Recursion and iteration in continuous theories: The “M-construction”

摘要

The purpose of this paper is two-fold: first to show how a natural mathematical formulation of the “solution” of a system of recursion equations is formally almost identical with well-known formulations of a solution of a system of “iteration equations.” The second aim is to present a construction which takes an algebraic theory T and yields another algebraic theory M(T) whose morphisms correspond to systems of recursion equations over T. This construction is highly uniform, i.e., the correspondence between T and M(T) is functorial.