What went wrong? perldoc -f exit says that exit evaluates EXPR and exits immediately with that value. My operating system is Debian testing (Jessie).

Indeed, and it does just that. But you're basically doing this:

((exit $var) > $tmp) ? 1 : 0;
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In other words, exit is called with $var, and the result is then compared to $tmp, and the whole expression evalutes to 1 or 0... or would, if exit returned at all, which it of course doesn't.

Here's a short illustration of how operator precedence works:

#!/usr/bin/perl

use feature qw/say/;
use strict;
use warnings;

sub half($) {
  return $_[0] / 2;
}

say half 3 > 2  ? 7 : 5 ; # 5
say half(3 > 2) ? 7 : 5 ; # 7
say half(3 > 2  ? 7 : 5); # 3.5
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EDIT: to clarify this a bit more: named unary operators (of which exit is an example) bind more tightly than >, which binds more tightly than ?:, which in turn binds more tightly than list operators do (rightward). So ?: takes precedence over print and say -- but exit takes precedence over ?:.

For more, see the "Operator Precedence and Associativity" table at the top of perlop, as well as chapter 3 ("Unary and Binary Operators") of Programming Perl.