I tested appending empty to empty of different data types.
   (3!:0) (0$0) , 0$0
1
   (3!:0) (0$0) , 0$' '
2
   (3!:0) (0$2) , 0$' '
4
   (3!:0) (0$2.2) , 0$' '
8
   (3!:0) (0$u:'a') ,~ 0$a:
131072
   (3!:0) (0$u:'a') , 0$a:
131072
   (3!:0) (0$' ') ,~ 0$a:
32
   (3!:0) (0$1r3) , 0$a:
128
   (3!:0) (0$0) , 0$a:
32
   (3!:0) (0$2) , 0$a:
32
   (3!:0) (0$2.2) , 0$a:
8
   (3!:0) (0$1j2) , 0$a:
16

At first, I thought data type is the larger of 3!:0, but a counter example in
the last line. It also seems data type does not depend on leftmost or rightmost
position. Does anyone know the rule of deriving the data type?

-- 
regards,
bill
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