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Ordering

Strnat<

Mixed alphanumeric string less-than test.

Signature
(strnat< x y) → *

(strnat< x y) determines if the string x is "smaller" than the string y, using an ordering that is nice for humans.

See charlistnat< for a description of this order.

We avoid coercing the strings into character lists, and this is altogether pretty fast.

Definitions and Theorems

Function: strnat<$inline

(defun strnat<$inline (x y)
 (declare (type string x)
          (type string y))
 (let ((acl2::__function__ 'strnat<))
   (declare (ignorable acl2::__function__))
   (mbe :logic (charlistnat< (explode x) (explode y))
        :exec (strnat<-aux (the string x)
                           (the string y)
                           (the integer 0)
                           (the integer 0)
                           (the integer (length (the string x)))
                           (the integer (length (the string y)))))))

Theorem: streqv-implies-equal-strnat<-1

(defthm streqv-implies-equal-strnat<-1
  (implies (streqv x x-equiv)
           (equal (strnat< x y)
                  (strnat< x-equiv y)))
  :rule-classes (:congruence))

Theorem: streqv-implies-equal-strnat<-2

(defthm streqv-implies-equal-strnat<-2
  (implies (streqv y y-equiv)
           (equal (strnat< x y)
                  (strnat< x y-equiv)))
  :rule-classes (:congruence))

Theorem: strnat<-irreflexive

(defthm strnat<-irreflexive
  (not (strnat< x x)))

Theorem: strnat<-antisymmetric

(defthm strnat<-antisymmetric
  (implies (strnat< x y)
           (not (strnat< y x))))

Theorem: strnat<-transitive

(defthm strnat<-transitive
  (implies (and (strnat< x y) (strnat< y z))
           (strnat< x z)))

Theorem: strnat<-transitive-alt

(defthm strnat<-transitive-alt
  (implies (and (strnat< y z) (strnat< x y))
           (strnat< x z)))

Subtopics

Strnat<-aux: Implementation of strnat<.