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• Fresh-ident-utility

Fresh-numbered-string-wrt

Signature

(fresh-numbered-string-wrt base number-prefix 
                           number number-suffix blacklist) 
 
  → 
string

Arguments

base — Guard (stringp base).

number-prefix — Guard (stringp number-prefix).

number — Guard (natp number).

number-suffix — Guard (stringp number-suffix).

blacklist — Guard (acl2::string-setp blacklist).

Returns

string — Type (stringp string).

Definitions and Theorems

Function: fresh-numbered-string-wrt0

(defun fresh-numbered-string-wrt0
       (base number-prefix
             number number-suffix blacklist steps)
  (declare (type (unsigned-byte 60) steps))
  (declare (xargs :guard (and (stringp base)
                              (stringp number-prefix)
                              (natp number)
                              (stringp number-suffix)
                              (acl2::string-setp blacklist))))
  (b*
   ((number (mbe :logic (nfix number) :exec number))
    (steps (mbe :logic (nfix steps)
                :exec (acl2::the-fixnat steps)))
    (blacklist (acl2::string-sfix blacklist))
    ((when (= 0 steps))
     (mbe :logic (acl2::str-fix base)
          :exec base))
    (numbered-string
         (make-numbered-string base
                               number-prefix number number-suffix)))
   (if
    (in numbered-string blacklist)
    (fresh-numbered-string-wrt0 base number-prefix (+ number 1)
                                number-suffix blacklist (- steps 1))
    numbered-string)))

Theorem: stringp-of-fresh-numbered-string-wrt0

(defthm stringp-of-fresh-numbered-string-wrt0
  (b* ((string (fresh-numbered-string-wrt0
                    base number-prefix
                    number number-suffix blacklist steps)))
    (stringp string))
  :rule-classes :rewrite)

Theorem: fresh-numbered-string-wrt0-of-str-fix-base

(defthm fresh-numbered-string-wrt0-of-str-fix-base
 (equal
   (fresh-numbered-string-wrt0 (acl2::str-fix base)
                               number-prefix
                               number number-suffix blacklist steps)
   (fresh-numbered-string-wrt0
        base number-prefix
        number number-suffix blacklist steps)))

Theorem: fresh-numbered-string-wrt0-streqv-congruence-on-base

(defthm fresh-numbered-string-wrt0-streqv-congruence-on-base
 (implies
  (acl2::streqv base base-equiv)
  (equal
   (fresh-numbered-string-wrt0 base number-prefix
                               number number-suffix blacklist steps)
   (fresh-numbered-string-wrt0
        base-equiv number-prefix
        number number-suffix blacklist steps)))
 :rule-classes :congruence)

Theorem: fresh-numbered-string-wrt0-of-str-fix-number-prefix

(defthm fresh-numbered-string-wrt0-of-str-fix-number-prefix
 (equal
   (fresh-numbered-string-wrt0 base (acl2::str-fix number-prefix)
                               number number-suffix blacklist steps)
   (fresh-numbered-string-wrt0
        base number-prefix
        number number-suffix blacklist steps)))

Theorem: fresh-numbered-string-wrt0-streqv-congruence-on-number-prefix

(defthm
      fresh-numbered-string-wrt0-streqv-congruence-on-number-prefix
 (implies
  (acl2::streqv number-prefix number-prefix-equiv)
  (equal
   (fresh-numbered-string-wrt0 base number-prefix
                               number number-suffix blacklist steps)
   (fresh-numbered-string-wrt0
        base number-prefix-equiv
        number number-suffix blacklist steps)))
 :rule-classes :congruence)

Theorem: fresh-numbered-string-wrt0-of-nfix-number

(defthm fresh-numbered-string-wrt0-of-nfix-number
 (equal (fresh-numbered-string-wrt0 base number-prefix (nfix number)
                                    number-suffix blacklist steps)
        (fresh-numbered-string-wrt0
             base number-prefix
             number number-suffix blacklist steps)))

Theorem: fresh-numbered-string-wrt0-nat-equiv-congruence-on-number

(defthm fresh-numbered-string-wrt0-nat-equiv-congruence-on-number
 (implies
  (acl2::nat-equiv number number-equiv)
  (equal
   (fresh-numbered-string-wrt0 base number-prefix
                               number number-suffix blacklist steps)
   (fresh-numbered-string-wrt0 base number-prefix number-equiv
                               number-suffix blacklist steps)))
 :rule-classes :congruence)

Theorem: fresh-numbered-string-wrt0-of-str-fix-number-suffix

(defthm fresh-numbered-string-wrt0-of-str-fix-number-suffix
 (equal
    (fresh-numbered-string-wrt0 base number-prefix
                                number (acl2::str-fix number-suffix)
                                blacklist steps)
    (fresh-numbered-string-wrt0
         base number-prefix
         number number-suffix blacklist steps)))

Theorem: fresh-numbered-string-wrt0-streqv-congruence-on-number-suffix

(defthm
      fresh-numbered-string-wrt0-streqv-congruence-on-number-suffix
 (implies
  (acl2::streqv number-suffix number-suffix-equiv)
  (equal
   (fresh-numbered-string-wrt0 base number-prefix
                               number number-suffix blacklist steps)
   (fresh-numbered-string-wrt0
        base number-prefix number
        number-suffix-equiv blacklist steps)))
 :rule-classes :congruence)

