pls somebody help me in clarifying a question about curch numerals.
I've coded an algorithm to interprete a lambda expression as a church numeral (i.e. puts out the corresponding integer). The question is not about the algorithm, it works more or less as expected. The point rather is that the algorithm also interprets expressions similar to church numerals but with leading "empty" abstractions as a church numeral. A simple example may be of the form:
"\z.\f.\x.fx" is interpreted as "1".
My question now is - can I consider this a valid church numeral, despite it does not follow the exact definition? I couldn't find anything about this in the literature and my mathematics skills do not suffice to try a correct mathematical proof or disproof.
It's clear that my algo can easily be modified to cover cases of this kind, but this would change my results sigificantly, because I'm considering populations for an optimization problem and this question is of outstanding importance for the statistics on the considered population.
Thank you very much for help!