I don't see how that works. The code still runs at run-time, and the use statement still runs at compile time. Using  $x instead of  $x == 1 in the ternary eliminates a "Use of uninitialized value $x in numeric eq (==) ..." warning, but that's all.

>perl -wMstrict -le
"my $x;
 BEGIN {
   my $m = `uname -m`;
   print qq{m '$m'} if $m =~ /x86/;
   $x = 1 if $m =~ /x86/;
   use constant FOO => ($x ? 'true' : 'false');
   }
 print FOO;
 print qq{x '$x'};
"
m 'x86
'
false
x '1'
[download]

Update: This seems to work:

>perl -wMstrict -le
"BEGIN {
   use constant X   => (`uname -m` =~ /x86/) ? 1 : 0;
   use constant FOO => (X ? 'true' : 'false');
   }
 print FOO;
 print q{X '}, X, q{'};
"
true
X '1'
[download]

Update: Oh, wait... I didn't catch the fact that the  use constant statement is outside the BEGIN block! tobyink's code works as advertised (per tobyink's reply which I didn't see until after I had posted this update). Evidently it helps if you test the actual code. Nevermind.

>perl -wMstrict -le
"my $x;
 BEGIN {
   my $m = `uname -m`;
   print qq{m '$m'} if $m =~ /x86/;
   $x = 1 if $m =~ /x86/;
   }
 use constant FOO => ($x ? 'true' : 'false');
 print FOO;
 print qq{x '$x'};
"
m 'x86
'
true
x '1'
[download]

Your use constant is inside the BEGIN block; my use constant was outside the BEGIN block. That's why mine works and yours does not.

If you have an inner BEGIN block within an outer BEGIN block, the inner one will execute first, even if it's at the end of the outer block. (And of course use is effectively a BEGIN block.)

$ perl -e'BEGIN { warn 2; BEGIN {warn 1} }'
1 at -e line 1.
2 at -e line 1.
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perl -E'sub Monkey::do{say$_,for@_,do{($monkey=[caller(0)]->[3])=~s{::}{ }and$monkey}}"Monkey say"->Monkey::do'

thanks tobyink, its working fine now.