Why can't a programming language becomes both fully recursive and polymorphism

Question

In my theory of computation class last Spring my professor said in passing that a programming language cannot be both fully recursive and polymorphism

Answer 1

I wouldn't go so far as can't, but it hasn't been done as yet. The issue is that the data types must be allowed to change over the recursive calls and nobody has figured out a generic way to allow that so a single coded function supports it.

Answer 2

I found your doppleganger. Seems like the professor has been sowing seeds of confusion. For some time now.
https://cs.stackexchange.com/questions/44954/why-cant-a-programming-language-be-both-fully-recursive-and-polymorphic

Answer 3

hmmmm