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Character-literals

Unicode-charlit-char

Fixtype of Unicode input characters usable in character literals.

This corresponds to the grammar rule for single-character [JLS14:3.10.4], whose definiens is input-character except for single quote and backslash, where input-character is defined in [JLS14:3.4] as a unicode-input-character except for CR and LF.

Since unicode-input-character is captured by unicode-input-char-p in our formalization, we define a Unicode character for a character literal (as conveyed by the charlit part of the type name) as a Unicode input character that is not CR, LF, single quote, and backslash.

We prefer the nomenclature `Unicode character for a character literal', on which this type name is based, to the nomenclature `single character' suggested by the grammar.

Definitions and Theorems

Function: unicode-charlit-char-p

(defun unicode-charlit-char-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'unicode-charlit-char-p))
    (declare (ignorable __function__))
    (and (unicode-input-char-p x)
         (not (member (unicode-input-char->unicode x)
                      (list (char-code #\Return)
                            (char-code #\Newline)
                            (char-code #\')
                            (char-code #\\)))))))

Theorem: booleanp-of-unicode-charlit-char-p

(defthm booleanp-of-unicode-charlit-char-p
  (b* ((yes/no (unicode-charlit-char-p x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Function: unicode-charlit-char-fix

(defun unicode-charlit-char-fix (x)
  (declare (xargs :guard (unicode-charlit-char-p x)))
  (mbe :logic
       (if (unicode-charlit-char-p x)
           x
         (make-unicode-input-char :unicode 0
                                  :umarker 0))
       :exec x))

Theorem: unicode-charlit-char-p-of-unicode-charlit-char-fix

(defthm unicode-charlit-char-p-of-unicode-charlit-char-fix
  (b* ((fixed-x (unicode-charlit-char-fix x)))
    (unicode-charlit-char-p fixed-x))
  :rule-classes :rewrite)

Theorem: unicode-charlit-char-fix-when-unicode-charlit-char-p

(defthm unicode-charlit-char-fix-when-unicode-charlit-char-p
  (implies (unicode-charlit-char-p x)
           (equal (unicode-charlit-char-fix x) x)))

Function: unicode-charlit-char-equiv$inline

(defun unicode-charlit-char-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (unicode-charlit-char-p acl2::x)
                              (unicode-charlit-char-p acl2::y))))
  (equal (unicode-charlit-char-fix acl2::x)
         (unicode-charlit-char-fix acl2::y)))

Theorem: unicode-charlit-char-equiv-is-an-equivalence

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

Theorem: unicode-charlit-char-equiv-implies-equal-unicode-charlit-char-fix-1

(defthm
 unicode-charlit-char-equiv-implies-equal-unicode-charlit-char-fix-1
 (implies (unicode-charlit-char-equiv acl2::x x-equiv)
          (equal (unicode-charlit-char-fix acl2::x)
                 (unicode-charlit-char-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: unicode-charlit-char-fix-under-unicode-charlit-char-equiv

(defthm unicode-charlit-char-fix-under-unicode-charlit-char-equiv
  (unicode-charlit-char-equiv (unicode-charlit-char-fix acl2::x)
                              acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-unicode-charlit-char-fix-1-forward-to-unicode-charlit-char-equiv

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

Theorem: equal-of-unicode-charlit-char-fix-2-forward-to-unicode-charlit-char-equiv

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

Theorem: unicode-charlit-char-equiv-of-unicode-charlit-char-fix-1-forward

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

Theorem: unicode-charlit-char-equiv-of-unicode-charlit-char-fix-2-forward

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