Rolf Ade boasted a question to the chat asking how to form the Cartesian product of a set of lists. That is, given a list like,

{ { a b c } { d e f } }

he wanted

{{a d} {a e} {a f} {b d} {b e} {b f} {c d} {c e} {c f}}

He also wanted it to generalize to higher dimension: given

{{a b} {c d} {e f}}

he wanted

{{a c e} {a c f} {a d e} {a d f} {b c e} {b c f} {b d e} {b d f}}

and so on.

Kevin Kenny proposed the following:

proc crossProduct { listOfLists } { if { [llength $listOfLists] == 0 } { return [list [list]] } else { set result [list] foreach elt [lindex $listOfLists 0] { foreach combination [crossProduct [lrange $listOfLists 1 end]] { lappend result [linsert $combination 0 $elt] } } return $result } } puts [crossProduct {{a b c} {d e f} {g h i}}]

This solution is by no means the fastest available, but it appears to work for the purpose.

Arjen Markus An interesting variation on this theme: how to generate the set of subsets containing 1, 2, 3 ... elements. For example:

{a b c d e}

will give rise to:

{{a} {b} {c} {d} {e}} {{a b} {a c} {a d} {a e} {b c} {b d} {b e} {c d} {c e} {d e}} ...

It does not seem quite trivial.

The answer is posted in Power set of a list.