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Mapping

Mapping-fix

Fixing function for mapping structures.

Signature
(mapping-fix x) → new-x
Arguments: x — Guard (mappingp x).
Returns: new-x — Type (mappingp new-x).

Definitions and Theorems

Function: mapping-fix$inline

(defun mapping-fix$inline (x)
 (declare (xargs :guard (mappingp x)))
 (let ((__function__ 'mapping-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((name (identifier-fix (cdr (std::da-nth 0 (cdr x)))))
     (key-name (identifier-fix (cdr (std::da-nth 1 (cdr x)))))
     (key-type (finalize-type-fix (cdr (std::da-nth 2 (cdr x)))))
     (value-name (identifier-fix (cdr (std::da-nth 3 (cdr x)))))
     (value-type (finalize-type-fix (cdr (std::da-nth 4 (cdr x))))))
    (cons :mapping (list (cons 'name name)
                         (cons 'key-name key-name)
                         (cons 'key-type key-type)
                         (cons 'value-name value-name)
                         (cons 'value-type value-type))))
   :exec x)))

Theorem: mappingp-of-mapping-fix

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

Theorem: mapping-fix-when-mappingp

(defthm mapping-fix-when-mappingp
  (implies (mappingp x)
           (equal (mapping-fix x) x)))

Function: mapping-equiv$inline

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

Theorem: mapping-equiv-is-an-equivalence

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

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

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

Theorem: mapping-fix-under-mapping-equiv

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

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

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

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

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

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

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

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

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