Why inductive datatypes forbid types like `data Bad a = C (Bad a -> a)` where the type recursion occurs in front of ->?

The data type you gave is special in that it is an embedding of the untyped lambda calculus.

An example how such a data type allows us to inhabit any type is given in Turner, D.A. (2004-07-28), Total Functional Programming, sect. 3.1, page 758 in Rule 2: Type recursion must be covariant.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.