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Icharlist<

Case-insensitive character-list less-than test.

(icharlist< x y) determines whether the character list x preceeds y in alphabetical order without regards to case. The characters are compared with ichar< and shorter strings are considered smaller than longer strings.

Definitions and Theorems

Function: icharlist<

(defun
 icharlist< (x y)
 (declare (xargs :guard (and (character-listp x)
                             (character-listp y))))
 (mbe
  :logic (cond ((atom y) nil)
               ((atom x) t)
               ((ichar< (car x) (car y)) t)
               ((ichar< (car y) (car x)) nil)
               (t (icharlist< (cdr x) (cdr y))))
  :exec
  (cond
   ((atom y) nil)
   ((atom x) t)
   (t
    (let* ((xc (the (unsigned-byte 8)
                    (char-code (the character (car x)))))
           (yc (the (unsigned-byte 8)
                    (char-code (the character (car y)))))
           (xc-fix (if (and (<= (big-a) (the (unsigned-byte 8) xc))
                            (<= (the (unsigned-byte 8) xc) (big-z)))
                       (the (unsigned-byte 8)
                            (+ (the (unsigned-byte 8) xc) 32))
                       (the (unsigned-byte 8) xc)))
           (yc-fix (if (and (<= (big-a) (the (unsigned-byte 8) yc))
                            (<= (the (unsigned-byte 8) yc) (big-z)))
                       (the (unsigned-byte 8)
                            (+ (the (unsigned-byte 8) yc) 32))
                       (the (unsigned-byte 8) yc))))
          (cond ((< (the (unsigned-byte 8) xc-fix)
                    (the (unsigned-byte 8) yc-fix))
                 t)
                ((< (the (unsigned-byte 8) yc-fix)
                    (the (unsigned-byte 8) xc-fix))
                 nil)
                (t (icharlist< (cdr x) (cdr y)))))))))

Theorem: icharlist<-irreflexive

(defthm icharlist<-irreflexive
        (equal (icharlist< x x) nil))

Theorem: icharlist<-antisymmetric

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

Theorem: icharlist<-transitive

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

Theorem: icharlist<-trichotomy-weak

(defthm icharlist<-trichotomy-weak
        (implies (and (not (icharlist< x y))
                      (not (icharlist< y x)))
                 (equal (icharlisteqv x y) t)))

Theorem: icharlisteqv-implies-equal-icharlist<-1

(defthm icharlisteqv-implies-equal-icharlist<-1
        (implies (icharlisteqv x x-equiv)
                 (equal (icharlist< x y)
                        (icharlist< x-equiv y)))
        :rule-classes (:congruence))

Theorem: icharlisteqv-implies-equal-icharlist<-2

(defthm icharlisteqv-implies-equal-icharlist<-2
        (implies (icharlisteqv y y-equiv)
                 (equal (icharlist< x y)
                        (icharlist< x y-equiv)))
        :rule-classes (:congruence))

Theorem: icharlist<-trichotomy-strong

(defthm icharlist<-trichotomy-strong
        (equal (icharlist< x y)
               (and (not (icharlisteqv x y))
                    (not (icharlist< y x))))
        :rule-classes ((:rewrite :loop-stopper ((x y)))))