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Modscope

Modscope-fix

Fixing function for modscope structures.

Signature
(modscope-fix x) → new-x
Arguments: x — Guard (modscope-p x).
Returns: new-x — Type (modscope-p new-x).

Definitions and Theorems

Function: modscope-fix$inline

(defun modscope-fix$inline (x)
 (declare (xargs :guard (modscope-p x)))
 (let ((__function__ 'modscope-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (modscope-kind x)
    (:top (b* ((modidx (nfix (cdr x))))
            (cons :top modidx)))
    (:nested
     (b*
      ((modidx (nfix (std::prod-car (std::prod-car (cdr x)))))
       (wireoffset (nfix (std::prod-cdr (std::prod-car (cdr x)))))
       (instoffset (nfix (std::prod-car (std::prod-cdr (cdr x)))))
       (upper
            (modscope-fix (std::prod-cdr (std::prod-cdr (cdr x))))))
      (cons :nested
            (std::prod-cons (std::prod-cons modidx wireoffset)
                            (std::prod-cons instoffset upper))))))
   :exec x)))

Theorem: modscope-p-of-modscope-fix

(defthm modscope-p-of-modscope-fix
  (b* ((new-x (modscope-fix$inline x)))
    (modscope-p new-x))
  :rule-classes :rewrite)

Theorem: modscope-fix-when-modscope-p

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

Function: modscope-equiv$inline

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

Theorem: modscope-equiv-is-an-equivalence

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

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

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

Theorem: modscope-fix-under-modscope-equiv

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

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

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

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

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

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

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

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

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

Theorem: modscope-kind$inline-of-modscope-fix-x

(defthm modscope-kind$inline-of-modscope-fix-x
  (equal (modscope-kind$inline (modscope-fix x))
         (modscope-kind$inline x)))

Theorem: modscope-kind$inline-modscope-equiv-congruence-on-x

(defthm modscope-kind$inline-modscope-equiv-congruence-on-x
  (implies (modscope-equiv x x-equiv)
           (equal (modscope-kind$inline x)
                  (modscope-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-modscope-fix

(defthm consp-of-modscope-fix
  (consp (modscope-fix x))
  :rule-classes :type-prescription)