1. A computer-implemented method for operating on stored objects, the method comprising: storing a base object handle representing a base object, the base object handle comprising a base object content association that links the base object to a base object content; storing a mapped object handle representing a mapped object, the mapped object handle comprising: a mapping that identifies the base object handle, and a mutable mapping type selected from a plurality of mapping types, each of the plurality of mapping types defining semantics of one or more operations on the mapped object; receiving a request to perform an operation on the mapped object; responding to the request to perform the operation by: determining one or more actions to perform based on a semantic of the operation defined by the mapping type of the mapped object handle; and performing the one or more actions; wherein the mapping type is a syntactic relationship type, the mapped object handle includes a name, and the base object content includes an evaluation of a function applied to the name; wherein the one or more actions to perform, based on the semantics defined by the mapping type, comprises providing the base object content when the operation is a read so that the mapped object has access to the evaluation; and wherein the method is performed by one or more computing devices.