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• 4v-sexprs

4v-sexpr-ind

Basic structural induction scheme for s-expressions.

Definitions and Theorems

Function: 4v-sexpr-ind

(defun 4v-sexpr-ind (x)
  (declare (xargs :guard t))
  (if (atom x)
      x
    (cons (car x)
          (4v-sexpr-ind-list (cdr x)))))

Function: 4v-sexpr-ind-list

(defun 4v-sexpr-ind-list (x)
  (declare (xargs :guard t))
  (if (atom x)
      nil
    (cons (4v-sexpr-ind (car x))
          (4v-sexpr-ind-list (cdr x)))))

Function: 4v-sexpr-flag

(defun 4v-sexpr-flag (flag x)
  (declare (xargs :non-executable t))
  (declare (ignorable x))
  (prog2$ (throw-nonexec-error '4v-sexpr-flag
                               (list flag x))
          (cond ((equal flag 'sexpr)
                 (if (consp x)
                     (cons (car x)
                           (4v-sexpr-flag 'sexpr-list (cdr x)))
                   x))
                (t (if (consp x)
                       (cons (4v-sexpr-flag 'sexpr (car x))
                             (4v-sexpr-flag 'sexpr-list (cdr x)))
                     'nil)))))

Theorem: 4v-sexpr-flag-equivalences

(defthm 4v-sexpr-flag-equivalences
  (and (equal (4v-sexpr-flag 'sexpr x)
              (4v-sexpr-ind x))
       (equal (4v-sexpr-flag 'sexpr-list x)
              (4v-sexpr-ind-list x))))