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• Namelist

Namelist-fix

(namelist-fix x) is a usual fty list fixing function.

Signature

(namelist-fix x) → fty::newx

Arguments

x — Guard (namelist-p x).

Returns

fty::newx — Type (namelist-p fty::newx).

In the logic, we apply name-fix to each member of the x. In the execution, none of that is actually necessary and this is just an inlined identity function.

Definitions and Theorems

Function: namelist-fix$inline

(defun namelist-fix$inline (x)
  (declare (xargs :guard (namelist-p x)))
  (let ((__function__ 'namelist-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (cons (name-fix (car x))
                 (namelist-fix (cdr x))))
         :exec x)))

Theorem: namelist-p-of-namelist-fix

(defthm namelist-p-of-namelist-fix
  (b* ((fty::newx (namelist-fix$inline x)))
    (namelist-p fty::newx))
  :rule-classes :rewrite)

Theorem: namelist-fix-when-namelist-p

(defthm namelist-fix-when-namelist-p
  (implies (namelist-p x)
           (equal (namelist-fix x) x)))

Function: namelist-equiv$inline

(defun namelist-equiv$inline (x y)
  (declare (xargs :guard (and (namelist-p x) (namelist-p y))))
  (equal (namelist-fix x)
         (namelist-fix y)))

Theorem: namelist-equiv-is-an-equivalence

(defthm namelist-equiv-is-an-equivalence
  (and (booleanp (namelist-equiv x y))
       (namelist-equiv x x)
       (implies (namelist-equiv x y)
                (namelist-equiv y x))
       (implies (and (namelist-equiv x y)
                     (namelist-equiv y z))
                (namelist-equiv x z)))
  :rule-classes (:equivalence))

Theorem: namelist-equiv-implies-equal-namelist-fix-1

(defthm namelist-equiv-implies-equal-namelist-fix-1
  (implies (namelist-equiv x x-equiv)
           (equal (namelist-fix x)
                  (namelist-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: namelist-fix-under-namelist-equiv

(defthm namelist-fix-under-namelist-equiv
  (namelist-equiv (namelist-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-namelist-fix-1-forward-to-namelist-equiv

(defthm equal-of-namelist-fix-1-forward-to-namelist-equiv
  (implies (equal (namelist-fix x) y)
           (namelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-namelist-fix-2-forward-to-namelist-equiv

(defthm equal-of-namelist-fix-2-forward-to-namelist-equiv
  (implies (equal x (namelist-fix y))
           (namelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: namelist-equiv-of-namelist-fix-1-forward

(defthm namelist-equiv-of-namelist-fix-1-forward
  (implies (namelist-equiv (namelist-fix x) y)
           (namelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: namelist-equiv-of-namelist-fix-2-forward

(defthm namelist-equiv-of-namelist-fix-2-forward
  (implies (namelist-equiv x (namelist-fix y))
           (namelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: car-of-namelist-fix-x-under-name-equiv

(defthm car-of-namelist-fix-x-under-name-equiv
  (name-equiv (car (namelist-fix x))
              (car x)))

Theorem: car-namelist-equiv-congruence-on-x-under-name-equiv

(defthm car-namelist-equiv-congruence-on-x-under-name-equiv
  (implies (namelist-equiv x x-equiv)
           (name-equiv (car x) (car x-equiv)))
  :rule-classes :congruence)

Theorem: cdr-of-namelist-fix-x-under-namelist-equiv

(defthm cdr-of-namelist-fix-x-under-namelist-equiv
  (namelist-equiv (cdr (namelist-fix x))
                  (cdr x)))

Theorem: cdr-namelist-equiv-congruence-on-x-under-namelist-equiv

(defthm cdr-namelist-equiv-congruence-on-x-under-namelist-equiv
  (implies (namelist-equiv x x-equiv)
           (namelist-equiv (cdr x) (cdr x-equiv)))
  :rule-classes :congruence)

Theorem: cons-of-name-fix-x-under-namelist-equiv

(defthm cons-of-name-fix-x-under-namelist-equiv
  (namelist-equiv (cons (name-fix x) y)
                  (cons x y)))

Theorem: cons-name-equiv-congruence-on-x-under-namelist-equiv

(defthm cons-name-equiv-congruence-on-x-under-namelist-equiv
  (implies (name-equiv x x-equiv)
           (namelist-equiv (cons x y)
                           (cons x-equiv y)))
  :rule-classes :congruence)

Theorem: cons-of-namelist-fix-y-under-namelist-equiv

(defthm cons-of-namelist-fix-y-under-namelist-equiv
  (namelist-equiv (cons x (namelist-fix y))
                  (cons x y)))

Theorem: cons-namelist-equiv-congruence-on-y-under-namelist-equiv

(defthm cons-namelist-equiv-congruence-on-y-under-namelist-equiv
  (implies (namelist-equiv y y-equiv)
           (namelist-equiv (cons x y)
                           (cons x y-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-namelist-fix

(defthm consp-of-namelist-fix
  (equal (consp (namelist-fix x))
         (consp x)))

Theorem: namelist-fix-under-iff

(defthm namelist-fix-under-iff
  (iff (namelist-fix x) (consp x)))

Theorem: namelist-fix-of-cons

(defthm namelist-fix-of-cons
  (equal (namelist-fix (cons a x))
         (cons (name-fix a) (namelist-fix x))))

Theorem: len-of-namelist-fix

(defthm len-of-namelist-fix
  (equal (len (namelist-fix x)) (len x)))

Theorem: namelist-fix-of-append

(defthm namelist-fix-of-append
  (equal (namelist-fix (append std::a std::b))
         (append (namelist-fix std::a)
                 (namelist-fix std::b))))

Theorem: namelist-fix-of-repeat

(defthm namelist-fix-of-repeat
  (equal (namelist-fix (repeat acl2::n x))
         (repeat acl2::n (name-fix x))))

Theorem: list-equiv-refines-namelist-equiv

(defthm list-equiv-refines-namelist-equiv
  (implies (list-equiv x y)
           (namelist-equiv x y))
  :rule-classes :refinement)

Theorem: nth-of-namelist-fix

(defthm nth-of-namelist-fix
  (equal (nth acl2::n (namelist-fix x))
         (if (< (nfix acl2::n) (len x))
             (name-fix (nth acl2::n x))
           nil)))

Theorem: namelist-equiv-implies-namelist-equiv-append-1

(defthm namelist-equiv-implies-namelist-equiv-append-1
  (implies (namelist-equiv x fty::x-equiv)
           (namelist-equiv (append x y)
                           (append fty::x-equiv y)))
  :rule-classes (:congruence))

Theorem: namelist-equiv-implies-namelist-equiv-append-2

(defthm namelist-equiv-implies-namelist-equiv-append-2
  (implies (namelist-equiv y fty::y-equiv)
           (namelist-equiv (append x y)
                           (append x fty::y-equiv)))
  :rule-classes (:congruence))

Theorem: namelist-equiv-implies-namelist-equiv-nthcdr-2

(defthm namelist-equiv-implies-namelist-equiv-nthcdr-2
  (implies (namelist-equiv acl2::l l-equiv)
           (namelist-equiv (nthcdr acl2::n acl2::l)
                           (nthcdr acl2::n l-equiv)))
  :rule-classes (:congruence))

Theorem: namelist-equiv-implies-namelist-equiv-take-2

(defthm namelist-equiv-implies-namelist-equiv-take-2
  (implies (namelist-equiv acl2::l l-equiv)
           (namelist-equiv (take acl2::n acl2::l)
                           (take acl2::n l-equiv)))
  :rule-classes (:congruence))