KDB+/Q: About unused parameters in inner functions

Question

I have this function f

f:{{z+x*y}[x]/[y]}

I am able to call f without a 3rd parameter and I get that, but how is the inner {z+x*y} able to complete without a third parameter?

Answer 1

You need to understand 2 things: 'over' behavior with dyadic functions and projection.

1. Understand how over/scan works on dyadic function: http://code.kx.com/q/ref/adverbs/#over

If you have a list like (x1,x2,x3) and funtion 'f' then

f/(x1,x2,x3) ~  f[ f[x1;x2];x3]

So in every iteration it takes one element from list which will be 'y' and result from last iteration will be 'x'. Except in first iteration where first element will be 'x' and second 'y'.

Ex:

  q)   f:{x*y}   / call with -> f/ (4 5 6)

first iteration : x=4, y=5, result=20

second iteration: x=20, y=6, result=120

2. Projection:

Lets take an example funtion f3 which takes 3 parameters:

   q) f3:{[a;b;c] a+b+c}

now we can project it to f2 by fixing (passing) one parameter

  q)  f2:f3[4]   / which means=> f2={[b;c] 4+b+c}

so f2 is dyadic now- it accepts only 2 parameters.

So now coming to your example and applying above 2 concepts, inner function will eventually become dyadic because of projection and then finally 'over' function works on this new dyadic function. We can rewrite the function as :

f:{
f3:{z+x*y};
f2:f3[x];
f2/y
}