I hope there are no directories named "*.abc". Here's another way:

#!/usr/bin/perl -w

use strict;
use File::Find;

my $dir = '.'; # or wherever

find(\&myrename, $dir);

sub myrename {
    return unless -f and /(.*?)\.abc$/s;
    my $new_name = $1.".edf";
    if (rename $_, $new_name) {
        print "renamed  $File::Find::name to $new_name\n";
    } else {
        warn "Couldn't rename $File::Find::name to $new_name: $!";
    }
}
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