Linear-time hierarchies for a functional language machine model

In STOC 1993, Jones showed the existence of a hierarchy within problems decidable in linear time by a canonical first-order functional language based on tree-structured data (F), as well as for an extension of that language based on graph-structured data maintained through selective updating (Fsu). In this paper, we prove the existence of a linear-time hierarchy for an authentic and realistic intermediate “machine” language featuring higher order constructs: the Categorical Abstract Machine. We show the existence of such a hierarchy for the Categorical Abstract Machine based on tree-structured data (CAM) as well as on graph-structured data (CAMsu). The existence is shown by constructing mutually efficient interpreters between CAM and F, and CAMsu and Fsu, two robustness results establishing that first-order functional programs written in F, and in Fsu, define the same class of linear-time decidable problems as the higher-order functional programs run in CAM, and in CAMsu, respectively.