
which completely gives the wrong result. Obviosuly the above function is not 
interesting, and I'm attempting more interesting things, but the principle is 
the same, how can I cache the initial value for use in each iteration when 
using ^:? Do I need to use explicit verbs instead?
Thanks,
Jon                           
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