• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
    • Ipasir
    • Aignet
    • Aig
    • Satlink
    • Truth
    • Ubdds
    • Bdd
    • Faig
    • Bed
    • 4v
      • 4v-sexprs
        • 4v-sexpr-vars
        • 4v-sexpr-eval
        • 4v-sexpr-to-faig
        • 4v-sexpr-restrict-with-rw
        • 4vs-constructors
        • 4v-sexpr-compose-with-rw
        • 4v-sexpr-restrict
        • 4v-sexpr-alist-extract
        • 4v-sexpr-compose
        • 4v-nsexpr-p
        • 4v-sexpr-purebool-p
        • 4v-sexpr-<=
        • Sfaig
        • Sexpr-equivs
        • 3v-syntax-sexprp
        • Sexpr-rewriting
        • 4v-sexpr-ind
        • 4v-alist-extract
      • 4v-monotonicity
      • 4v-operations
      • Why-4v-logic
      • 4v-<=
      • 4vp
      • 4vcases
      • 4v-fix
      • 4v-lookup
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Testing-utilities
  • Math

• 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))))