Re: [isabelle] Defining finite list functions recursively

Hi John,

I'm having problems proving termination of the well-founded recursive function xs_strm defined below, and other functions like it.

Good to see that you are driving all available tools to their limits and beyond, as usual :-) But it might actually work...

The problem is that nth_take_cong has the premise about the lengths being equal. In the function definition, a "recursive call" will be generated by this premise because the instance occuring contains the function being defined. But this simplifies away in your manual proof because "length (strm_to_list n f)" does not depend on f.

So you need just one more cong rule to tell function about this:

lemma length_strm_to_list_cong[fundef_cong]:
  "n = n' ==> length (strm_to_list n f) = length (strm_to_list n' f')"
  by simp

Then it works.


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