(defmacro define-valid-functions (function=arity-pairs) ;Takes dotted lists because why not.
  (loop
     for i in function=arity-pairs
     if (numberp (cdr i))
     do `(define-valid-function ,(car i) ,(cdr i))
     else `(define-valid-function ,(car i))))


(define-valid-functions '((+) (-) (*) (/)
              (sin . 1) (cos . 1) (tan . 1)
              (sqrt . 1) (random . 0) (pow . 2)))

(defun eval-maths (form)
  (when (math-expr-p form) form))