A new approach to abstract data types II computation on ADTs as ordinary computation

Abstract

A notion of abstract computational procedure is introduced here which meets the criteria for computation over ADTs, for the general theory of such presented in Part I of this paper. This is provided by a form of generalized recursion theory (g.r.t.) which uses schemata for explicit definition, conditional definition and least fixed point (LFP) recursion in partial functions and functionals of type level ≤ 2 over any appropriate structure. It is shown that each such procedure is preserved under isomorphism and thus determines an abstract procedure over ADTs. The main new feature of the g.r.t, developed here is that abstract computational procedures reduce to computational procedures in the ordinary sense when confined to data structures in a recursion-theoretic interpretation.