Linear Time Hierarchies for a Functional Language Machine Model

In STOC 93, Jones sketched the existence of a hierarchy within problems decidable in linear time by a first-order functional language based on tree-structured data (F), as well as for an extension of that language based on graph-structured data (F). We consider the Categorical Abstract Machine (CAM), a canonical machine model for implementing higher order functional languages. We show the existence of such a hierarchy for the CAM based on tree-structured data (without selective updating facilities), as well as in the case of graphstructured data (with selective updating). In conclusion we establish two local robustness results where first-order functional programs and higher order functional programs define the same class of linear-time decidable problems.