TCL proc to generate : variable nb of lists which contain a variable nb of elem

Hello,
I would like to implement in Tcl a procedure which generates the following element lists (example with 4 lists) :


list1_1 list2_1 list3_1 list4_1
list1_1 list2_1 list3_1 list4_2
list1_1 list2_1 list3_1 list4_3
list1_1 list2_1 list3_2 list4_1
list1_1 list2_1 list3_2 list4_2
list1_1 list2_1 list3_2 list4_3
list1_1 list2_2 list3_1 list4_1
list1_1 list2_2 list3_1 list4_2
list1_1 list2_2 list3_1 list4_3
list1_1 list2_2 list3_2 list4_1
list1_1 list2_2 list3_2 list4_2
list1_1 list2_2 list3_2 list4_3
list1_1 list2_3 list3_1 list4_1
list1_1 list2_3 list3_1 list4_2
list1_1 list2_3 list3_1 list4_3
list1_1 list2_3 list3_2 list4_1
list1_1 list2_3 list3_2 list4_2
list1_1 list2_3 list3_2 list4_3
list1_1 list2_4 list3_1 list4_1
list1_1 list2_4 list3_1 list4_2
list1_1 list2_4 list3_1 list4_3
list1_1 list2_4 list3_2 list4_1
list1_1 list2_4 list3_2 list4_2
list1_1 list2_4 list3_2 list4_3
list1_2 list2_1 list3_1 list4_1
list1_2 list2_1 list3_1 list4_2
list1_2 list2_1 list3_1 list4_3
list1_2 list2_1 list3_2 list4_1
list1_2 list2_1 list3_2 list4_2
list1_2 list2_1 list3_2 list4_3
list1_2 list2_2 list3_1 list4_1
list1_2 list2_2 list3_1 list4_2
...
list1_3 list2_4 list3_1 list4_2
list1_3 list2_4 list3_1 list4_3
list1_3 list2_4 list3_2 list4_1
list1_3 list2_4 list3_2 list4_2
list1_3 list2_4 list3_2 list4_3



However, the difficulty comes from the fact that the number of lists is variable, and the number of the elements of each list is also variable.




Example :


set list_1 "list1_1 list1_2 list1_3"
set list_2 "list2_1 list2_2 list2_3 list2_4"
set list_3 "list3_1 list3_2"
set list_4 "list4_1 list4_2 list4_3"


list1_1 is the first element of the list_1 and so on.






I have already made the following procedure but it works only for a fixed number of lists. I would like to implement a procedure for a variable number of lists which contains a variable numbe rof elements.


proc generation_foreach {} {

global list_1 list_2 list_3 list_4

set number_combi 0
foreach element_list_1 $list_1 {
foreach element_list_2 $list_2 {
foreach element_list_3 $list_3 {
foreach element_list_4 $list_4 {
puts "$element_list_1 $element_list_2 $element_list_3 $element_list_4"
}
}
}
}


return 0
}




Can someone help me ?

Thanking advanced.


Pierre