• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
    • Fgl
      • Fgl-rewrite-rules
      • Fgl-function-mode
      • Fgl-object
      • Fgl-solving
      • Fgl-handling-if-then-elses
      • Fgl-getting-bits-from-objects
      • Fgl-primitive-and-meta-rules
      • Fgl-counterexamples
      • Fgl-interpreter-overview
      • Fgl-correctness-of-binding-free-variables
      • Fgl-debugging
      • Fgl-testbenches
      • Def-fgl-boolean-constraint
      • Fgl-stack
        • Scratchobj
        • Minor-frame
        • Major-frame
        • Major-stack
          • Major-stack-fix
          • Major-stack-equiv
          • Major-stack-p
        • Scratchlist
        • Minor-stack
      • Fgl-rewrite-tracing
      • Def-fgl-param-thm
      • Def-fgl-thm
      • Fgl-fast-alist-support
      • Fgl-array-support
      • Advanced-equivalence-checking-with-fgl
      • Fgl-fty-support
      • Fgl-internals
    • Vwsim
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Major-stack

Major-stack-fix

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

Signature

(major-stack-fix x) → fty::newx

Arguments

x — Guard (major-stack-p x).

Returns

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

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

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

Theorem: major-stack-p-of-major-stack-fix

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

Theorem: major-stack-fix-when-major-stack-p

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

Function: major-stack-equiv$inline

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

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

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

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

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

Theorem: major-stack-fix-under-major-stack-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-major-stack-fix

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

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

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

Theorem: car-of-major-stack-fix

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

Theorem: major-stack-fix-under-iff

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

Theorem: major-stack-fix-of-cons

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

Theorem: len-of-major-stack-fix

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