Since further down in the thread you seem to say that other modules would be acceptable: I use Data::Dump::Filtered for these kind of things. Since in this case Math::GMP deals with integers, I think it's probably safe to not worry about escaping the stringified objects, but in theory one could use the pp function for escaping values as well.

use warnings;
use strict;
use Math::GMP;
use Data::Dump qw/dd pp/;
use Data::Dump::Filtered qw/add_dump_filter/;

add_dump_filter( sub {
    my ($ctx, $objref) = @_;
    return { dump => "Math::GMP->new(\"$objref\")" }
        if $ctx->object_isa('Math::GMP');
    return; # normal dumping
} );

dd( Math::GMP->new("123"),
    Math::GMP->new("546745634563453111035453452346") );

__END__

(
  Math::GMP->new("123"),
  Math::GMP->new("546745634563453111035453452346"),
)
[download]

One's reminded of (well, I was at least) prin1 and friends in Lisp. There's a princ that's meant for displaying things in a pretty notation for hyooman consumption, whereas prin1 produces something that the read function could conceivably re-ingest and produce an equivalent value.

The cake is a lie.
The cake is a lie.
The cake is a lie.

Thanks, and sorry I wasn't clear - I was absolutely expecting that the solution would need some other module, that's certainly acceptable. I've added a note to that effect on the OP.

I'll have to have a play with this - I guess I skipped past it too quickly when looking at the Data::Dump docs, possibly because the only mention I saw there was the unwieldy-seeming dumpf(..., \&filter).

...Freezer = 'stringify';
local *UNIVERSAL::stringify = sub {
$_[0]->isa('Math::GMP')
 ? "$_[0]" 
 : $_[0]
};
...Dumper...
[download]

Sadly that doesn't appear to do what I want (though I'd love it to): the docs for $Data::Dumper::Freezer talk only about modifying the object passed in, not about a return value. And indeed, trying it (with a different name to avoid the existing Math::GMP::stringify method) shows it is called but has no effect on the Data::Dumper output:

% perl -MData::Dumper -MMath::GMP -wle '
  $Data::Dumper::Freezer = "zify";
  local *UNIVERSAL::zify = sub { warn "zify $_[0]"; $_[0]->isa("Math::
+GMP") ? "z$_[0]" : $_[0] };
  my $x = [ Math::GMP->new(1) ];
  print "x[0]=$x->[0]";
  print Dumper($x);
  print "x[0]=$x->[0]";
'
Name "UNIVERSAL::zify" used only once: possible typo at -e line 3.
x[0]=1
zify 1 at -e line 3.
$VAR1 = [
          bless( do{\(my $o = 40040032)}, 'Math::GMP' )
        ];

x[0]=1
[download]

If I change it to assign back to $_[0] instead, Dumper outputs garbage ("\undef") and the data structure is corrupted to have the new string instead of the original object:

% perl -MData::Dumper -MMath::GMP -wle '
  $Data::Dumper::Freezer = "zify";
  local *UNIVERSAL::zify = sub { warn "zify $_[0]"; $_[0]->isa("Math::
+GMP") ? "z$_[0]" : $_[0] };
  my $x = [ Math::GMP->new(1) ];
  print "x[0]=$x->[0]";
  print Dumper($x);
  print "x[0]=$x->[0]";
'
Name "UNIVERSAL::zify" used only once: possible typo at -e line 1.
x[0]=1
zify 1 at -e line 1.
$VAR1 = [
          \undef
        ];

x[0]=z1
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Hi hv,

I was able to get a Dumper() that appears more meaningful (to me, at least) with:

## dumper.pl ##

use strict;
use warnings;

use Data::Dumper;
use Math::GMP;

my $x = [ Math::GMP->new(101), Math::GMP->new(203), Math::GMP->new(116
+7) ];

print Dumper("@$x");

__END__

C:\_32\pscrpt>perl dumper.pl
$VAR1 = '101 203 1167';
[download]

However, I'm not familiar with Data::Dumper and I've no idea if that's of any use to you.

Cheers,
Rob