First Steps towards Categorical Algebraic Artificial Chemistry
This work addresses the formalization of artificial chemistry models for researchers in artificial life and theoretical computer science, but it is incremental as it builds on existing AlChemy models.
The authors tackled the problem of modeling interacting components in artificial chemistry by constructing a functor that provides dynamics to an algebraic model, generalizing the AlChemy computational model. The result is a formal approach that connects algebraic and dynamical aspects, with future directions focused on applying category theory as an organizational tool.
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.