In the excellent Programming and Proving in Isabelle/HOL it says
[...] in contrast to recursive functions, there is no termination requirement
for inductive definitions. (pdf p. 40)
- Does this mean there are inductive definitions where it's possible to have an infinitely deep derivation tree?
- What is an example of such a non-terminating derivation (preferably one with infinite height)? How do you 'construct' these?
- How are rule induction principles on these still sound?