What is the minimum set of primitives required such that a language is Turing complete and a lisp variant?
Seems like car, cdr and some flow control and something for REPL is enough. It be nice if there is such list.
Assume there are only 3 types of data, integers, symbols and lists.(like in picolisp)
The lambda calculus is turing complete. It has one primitive - the lambda. Translating that to a lisp syntax is pretty trivial.
I believe the minimum set is what John McCarthy published in the original paper.
There's a good discussion of this in the Lisp FAQ. It depends on your choice of primitives. McCarthy's original "LISP 1.5 Programmer's Manual" did it with five functions: CAR, CDR, CONS, EQ, and ATOM.
Depends if by LISP-variant you include some kind of "set", if it is the case, you have more work to do (i.e. the interpreter needs to support environments, see SICP).