Create simple C function for PostgreSQL with array input and array output

Your code won't even remotely begin to work as written. PostgreSQL doesn't pass Pg-level arrays as int[], it passes them via the function context in PG_FUNCTION_ARGS (fcinfo) and they're accessed via PG_GETARG_ARRAYTYPE_P macros.

For basic extension function guidance see the docs on C language functions.

Take a look at the definition of array_cat in src/backend/utils/adt/array_userfuncs.c, or array_remove in src/backend/utils/adt/arrayfuncs.c. Or numerous other options.

Your skeleton will look something like:

PG_FUNCTION_INFO_V1(add_arrays);

Datum
add_arrays(PG_FUNCTION_ARGS)
{
    ArrayType  *array1, *array2, *resultarray;

    array1 = PG_GETARG_ARRAYTYPE_P(0);
    array2 = PG_GETARG_ARRAYTYPE_P(1);

    /* Loop over the array bodies and do your mapping to generate resultarray here */

    PG_RETURN_ARRAYTYPE_P(resultarray);
}

The PostgreSQL C array API is awful so I won't have time to fill out the function body. The point is that your function signature is dead wrong - you've totally misunderstood how it works, and what you wrote can't possibly even get executed.

It'd then be declared as:

create or replace function add_arrays(integer[], integer[])
returns integer[] as
'add_arrays', 'add_arrays'
language c immutable strict;

The strict is important; the function skeleton I provided doesn't check for null inputs, so you need to tell the executor not to invoke it with them.

It'd be nice if array_map from src/backend/utils/adt/arrayfuncs.c had a map2 or zip variant that did lockstep iteration of two arrays. Unfortunately it doesn't, so you'll need to iterate over them yourself.

After re-reading your question I'm now wondering if you mean a single array of int[] with two elements and you want the integer result that is the sum of the array. If so, take a look at how the intarray module works; it has simplified functions for handling simple integer arrays.