A unified model of pointwise equivalence of procedural computations

The execution of a program on a processor is viewed as a representation of that program going through a sequence of states. Each state change is manifested by the execution of a single instruction. Models that depend on this perspective are presented. The first is a static model of a description of a procedural computation. This model formalizes the description of the information in an executable module. Following this dynamic model of a procedural computation is given. This second model describes how a computation transitions from state to state and how the states of a computation are represented. Next, the state of a procedural computation is defined at certain well-defined points in its progression. These points represent potential points of correspondence to another instance of the computation. Then, the equivalence of these well-defined computation states is described. This refinement eliminates the nonmatching potential correspondences. The remaining points describe where the two computations are in the same state. These are precisely the points of equivalence of procedural computations. This final model of pointwise equivalence can be applied to the problem of migrating a computation from one processor to another (possibly architecturally dissimilar) processor.