The SQL

select sum(sum(a)) from myt1 group by a;

This note focuses only on sum(sum(a)) and it's about how postgres rejects the sql above.

Notes

sum(sum(a))
 |   |  |
 |   |  \_ inner most argument, Var node
 |   \_	 function call
 \_ function call	 

Function call is handled by function transformFuncCall. Here's overview how tranformFuncCall works:

• transform arguments first
• if it's an aggregate function, transform aggregate call.
• check_agg_arguments

For sum(sum(a)), the recursive way is like this:

FuncCall
    FuncCall
    AggCall
    check_agg_arguments
AggCall
check_agg_arguments

Here's the detail,

• sum(sum(a)) is a FuncCall, handle its arguements sum(a).
• sum(a) is a FuncCall, handle its arguments a.
• check the arguments a, is's a simple Var node, that's fine.
• sum(a) is an AggCall, check_agg_arguments of sum(a). A Var node, that's fine.
• sum(sum(a)) is an AggCall, check_agg_arguments of sum(sum(a)), which is sum(a). Since sum(a)
  is an AggCall, postgres rejects this sql.