Fixpoint semantics and simulation

A general functorial framework for recursive deenitions is presented in which simulation of a deenition scheme by another one implies an ordering between the values deened by these schemes in an arbitrary model. Under mild conditions on the functor involved, the converse implication also holds: a model is constructed such that, if the values deened are ordered, there is a simulation between the deenition schemes. The theory is illustrated by applications to context-free grammars, recursive procedures in imperative languages, and simulation and bisimulation of processes.