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Identifiers

Identifier

Fixtype of Java identifiers, for most contexts.

These are Java identifiers that exclude just the non-restricted keywords, as discussed in the topic on identifiers. Since these are used in most contexts (except for some module-related contexts), we use the general name identifierp for this recognizer. See midentifier for the kind of identifiers used in module-related contexts.

We model these Java identifiers as lists of Java Unicode characters that are not empty, that start with a character satisfying identifier-start-p, that continue with characters satisfying identifier-part-p, that differ from all the non-restricted keywords, and that differ from the boolean and null literals. See [JLS14:3.8].

Definitions and Theorems

Function: identifierp

(defun identifierp (x)
  (declare (xargs :guard t))
  (let ((__function__ 'identifierp))
    (declare (ignorable __function__))
    (and (unicode-listp x)
         (consp x)
         (identifier-start-p (car x))
         (identifier-part-listp (cdr x))
         (not (jkeywordp x))
         (not (boolean-literalp x))
         (not (null-literalp x)))))

Theorem: booleanp-of-identifierp

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

Function: identifier-fix

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

Theorem: identifierp-of-identifier-fix

(defthm identifierp-of-identifier-fix
  (b* ((fixed-x (identifier-fix x)))
    (identifierp fixed-x))
  :rule-classes :rewrite)

Theorem: identifier-fix-when-identifierp

(defthm identifier-fix-when-identifierp
  (implies (identifierp x)
           (equal (identifier-fix x) x)))

Function: identifier-equiv$inline

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

Theorem: identifier-equiv-is-an-equivalence

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

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

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

Theorem: identifier-fix-under-identifier-equiv

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

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

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

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

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

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

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

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

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