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Ichareqv

Case-insensitive character equivalence test.

Signature

(ichareqv x y) → bool

(ichareqv x y) determines if x and y are equivalent when interpreted as characters without regard to case. For instance, upper-case C is equivalent to lower-case c under this relation.

ACL2 has a built-in version of this function, char-equal, but it is irritating to use because it has standard-char-p guards. In contrast, ichareqv works on arbitrary characters, with some loss of efficiency.

Definitions and Theorems

Function: ichareqv$inline

(defun ichareqv$inline (x y)
  (declare (type character x)
           (type character y))
  (let ((acl2::__function__ 'ichareqv))
    (declare (ignorable acl2::__function__))
    (eql (downcase-char x)
         (downcase-char y))))

Theorem: ichareqv-is-an-equivalence

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

Theorem: chareqv-refines-ichareqv

(defthm chareqv-refines-ichareqv
  (implies (chareqv x y) (ichareqv x y))
  :rule-classes (:refinement))

Theorem: equal-of-upcase-char-and-upcase-char

(defthm equal-of-upcase-char-and-upcase-char
  (equal (equal (upcase-char x) (upcase-char y))
         (ichareqv x y)))

Theorem: ichareqv-implies-equal-downcase-char-1

(defthm ichareqv-implies-equal-downcase-char-1
  (implies (ichareqv x x-equiv)
           (equal (downcase-char x)
                  (downcase-char x-equiv)))
  :rule-classes (:congruence))

Theorem: ichareqv-implies-equal-upcase-char-1

(defthm ichareqv-implies-equal-upcase-char-1
  (implies (ichareqv x x-equiv)
           (equal (upcase-char x)
                  (upcase-char x-equiv)))
  :rule-classes (:congruence))

Theorem: ichareqv-implies-equal-upcase-char-str-1

(defthm ichareqv-implies-equal-upcase-char-str-1
  (implies (ichareqv x x-equiv)
           (equal (upcase-char-str x)
                  (upcase-char-str x-equiv)))
  :rule-classes (:congruence))

Theorem: ichareqv-implies-equal-downcase-char-str-1

(defthm ichareqv-implies-equal-downcase-char-str-1
  (implies (ichareqv x x-equiv)
           (equal (downcase-char-str x)
                  (downcase-char-str x-equiv)))
  :rule-classes (:congruence))