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Compdecl

Compdecl-fix

Fixing function for compdecl structures.

Signature
(compdecl-fix x) → new-x
Arguments: x — Guard (compdeclp x).
Returns: new-x — Type (compdeclp new-x).

Definitions and Theorems

Function: compdecl-fix$inline

(defun compdecl-fix$inline (x)
  (declare (xargs :guard (compdeclp x)))
  (let ((__function__ 'compdecl-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (identifier-fix (cdr (std::da-nth 0 (cdr x)))))
              (type (type-fix (cdr (std::da-nth 1 (cdr x))))))
           (cons :compdecl (list (cons 'name name)
                                 (cons 'type type))))
         :exec x)))

Theorem: compdeclp-of-compdecl-fix

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

Theorem: compdecl-fix-when-compdeclp

(defthm compdecl-fix-when-compdeclp
  (implies (compdeclp x)
           (equal (compdecl-fix x) x)))

Function: compdecl-equiv$inline

(defun compdecl-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (compdeclp acl2::x)
                              (compdeclp acl2::y))))
  (equal (compdecl-fix acl2::x)
         (compdecl-fix acl2::y)))

Theorem: compdecl-equiv-is-an-equivalence

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

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

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

Theorem: compdecl-fix-under-compdecl-equiv

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

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

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

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

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

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

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

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

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