Migration revisited using the Category Theory: Application to Biological Modelling Languages

Since the early seventies, numerous numerical programs have been developed to simulate biophysical processes. The current challenge facing scientific communities is to access any program using their usual language. Migration is a way of dealing with the challenge. The conventional methodology to build up migration functions is the rule-based method. An alternative consists in using the category theory. This paper illustrates the methodology applied to bidirectional migration of a program written using a language based on the system theory (SIMILE) to a biological modelling language (APES EU SEAMLESS integrated project) constructed using design patterns. Using the category theory enabled us (i) to provide a mathematical formalism for composition of the program features, i.e. the architecture and semantic function, (ii) to identify aspects which could not be preserved in the migration because of language expressiveness, and (iii) to automate the migration.