Yet concepts like gene and fitness depend on a functionally organized context known as phenotype. To address problems like the origin of life or the major transitions in evolution, the traditional dynamical systems approach has to be extended with a theory of functional organization. At the most basic level such a theory must apply to organized molecular reaction networks. The study of the emergence and evolution of molecular organization requires a formalization of chemistry. In the absence of such a formalism, Walter Fontana and collaborator Leo Buss started out by exploring -calculus as a formal metaphor for chemistry.
Chemical reactions appear as functional applications constructing new functions.
The main conceptual result is a useful working definition of what we mean by an organization. An organization is a kinetically self-maintaining algebraic structure. The members of an organization maintain each other in the reactor by mutual production, and they can be characterized by syntactical regularities and algebraic laws. In the context of this project the reserachers applied analytical methods to determine all organizations generated by just iterating the simplest initial sets of expressions. For actual calculations, we use a variant of the above iteration.