I'm more or less talking just about infinite streams, which is a well-known structure in math. You can try looking at the following references. Or find something else.

P. Cousot & R. Cousot (1992). `Inductive definitions, semantics and abstract interpretations'. In POPL '92: Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 83-94, New York, NY, USA. ACM. http://www.di.ens.fr/~cousot/COUSOTpapers/POPL92.shtml

J. J. M. M. Rutten (2003). `Behavioural differential equations: a coinductive calculus of streams, automata, and power series'. Theor. Comput. Sci. 308(1-3):1-53. http://www.cwi.nl/~janr/papers/files-of-papers/tcs308.pdf