• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
    • Std/lists
      • Std/lists/abstract
        • Element-list-p
        • Element-list-equiv
        • Element-list-nonempty-p
        • Elementlist-projection
        • Element-equiv
        • Generic-eval-requirement
        • Element-list-fix
        • Elementlist-mapappend
        • Element-fix
        • Outelement-list-p
        • Outelement-p
        • Element-xformer
        • Element-listxformer
        • Element-p
        • Def-listp-rule
        • Def-projection-rule
        • Def-nonempty-listp-rule
        • Def-mapappend-rule
        • Def-listfix-rule
      • Rev
      • Defsort
      • List-fix
      • Std/lists/nth
      • Hons-remove-duplicates
      • Std/lists/update-nth
      • Set-equiv
      • Duplicity
      • Prefixp
      • Std/lists/take
      • Std/lists/intersection$
      • Nats-equiv
      • Repeat
      • Index-of
      • All-equalp
      • Sublistp
      • Std/lists/nthcdr
      • Listpos
      • List-equiv
      • Final-cdr
      • Std/lists/append
      • Std/lists/remove
      • Subseq-list
      • Rcons
      • Std/lists/revappend
      • Std/lists/remove-duplicates-equal
      • Std/lists/reverse
      • Std/lists/last
      • Std/lists/resize-list
      • Flatten
      • Suffixp
      • Std/lists/butlast
      • Std/lists/set-difference
      • Std/lists/len
      • Std/lists/intersectp
      • Std/lists/true-listp
      • Intersectp-witness
      • Subsetp-witness
      • Std/lists/remove1-equal
      • Rest-n
      • First-n
      • Std/lists/union
      • Std/lists/add-to-set
      • Append-without-guard
      • Std/lists/subsetp
      • Std/lists/member
    • Std/alists
    • Obags
    • Std/util
    • Std/strings
    • Std/io
    • Std/osets
    • Std/basic
    • Std/system
    • Std/typed-lists
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Std/lists/abstract

Element-list-fix

Generic typed list fixing function.

Definitions and Theorems

Function: element-list-fix

(defun element-list-fix (x)
  (if (atom x)
      (and (element-list-final-cdr-p t) x)
    (cons (element-fix (car x))
          (element-list-fix (cdr x)))))

Theorem: element-list-p-of-element-list-fix

(defthm element-list-p-of-element-list-fix
  (implies (element-p (element-example))
           (element-list-p (element-list-fix x)))
  :rule-classes :rewrite)

Theorem: element-list-fix-when-element-list-p

(defthm element-list-fix-when-element-list-p
  (implies (element-list-p x)
           (equal (element-list-fix x) x))
  :rule-classes :rewrite)

Theorem: consp-of-element-list-fix

(defthm consp-of-element-list-fix
  (equal (consp (element-list-fix x))
         (consp x))
  :rule-classes :rewrite)

Theorem: element-list-fix-of-cons

(defthm element-list-fix-of-cons
  (equal (element-list-fix (cons a x))
         (cons (element-fix a)
               (element-list-fix x)))
  :rule-classes :rewrite)

Theorem: len-of-element-list-fix

(defthm len-of-element-list-fix
  (equal (len (element-list-fix x))
         (len x))
  :rule-classes :rewrite)

Theorem: element-fix-of-append

(defthm element-fix-of-append
  (equal (element-list-fix (append a b))
         (append (element-list-fix a)
                 (element-list-fix b)))
  :rule-classes :rewrite)