Composing addition and division verbs over lists

If data =: 3 1 4 and frac =: % +/, why does % +/ data result in 0.125 but frac data result in 0.375 0.125 0.5?

Solution

%+/ 3 1 4 is "sum, then find reciprocal of that sum", that is:

   +/ 3 1 4
8
   % 8       NB. same as 1%8
0.125

But if you define frac =: %+/, then %+/ becomes a group of two verbs isolated from their arguments (aka tacit definition), that is, a hook:

   (%+/) 3 1 4
0.375 0.125 0.5

Which reads "sum, then divide original vector by that sum":

   +/ 3 1 4
8
   3 1 4 % 8
0.375 0.125 0.5

If you want frac to behave as in the first example, then you need to either use an explicit definition:

   frac =: 3 : '%+/y'
   frac 3 1 4
0.125

Or to compose % and +/, e.g. with atop conjunction or clever use of dyadic fork with capped left branch:

   %@(+/) 3 1 4
0.125
   ([:%+/) 3 1 4
0.125