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Ident-sinfo

Ident-sinfo-fix

Fixing function for ident-sinfo structures.

Signature
(ident-sinfo-fix x) → new-x
Arguments: x — Guard (ident-sinfop x).
Returns: new-x — Type (ident-sinfop new-x).

Definitions and Theorems

Function: ident-sinfo-fix$inline

(defun ident-sinfo-fix$inline (x)
 (declare (xargs :guard (ident-sinfop x)))
 (let ((__function__ 'ident-sinfo-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (ident-sinfo-kind x)
     (:var/const
          (b* ((get (var/const-sinfo-fix (std::da-nth 0 (cdr x)))))
            (cons :var/const (list get))))
     (:function
          (b* ((get (function-sinfo-fix (std::da-nth 0 (cdr x)))))
            (cons :function (list get))))
     (:struct (b* ((get (struct-sinfo-fix (std::da-nth 0 (cdr x)))))
                (cons :struct (list get)))))
   :exec x)))

Theorem: ident-sinfop-of-ident-sinfo-fix

(defthm ident-sinfop-of-ident-sinfo-fix
  (b* ((new-x (ident-sinfo-fix$inline x)))
    (ident-sinfop new-x))
  :rule-classes :rewrite)

Theorem: ident-sinfo-fix-when-ident-sinfop

(defthm ident-sinfo-fix-when-ident-sinfop
  (implies (ident-sinfop x)
           (equal (ident-sinfo-fix x) x)))

Function: ident-sinfo-equiv$inline

(defun ident-sinfo-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (ident-sinfop acl2::x)
                              (ident-sinfop acl2::y))))
  (equal (ident-sinfo-fix acl2::x)
         (ident-sinfo-fix acl2::y)))

Theorem: ident-sinfo-equiv-is-an-equivalence

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

Theorem: ident-sinfo-equiv-implies-equal-ident-sinfo-fix-1

(defthm ident-sinfo-equiv-implies-equal-ident-sinfo-fix-1
  (implies (ident-sinfo-equiv acl2::x x-equiv)
           (equal (ident-sinfo-fix acl2::x)
                  (ident-sinfo-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ident-sinfo-fix-under-ident-sinfo-equiv

(defthm ident-sinfo-fix-under-ident-sinfo-equiv
  (ident-sinfo-equiv (ident-sinfo-fix acl2::x)
                     acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ident-sinfo-fix-1-forward-to-ident-sinfo-equiv

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

Theorem: equal-of-ident-sinfo-fix-2-forward-to-ident-sinfo-equiv

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

Theorem: ident-sinfo-equiv-of-ident-sinfo-fix-1-forward

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

Theorem: ident-sinfo-equiv-of-ident-sinfo-fix-2-forward

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

Theorem: ident-sinfo-kind$inline-of-ident-sinfo-fix-x

(defthm ident-sinfo-kind$inline-of-ident-sinfo-fix-x
  (equal (ident-sinfo-kind$inline (ident-sinfo-fix x))
         (ident-sinfo-kind$inline x)))

Theorem: ident-sinfo-kind$inline-ident-sinfo-equiv-congruence-on-x

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

Theorem: consp-of-ident-sinfo-fix

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