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• Minor-stack

Minor-stack-fix

(minor-stack-fix x) is a usual ACL2::fty list fixing function.

Signature

(minor-stack-fix x) → fty::newx

Arguments

x — Guard (minor-stack-p x).

Returns

fty::newx — Type (minor-stack-p fty::newx).

In the logic, we apply minor-frame-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: minor-stack-fix$inline

(defun minor-stack-fix$inline (x)
  (declare (xargs :guard (minor-stack-p x)))
  (let ((__function__ 'minor-stack-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (consp (cdr x))
             (cons (minor-frame-fix (car x))
                   (minor-stack-fix (cdr x)))
           (cons (minor-frame-fix (car x)) nil))
         :exec x)))

Theorem: minor-stack-p-of-minor-stack-fix

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

Theorem: minor-stack-fix-when-minor-stack-p

(defthm minor-stack-fix-when-minor-stack-p
  (implies (minor-stack-p x)
           (equal (minor-stack-fix x) x)))

Function: minor-stack-equiv$inline

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

Theorem: minor-stack-equiv-is-an-equivalence

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

Theorem: minor-stack-equiv-implies-equal-minor-stack-fix-1

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

Theorem: minor-stack-fix-under-minor-stack-equiv

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

Theorem: equal-of-minor-stack-fix-1-forward-to-minor-stack-equiv

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

Theorem: equal-of-minor-stack-fix-2-forward-to-minor-stack-equiv

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

Theorem: minor-stack-equiv-of-minor-stack-fix-1-forward

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

Theorem: minor-stack-equiv-of-minor-stack-fix-2-forward

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

Theorem: car-of-minor-stack-fix-x-under-minor-frame-equiv

(defthm car-of-minor-stack-fix-x-under-minor-frame-equiv
  (minor-frame-equiv (car (minor-stack-fix x))
                     (car x)))

Theorem: car-minor-stack-equiv-congruence-on-x-under-minor-frame-equiv

(defthm
      car-minor-stack-equiv-congruence-on-x-under-minor-frame-equiv
  (implies (minor-stack-equiv x x-equiv)
           (minor-frame-equiv (car x)
                              (car x-equiv)))
  :rule-classes :congruence)

Theorem: cdr-of-minor-stack-fix-x-under-minor-stack-equiv

(defthm cdr-of-minor-stack-fix-x-under-minor-stack-equiv
  (minor-stack-equiv (cdr (minor-stack-fix x))
                     (cdr x)))

Theorem: cdr-minor-stack-equiv-congruence-on-x-under-minor-stack-equiv

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

Theorem: cons-of-minor-frame-fix-x-under-minor-stack-equiv

(defthm cons-of-minor-frame-fix-x-under-minor-stack-equiv
  (minor-stack-equiv (cons (minor-frame-fix x) y)
                     (cons x y)))

Theorem: cons-minor-frame-equiv-congruence-on-x-under-minor-stack-equiv

(defthm
     cons-minor-frame-equiv-congruence-on-x-under-minor-stack-equiv
  (implies (minor-frame-equiv x x-equiv)
           (minor-stack-equiv (cons x y)
                              (cons x-equiv y)))
  :rule-classes :congruence)

Theorem: consp-of-minor-stack-fix

(defthm consp-of-minor-stack-fix
  (consp (minor-stack-fix x)))

Theorem: consp-cdr-of-minor-stack-fix

(defthm consp-cdr-of-minor-stack-fix
  (equal (consp (cdr (minor-stack-fix x)))
         (consp (cdr x))))

Theorem: car-of-minor-stack-fix

(defthm car-of-minor-stack-fix
  (equal (car (minor-stack-fix x))
         (minor-frame-fix (car x))))

Theorem: minor-stack-fix-under-iff

(defthm minor-stack-fix-under-iff
  (minor-stack-fix x))

Theorem: minor-stack-fix-of-cons

(defthm minor-stack-fix-of-cons
  (equal (minor-stack-fix (cons a x))
         (cons (minor-frame-fix a)
               (and (consp x) (minor-stack-fix x)))))

Theorem: len-of-minor-stack-fix

(defthm len-of-minor-stack-fix
  (equal (len (minor-stack-fix x))
         (max 1 (len x))))