list comparison, elementwise

wdb -- looking for list comparison similar to equal? in Scheme, I found that it is surprisingly difficult due to the lack of types. Here my approach in Tcl. The procedure lequal checks recursively on elementwise equality:

proc lequal {a b} {
  if {![string is list $a] ||
      ![string is list $b]} then {
    string equal $a $b
  } elseif {[llength $a] != [llength $b]} then {
    return 0
  } elseif {[llength $a] == 0} then {
    return 1
  } elseif {[llength $a] > 1} then {        
    expr {[lequal [lindex $a 0] [lindex $b 0]]] &&
          [lequal [lrange $a 1 end] [lrange $b 1 end]]]}
  } elseif {$a eq [lindex $a 0] || $b eq [lindex $b 0]} then {
    string equal $a $b
  } else {
    lequal [lindex $a 0] [lindex $b 0]

Don't know if in real life necessary, but by reasons of completeness, I did it.

NEM 2009-10-19: The lack of type information in Tcl makes these kinds of generic operations slightly more difficult, as you say. I suspect string is list is not going to be very reliable. For instance simple numbers like "12" return true for that test, where you probably want them to be compared as numbers and not lists. The easiest way to solve the lack of type information is to add a third argument which is the command to use for comparing each element, as used in dictutils:

proc lequal {p xs ys} {
    if {[llength $xs] != [llength $ys]} { return 0 }
    foreach x $xs y $ys {
        if {![{*}$p $x $y]} { return 0 }
    return 1

That way the caller can unambiguously say how they want comparisons to be performed. To compare two lists of strings you would do:

lequal {string equal} $a $b

While, to compare two lists of lists of integers, you could do:

set xxs {{1 2 3} {4.0 5 6}}
set yys {{1 2.0 3} {4 5e0 6}}
proc inteq {a b} { expr {int($a) == int($b)} }
lequal {lequal inteq} $xxs $yys

There is a further complication, however, in that this assumes that the list is of homogenous type: i.e., all elements have the same notion of equality. If you are using a list more like a tuple, then each element position may have a different type and thus need to be compared in a different way. This requires a different comparison method that takes a list of element comparison commands:

# tequal: tuple equality
proc tequal {types xs ys} {
    if {[llength $types] != [llength $xs] || [llength $xs] != [llength $ys]} { return 0 }
    foreach type $types x $xs y $ys {
        if {![{*}$type $x $y]} { return 0 }
    return 1
# Test on tuples of type: integer x case-insensitive string x list of characters.
set type {inteq {string equal -nocase} {lequal {string equal}}}
set a {12.0 "Hello!" {a b c}}
set b {12 hello! {a b c}}
tequal $type $a $b

Ironically, notions of equality vary tremendously.

wdb My core aspect is the difference of list and atom in arbitrary nested lists, not strings and numbers. My proc lequal above treats both " a " and "{a}" as list with 1 element (because enclosed with braces or spaces), but "a" as atom. Perhaps a questionable decision, but I found no better one.

In the other aspects (.1 == 0.1, but .1 ne 0.1), you are right, but I did not care of that aspect.