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Acre-internals

Parse-g-backref

Signature
(parse-g-backref x index) → (mv err pat new-index)
Arguments: x — Guard (stringp x).; index — Guard (natp index).
Returns: err — Type (acl2::maybe-stringp err).; pat — Type (implies (not err) (regex-p pat)).; new-index — Type (natp new-index).

Definitions and Theorems

Function: parse-g-backref

(defun parse-g-backref (x index)
  (declare (xargs :guard (and (stringp x) (natp index))))
  (declare (xargs :guard (<= index (strlen x))))
  (let ((__function__ 'parse-g-backref))
    (declare (ignorable __function__))
    (b* ((index (lnfix index))
         ((when (<= (strlen x) (lnfix index)))
          (mv "EOS parsing \\g backref" nil index))
         (char (char x index))
         ((when (str::dec-digit-char-p char))
          (b* (((mv val len)
                (str::parse-nat-from-string x 0 0 index (strlen x)))
               (index (+ index len)))
            (mv nil (regex-backref val) index)))
         (index (+ 1 index))
         ((unless (eql char #\{))
          (mv "Bad delimiter in \\g backref"
              nil index))
         (idx (find-substr "}" x index))
         ((unless idx)
          (mv "Unclosed name in \\g capture form"
              nil index))
         (name (subseq x index idx))
         ((mv val len)
          (str::parse-nat-from-string name 0 0 0 (strlen name)))
         ((when (eql len (strlen name)))
          (mv nil (regex-backref val) (+ 1 idx))))
      (mv nil (regex-backref name)
          (+ 1 idx)))))

Theorem: maybe-stringp-of-parse-g-backref.err

(defthm maybe-stringp-of-parse-g-backref.err
  (b* (((mv ?err ?pat ?new-index)
        (parse-g-backref x index)))
    (acl2::maybe-stringp err))
  :rule-classes :type-prescription)

Theorem: return-type-of-parse-g-backref.pat

(defthm return-type-of-parse-g-backref.pat
  (b* (((mv ?err ?pat ?new-index)
        (parse-g-backref x index)))
    (implies (not err) (regex-p pat)))
  :rule-classes :rewrite)

Theorem: natp-of-parse-g-backref.new-index

(defthm natp-of-parse-g-backref.new-index
  (b* (((mv ?err ?pat ?new-index)
        (parse-g-backref x index)))
    (natp new-index))
  :rule-classes :type-prescription)

Theorem: new-index-of-parse-g-backref

(defthm new-index-of-parse-g-backref
  (b* (((mv ?err ?pat ?new-index)
        (parse-g-backref x index)))
    (<= (nfix index) new-index))
  :rule-classes :linear)

Theorem: new-index-of-parse-g-backref-strong

(defthm new-index-of-parse-g-backref-strong
  (b* (((mv ?err ?pat ?new-index)
        (parse-g-backref x index)))
    (implies (not err)
             (< (nfix index) new-index)))
  :rule-classes :linear)

Theorem: new-index-of-parse-g-backref-less-than-length

(defthm new-index-of-parse-g-backref-less-than-length
  (b* (((mv ?err ?pat ?new-index)
        (parse-g-backref x index)))
    (implies (<= (nfix index)
                 (len (acl2::explode x)))
             (<= new-index (len (acl2::explode x)))))
  :rule-classes :linear)

Theorem: parse-g-backref-of-str-fix-x

(defthm parse-g-backref-of-str-fix-x
  (equal (parse-g-backref (acl2::str-fix x)
                          index)
         (parse-g-backref x index)))

Theorem: parse-g-backref-streqv-congruence-on-x

(defthm parse-g-backref-streqv-congruence-on-x
  (implies (acl2::streqv x x-equiv)
           (equal (parse-g-backref x index)
                  (parse-g-backref x-equiv index)))
  :rule-classes :congruence)

Theorem: parse-g-backref-of-nfix-index

(defthm parse-g-backref-of-nfix-index
  (equal (parse-g-backref x (nfix index))
         (parse-g-backref x index)))

Theorem: parse-g-backref-nat-equiv-congruence-on-index

(defthm parse-g-backref-nat-equiv-congruence-on-index
  (implies (acl2::nat-equiv index index-equiv)
           (equal (parse-g-backref x index)
                  (parse-g-backref x index-equiv)))
  :rule-classes :congruence)