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• Unicode-characters

Ascii

Fixtype of ASCII characters.

The ASCII characters are the first 128 Unicode characters.

Since we model Java Unicode characters as unsigned 16-bit integers, we model ASCII characters as unsigned 7-bit integers.

Definitions and Theorems

Function: ascii-equiv$inline

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

Theorem: ascii-equiv-is-an-equivalence

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

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

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

Theorem: ascii-fix-under-ascii-equiv

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

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

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

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

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

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

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

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

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

Theorem: unicodep-when-asciip

(defthm unicodep-when-asciip
  (implies (asciip x) (unicodep x)))

Subtopics

Asciip

Recognizer for ascii.

Ascii-fix

Fixer for ascii.