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. Using (instead of recursion) another [foreach] for the loop over the ''listOfLists'', the above can also be coded as proc crossProduct { listOfLists } { # args might be better in a real-life API set result [list [list]] ; # The set of one 0-tuple foreach factor $listOfLists { set newResult [list] ; # Empty set foreach combination $result { foreach elt $factor { lappend newResult [linsert $combination end $elt] } } set result $newResult } return $result } ---- [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" } ---- [Eric Boudaillier] 2004-07-29: I also needed such procedure to generate test code and wrote the following procedure, which build the [foreach] imbrication script and evaluate it: proc forall {args} { if {[llength $args] < 3 || [llength $args] % 2 == 0} { return -code error "wrong \# args: should be \"forall varList list ?varList list ...? body\"" } set body [lindex $args end] set args [lrange $args 0 end-1] while {[llength $args]} { set varName [lindex $args end-1] set list [lindex $args end] set args [lrange $args 0 end-2] set body [list foreach $varName $list $body] } uplevel 1 $body } ---- 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] | [Category Control Structure] |%