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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))