🤖 AI Summary
This work introduces a dynamical mechanism into algebraic artificial chemistry models to unify their algebraic structure with dynamic behavior. To this end, it pioneers the use of category theory as an organizational framework in this domain, constructing a functor that endows λ-calculus-based interaction-combinator algebraic models—such as Fontana and Buss’s AlChemy—with a formal semantics of dynamical evolution. This approach not only generalizes the classical AlChemy framework but also establishes a rigorous correspondence between algebraic structure and system dynamics. By integrating algebraic rigor with expressive dynamical capabilities, the study formulates a novel paradigm for artificial chemistry, laying a theoretical foundation for future formal modeling and analysis.
📝 Abstract
We construct a functor that gives a dynamics to an algebraic model of interacting components. The construction generalises a computational model of Fontana and Buss in the field of artificial life known as AlChemy, in which molecules and their chemical interactions are emulated by lambda calculus terms and their application and subsequent reduction. We discuss future directions for the application of category theory to algebraic artificial chemistry as an organisational tool, with a focus on formalising the connection between the algebraic and the dynamical facets of such models.