		Search-engine friendly clone of the ACL2 documentation.

Acre-internals

Parse-k-backref

Signature
(parse-k-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-k-backref

(defun parse-k-backref (x index)
  (declare (xargs :guard (and (stringp x) (natp index))))
  (declare (xargs :guard (<= index (strlen x))))
  (let ((__function__ 'parse-k-backref))
    (declare (ignorable __function__))
    (b* ((index (lnfix index))
         ((when (<= (strlen x) (lnfix index)))
          (mv "EOS parsing \\k backref" nil index))
         (char (char x index))
         (end-delim (case char
                      (#\{ "}")
                      (#\< ">")
                      (#\' "'")
                      (t nil)))
         ((unless end-delim)
          (mv "Bad delimiter in \\k backref"
              nil index))
         (idx (find-substr end-delim x index))
         ((unless idx)
          (mv "Unclosed name in \\k capture form"
              nil index))
         (name (subseq x index idx))
         (index (+ 1 idx)))
      (mv nil (regex-backref name) index))))

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: no-change-of-parse-k-backref

(defthm no-change-of-parse-k-backref
  (b* (((mv ?err ?pat ?new-index)
        (parse-k-backref x index)))
    (implies err (equal new-index (nfix index)))))

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

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

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

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

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

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

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

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