You are tieing your data structures too closely to your functionality. There are no practical infinities in software design, so you don't really need negative coordinates; you can just relocate your origin to a point inside the array.

If however, you don't want to create arbitrary limits, and you plan on designing a non-static gameboard, which expands to theoretical infinities in all directions as the game progresses and objects are moved, then you should use an object to encapsulate the functionality of your gameboard, and as part of that object's state, store an offset or any other data required to translate between the coordinates you use in gameplay, and the indexes necessary to reference your data structures.

If you plan on having a very large gameboard, and you are concerned with performance and efficiency, consider using a bit vector or even PDL to internally represent your gameboard. Native lists and hashes are not the way to go. Then again, if you really were concerned about those things, you wouldn't choose Perl to write your game in :)

   MeowChow                                   
               s aamecha.s a..a\u$&owag.print