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Identifiers

Tidentifier

Fixtype of Java type identifiers.

The grammar rule for type-identifier in [JLS14:3.8] defines a type identifier as a regular identifier that is not var or yield.

Accordingly, we model Java type identifiers as regular identifiers (the kinds used in most contexts, not in module-related contexts) that differ from the Unicode sequences for var and yield.

Definitions and Theorems

Function: tidentifierp

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

Theorem: booleanp-of-tidentifierp

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

Function: tidentifier-fix

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

Theorem: tidentifierp-of-tidentifier-fix

(defthm tidentifierp-of-tidentifier-fix
  (b* ((fixed-x (tidentifier-fix x)))
    (tidentifierp fixed-x))
  :rule-classes :rewrite)

Theorem: tidentifier-fix-when-tidentifierp

(defthm tidentifier-fix-when-tidentifierp
  (implies (tidentifierp x)
           (equal (tidentifier-fix x) x)))

Function: tidentifier-equiv$inline

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

Theorem: tidentifier-equiv-is-an-equivalence

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

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

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

Theorem: tidentifier-fix-under-tidentifier-equiv

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

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

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

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

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

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

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

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

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