Creates a fake NAND gate and then creates all gates from NAND.

gates.lisp

;;;; Creates a fake NAND gate and then creates all gates from NAND.
;;;; This is just an exercise, obviously has no practical application.

;;; NAND
(defun !& (a b) (if (and (= a 1) (= b 1)) 0 1))

;;; NOT
(defun ! (a) (!& a 1))

;;; AND
(defun && (a b) (! (!& a b)))

;;; OR
(defun || (a b) (!& (! a) (! b)))

;;; NOR
(defun nor (a b) (! (|| a b)))

;;; XOR
(defun xor (a b) (&& (|| a b) (!& a b)))

;;; XNOR
(defun xnor (a b) (! (xor a b)))