On this site they say there are 10 LISP primitives.
The primitives are: atom, quote, eq, car, cdr, cons, cond, lambda, label, apply
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http://hyperpolygl
The best way to actually know this for sure is if you implement it. I used 3 summers to create Zozotez which is a McCarty-ish LISP running on Brainfuck.
I tried to find out what I needed and on a forum you'll find a thread that says You only need lambda. Thus, you can make a whole LISP in lambda calculus I you'd like. I found it interesting, but it's hardly the way to go if you want something that eventually has side effects and works in the real world.
For a Turing complete LISP I used Paul Grahams explanation of McCarthy's paper and all you really need is:
Thats 10. In addition to this, to have a implementation that you can test and not just on a drawing board:
Thats 12. In my Zozotez I implemeted set and flambda (anonymous macroes, like lambda) as well. I could feed it a library implementing any dynamic bound lisp (Elisp, picoLisp) with the exception of file I/O (because the underlying BF does not support it other than stdin/stdout).
I recommend anyone to implement a LISP1-interpreter in both LISP and (not LISP) to fully understand how a language is implemented. LISP has a very simple syntax so it's a good starting point for a parser. I'm currently working on a scheme compiler written in scheme with different targets (like Stalin is for target C), hopefully BF as one of them.