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In this paper we study the uniqueness of solutions to ordinary differential equations which fail to satisfy both accretivity condition and the uniqueness condition of Nagumo, Osgood and Kamke. The evolution systems considered here are governed by a continuous operators $A$ defined on $mathbb{R}^N$ such that $A$ is a derivor; i.e., $-A$ is quasi-monotone with respect to $(mathbb{R}^{+})^N$.

An algebraic view of recursive definitions is presented, extending an already familiar analogy with homomorphisms. A notion of simulation of one recursive definition by another is then defined. This leads to a particular approach to verification and transformation, which places emphasis on the arrows between programs, rather than the programs themselves. These arrows are the program morphisms of the title. Examples are given, together with certain extensions of the idea. Also indicated is a methodology which can lead to the discovery of program morphisms and new equivalent versions of a given program. [ABSTRACT FROM AUTHOR]