A coinduction principle for recursive data types based on bisimulation

The concept of bisimulation from concurrency theory is used to reason about recursively defined data types. From two strong-extensionality theorems stating that the equality (resp. inequality) relation is maximal among all bisimulations, a proof principle for the final coalgebra of an endofunctor on a category of data types (resp. domains) is obtained. As an application of the theory developed, an internal full abstraction result for the canonical model of the untyped call-by-value lambda -calculus is proved. The operations notion of bisimulation and the denotational notion of final semantics are related by means of conditions under which both coincide.<>