The current gas costs are for all nodes to process a transaction or contract function call. Once we have sharding, only a subset on the nodes(1 shard) will process that transaction/contract function call. So is it safe to assume that gas costs will basically be current gas costs/total number of shards?
Sure, assuming total tx's stay the same, then it will be something like current gas price / shards. I would assume that total tx's will increase however, when sharding goes into effect.
But yes, overall, as a scaling solution, sharding is meant to decrease load on each individual node, and decrease gas prices.