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• Comb-transform

Comb-transform-fix

(comb-transform-fix x) is a ACL2::fty fixing function.

Signature

(comb-transform-fix x) → fty::newx

Arguments

x — Guard (comb-transform-p x).

Returns

fty::newx — Type (comb-transform-p fty::newx).

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: comb-transform-fix$inline

(defun comb-transform-fix$inline (x)
  (declare (xargs :guard (comb-transform-p x)))
  (let ((__function__ 'comb-transform-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (tag x)
           ((:balance-config)
            (balance-config-fix x))
           ((:fraig-config) (fraig-config-fix x))
           ((:rewrite-config)
            (rewrite-config-fix x))
           ((:abc-comb-simp-config)
            (abc-comb-simp-config-fix x))
           ((:obs-constprop-config)
            (obs-constprop-config-fix x))
           ((:observability-config)
            (observability-config-fix x))
           ((:constprop-config)
            (constprop-config-fix x))
           ((:snapshot-config)
            (snapshot-config-fix x))
           ((:prune-config) (prune-config-fix x))
           ((:unreachability-config)
            (unreachability-config-fix x))
           (otherwise (dom-supergates-sweep-config-fix x)))
         :exec x)))

Theorem: comb-transform-p-of-comb-transform-fix

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

Theorem: comb-transform-fix-when-comb-transform-p

(defthm comb-transform-fix-when-comb-transform-p
  (implies (comb-transform-p x)
           (equal (comb-transform-fix x) x)))

Function: comb-transform-equiv$inline

(defun comb-transform-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (comb-transform-p x)
                              (comb-transform-p acl2::y))))
  (equal (comb-transform-fix x)
         (comb-transform-fix acl2::y)))

Theorem: comb-transform-equiv-is-an-equivalence

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

Theorem: comb-transform-equiv-implies-equal-comb-transform-fix-1

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

Theorem: comb-transform-fix-under-comb-transform-equiv

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

Theorem: equal-of-comb-transform-fix-1-forward-to-comb-transform-equiv

(defthm
      equal-of-comb-transform-fix-1-forward-to-comb-transform-equiv
  (implies (equal (comb-transform-fix x) acl2::y)
           (comb-transform-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-comb-transform-fix-2-forward-to-comb-transform-equiv

(defthm
      equal-of-comb-transform-fix-2-forward-to-comb-transform-equiv
  (implies (equal x (comb-transform-fix acl2::y))
           (comb-transform-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: comb-transform-equiv-of-comb-transform-fix-1-forward

(defthm comb-transform-equiv-of-comb-transform-fix-1-forward
  (implies (comb-transform-equiv (comb-transform-fix x)
                                 acl2::y)
           (comb-transform-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: comb-transform-equiv-of-comb-transform-fix-2-forward

(defthm comb-transform-equiv-of-comb-transform-fix-2-forward
  (implies (comb-transform-equiv x (comb-transform-fix acl2::y))
           (comb-transform-equiv x acl2::y))
  :rule-classes :forward-chaining)

Theorem: tag-of-comb-transform-fix-forward

(defthm tag-of-comb-transform-fix-forward
  (or (equal (tag (comb-transform-fix x))
             :balance-config)
      (equal (tag (comb-transform-fix x))
             :fraig-config)
      (equal (tag (comb-transform-fix x))
             :rewrite-config)
      (equal (tag (comb-transform-fix x))
             :abc-comb-simp-config)
      (equal (tag (comb-transform-fix x))
             :obs-constprop-config)
      (equal (tag (comb-transform-fix x))
             :observability-config)
      (equal (tag (comb-transform-fix x))
             :constprop-config)
      (equal (tag (comb-transform-fix x))
             :snapshot-config)
      (equal (tag (comb-transform-fix x))
             :prune-config)
      (equal (tag (comb-transform-fix x))
             :unreachability-config)
      (equal (tag (comb-transform-fix x))
             :dom-supergates-sweep-config))
  :rule-classes
  ((:forward-chaining
        :trigger-terms ((tag (comb-transform-fix x))))))