Rolf Ade posted 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. ---- [KBK] 2004-07-28: Note that expanding a large Cartesian product can consume large amounts of memory. It's often more useful to iterate some script for each element of the cross product. Something like the following code gives a rough approximation of a control structure to do so. proc rforeach { varlist vallist args } { set i 0 foreach v \$varlist { set localName x\$[incr i] lappend localNames \$localName upvar 1 \$v \$localName } foreach \$localNames \$vallist { if { [llength \$args] <= 1 } { set status [catch { uplevel 1 [lindex \$args 0] } result] } else { set status [catch { uplevel 1 [linsert \$args 0 rforeach_nested] } result] } if { \$status != 0 && \$status != 4 } break } switch -exact -- \$status { 0 - 3 - 4 { return } 1 { return -code error -errorcode \$::errorCode \$result } 2 { return -code return \$result } } } proc rforeach_nested { varlist vallist args } { set i 0 foreach v \$varlist { set localName x\$[incr i] lappend localNames \$localName upvar 1 \$v \$localName } foreach \$localNames \$vallist { if { [llength \$args] <= 1 } { set status [catch { uplevel 1 [lindex \$args 0] } result] } else { set status [catch { uplevel 1 [linsert \$args 0 rforeach_nested] } result] } if { \$status != 0 && \$status != 4 } break } switch -exact -- \$status { 0 - 4 { return } 1 { return -code error -errorcode \$::errorCode \$result } 2 { return -code return \$result } 3 { return -code break } } } rforeach a {a1 a2} b {b1 b2 b3} {c d} {c1 d1 c2 d2} e e1 { puts [list \$a \$b \$c \$d \$e] if { \$b eq {b3} } continue puts "b isn't b3; didn't continue" if { \$a eq {a2} } break puts "a isn't a2; didn't break" } ---- See also [Nested-loop join] ---- [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]. ---- [Category Mathematics]