How can I implement such a map-like operation in mathematica

Question

I have a list and an arbitrary function taking 4 parameters, let's say {1, 11, 3, 13, 9, 0, 12, 7} and f[{x,y,z,w}]={x+y, z+w}, what I want to do is to form a new list such that 4 consecutive elements in the original list are evaluated to get a new value as the new list's component, and the evaluation has to be done in every 2 positions in the original list, in this case, the resulting list is:

{{12, 16}, {16, 9}, {9, 19}}

Note here 4 and 2 can change. How to do this conveniently in Mathematica? I imagine this as something like Map, but not sure how to relate.

Answer 1

There's an alternative to Map[f, Partition[...]]: Developer`PartitionMap. Which works exactly like Map[f, Partition[list, n, ...]]. So, your code would be

Needs["Developer`"]
f[{x_, y_, z_, w_}] = {x + y, z + w};
list = {1, 11, 3, 13, 9, 0, 12, 7};
PartitionMap[f,list, 4, 2]

giving the same result as Mark's answer.

Answer 2

f[{x_, y_, z_, w_}] = {x + y, z + w};
list = {1, 11, 3, 13, 9, 0, 12, 7};
f /@ Partition[list, 4, 2]