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Identifiers

Umidentifier

Fixtype of Java unqualified method identifiers.

The grammar rule for unqualified-method-identifier in [JLS14:3.8] defines an unqualified method identifier as a regular identifier that is not yield.

Accordingly, we model Java unqualified method identifiers as regular identifiers (the kinds used in most contexts, not in module-related contexts) that differ from the Unicode sequence for yield.

Definitions and Theorems

Function: umidentifierp

(defun umidentifierp (x)
  (declare (xargs :guard t))
  (let ((__function__ 'umidentifierp))
    (declare (ignorable __function__))
    (and (identifierp x)
         (not (equal x (string=>unicode "yield"))))))

Theorem: booleanp-of-umidentifierp

(defthm booleanp-of-umidentifierp
  (b* ((yes/no (umidentifierp x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Function: umidentifier-fix

(defun umidentifier-fix (x)
  (declare (xargs :guard (umidentifierp x)))
  (mbe :logic
       (if (umidentifierp x)
           x
         (list (char-code #\$)))
       :exec x))

Theorem: umidentifierp-of-umidentifier-fix

(defthm umidentifierp-of-umidentifier-fix
  (b* ((fixed-x (umidentifier-fix x)))
    (umidentifierp fixed-x))
  :rule-classes :rewrite)

Theorem: umidentifier-fix-when-umidentifierp

(defthm umidentifier-fix-when-umidentifierp
  (implies (umidentifierp x)
           (equal (umidentifier-fix x) x)))

Function: umidentifier-equiv$inline

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

Theorem: umidentifier-equiv-is-an-equivalence

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

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

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

Theorem: umidentifier-fix-under-umidentifier-equiv

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

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

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

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

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

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

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

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

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