"Francisco J. Valverde Albacete" <fva@tsc.uc3m.es> writes:

   although I may be out on a limb here, I recall reading *somewhere* :(
   that while initial algebras where good models for stateless abstract
   data types (and (structural) induction the way to work over terms in
   the free algebra defined by constructors modulo the laws of the ADT),
   final algebras where good models for *stateful* datatypes (and
   coinduction the way to work over the finer "state descriptors" modulo
   the laws of state equivalence), hence they *might* be better models
   for *objects* (as stateful datatypes) than initial algebras.
   
That's precisely what many people in the field of coalgebras
believe. There are many papers on coalgebras as semantics for
object-orientation. There are coalgebraic specification languages
with an OO touch, etc.

Hendrik Tews