Theorem: fresh-numbered-string-wrt0-of-string-sfix-blacklist

(defthm fresh-numbered-string-wrt0-of-string-sfix-blacklist
  (equal (fresh-numbered-string-wrt0
              base number-prefix number number-suffix
              (acl2::string-sfix blacklist)
              steps)
         (fresh-numbered-string-wrt0
              base number-prefix
              number number-suffix blacklist steps)))

Theorem: fresh-numbered-string-wrt0-string-sequiv-congruence-on-blacklist

(defthm
   fresh-numbered-string-wrt0-string-sequiv-congruence-on-blacklist
 (implies
  (acl2::string-sequiv blacklist blacklist-equiv)
  (equal
   (fresh-numbered-string-wrt0 base number-prefix
                               number number-suffix blacklist steps)
   (fresh-numbered-string-wrt0
        base number-prefix number
        number-suffix blacklist-equiv steps)))
 :rule-classes :congruence)

Function: fresh-numbered-string-wrt

(defun fresh-numbered-string-wrt
       (base number-prefix
             number number-suffix blacklist)
  (declare (xargs :guard (and (stringp base)
                              (stringp number-prefix)
                              (natp number)
                              (stringp number-suffix)
                              (acl2::string-setp blacklist))))
  (fresh-numbered-string-wrt0
       base number-prefix
       number number-suffix blacklist
       (acl2::the-fixnat (- (expt 2 acl2::*fixnat-bits*) 1))))

Theorem: stringp-of-fresh-numbered-string-wrt

(defthm stringp-of-fresh-numbered-string-wrt
 (b*
  ((string
        (fresh-numbered-string-wrt base number-prefix
                                   number number-suffix blacklist)))
  (stringp string))
 :rule-classes :rewrite)

Theorem: fresh-numbered-string-wrt-of-str-fix-base

(defthm fresh-numbered-string-wrt-of-str-fix-base
 (equal (fresh-numbered-string-wrt (acl2::str-fix base)
                                   number-prefix
                                   number number-suffix blacklist)
        (fresh-numbered-string-wrt base number-prefix
                                   number number-suffix blacklist)))

Theorem: fresh-numbered-string-wrt-streqv-congruence-on-base

(defthm fresh-numbered-string-wrt-streqv-congruence-on-base
 (implies
   (acl2::streqv base base-equiv)
   (equal
        (fresh-numbered-string-wrt base number-prefix
                                   number number-suffix blacklist)
        (fresh-numbered-string-wrt base-equiv number-prefix
                                   number number-suffix blacklist)))
 :rule-classes :congruence)

Theorem: fresh-numbered-string-wrt-of-str-fix-number-prefix

(defthm fresh-numbered-string-wrt-of-str-fix-number-prefix
  (equal
       (fresh-numbered-string-wrt base (acl2::str-fix number-prefix)
                                  number number-suffix blacklist)
       (fresh-numbered-string-wrt base number-prefix
                                  number number-suffix blacklist)))

Theorem: fresh-numbered-string-wrt-streqv-congruence-on-number-prefix

(defthm fresh-numbered-string-wrt-streqv-congruence-on-number-prefix
 (implies
   (acl2::streqv number-prefix number-prefix-equiv)
   (equal
        (fresh-numbered-string-wrt base number-prefix
                                   number number-suffix blacklist)
        (fresh-numbered-string-wrt base number-prefix-equiv
                                   number number-suffix blacklist)))
 :rule-classes :congruence)

Theorem: fresh-numbered-string-wrt-of-nfix-number

(defthm fresh-numbered-string-wrt-of-nfix-number
 (equal (fresh-numbered-string-wrt base number-prefix (nfix number)
                                   number-suffix blacklist)
        (fresh-numbered-string-wrt base number-prefix
                                   number number-suffix blacklist)))

Theorem: fresh-numbered-string-wrt-nat-equiv-congruence-on-number

(defthm fresh-numbered-string-wrt-nat-equiv-congruence-on-number
 (implies
   (acl2::nat-equiv number number-equiv)
   (equal (fresh-numbered-string-wrt base number-prefix
                                     number number-suffix blacklist)
          (fresh-numbered-string-wrt
               base number-prefix
               number-equiv number-suffix blacklist)))
 :rule-classes :congruence)

Theorem: fresh-numbered-string-wrt-of-str-fix-number-suffix

(defthm fresh-numbered-string-wrt-of-str-fix-number-suffix
 (equal
     (fresh-numbered-string-wrt base number-prefix
                                number (acl2::str-fix number-suffix)
                                blacklist)
     (fresh-numbered-string-wrt base number-prefix
                                number number-suffix blacklist)))

Theorem: fresh-numbered-string-wrt-streqv-congruence-on-number-suffix

(defthm fresh-numbered-string-wrt-streqv-congruence-on-number-suffix
 (implies
   (acl2::streqv number-suffix number-suffix-equiv)
   (equal (fresh-numbered-string-wrt base number-prefix
                                     number number-suffix blacklist)
          (fresh-numbered-string-wrt
               base number-prefix
               number number-suffix-equiv blacklist)))
 :rule-classes :congruence)