It should work like this. I know I've exported constants before, anyway. 
package MyPackage;
use 5.006;
use strict;
use warnings;

use Data::Dumper;
use constant VALID => 1;
use constant INVALID => 2;
use constant ERROR => 0;

use base qw(Exporter);

our @EXPORT_OK = qw(VALID INVALID ERROR);

our %EXPORT_TAGS = (
   'all' => \@EXPORT_OK,
   'codes' => [ qw(VALID INVALID ERROR)],
);

our @EXPORT;  #Intentionally left blank

our $VERSION = v0.0.1;

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Makeshifts last the longest.

In reply to Re: use constant and exporter by Aristotle
in thread use constant and exporter by Flame

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