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Streqv

Case-sensitive string equivalence test.

(streqv x y) determines if x and y are equivalent when interpreted as strings. That is, non-strings are first coerced to be the empty string (via str-fix), then we see if these coerced arguments are equal.

See also str::istreqv for a case-insensitive alternative.

Definitions and Theorems

Function: streqv$inline

(defun streqv$inline (x y)
  (declare (xargs :guard t))
  (equal (str-fix x) (str-fix y)))

Theorem: streqv-is-an-equivalence

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

Theorem: streqv-of-str-fix

(defthm streqv-of-str-fix
  (streqv (str-fix x) x))

Theorem: streqv-implies-equal-str-fix-1

(defthm streqv-implies-equal-str-fix-1
  (implies (streqv x x-equiv)
           (equal (str-fix x) (str-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: streqv-implies-equal-char-1

(defthm streqv-implies-equal-char-1
  (implies (streqv x x-equiv)
           (equal (char x n) (char x-equiv n)))
  :rule-classes (:congruence))

Theorem: streqv-implies-equal-string-append-1

(defthm streqv-implies-equal-string-append-1
  (implies (streqv x x-equiv)
           (equal (string-append x y)
                  (string-append x-equiv y)))
  :rule-classes (:congruence))

Theorem: streqv-implies-equal-string-append-2

(defthm streqv-implies-equal-string-append-2
  (implies (streqv y y-equiv)
           (equal (string-append x y)
                  (string-append x y-equiv)))
  :rule-classes (:congruence))