@files = glob ('/export/home/date_file*);
               ^                       ^<-- not there

##</code><code>##

use warnings;
use strict;
use Data::Dumper;

my %type;
@type{qw(is a an at)} = (0) x 4;

for my $file ( glob "*.txt" ) {
    open my $fh, '<', $file or die $!;
    while (<$fh>) {
        for (split) {
            $type{$_}++ if exists $type{$_};
        }
    }
}

print Dumper \%type;

my $total = 0;

$total += $type{$_} for keys %type;
print $total, $/;