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Acre-internals

Parse-charset-aux

Signature
(parse-charset-aux x index) → (mv err chars new-index)
Arguments: x — Guard (stringp x).; index — Guard (natp index).
Returns: err — Type (acl2::maybe-stringp err).; chars — Type (character-listp chars).; new-index — Type (natp new-index).

Definitions and Theorems

Function: parse-charset-aux

(defun parse-charset-aux (x index)
  (declare (xargs :guard (and (stringp x) (natp index))))
  (declare (xargs :guard (<= index (strlen x))))
  (let ((__function__ 'parse-charset-aux))
    (declare (ignorable __function__))
    (b* (((when (mbe :logic (zp (- (strlen x) (nfix index)))
                     :exec (eql (strlen x) index)))
          (mv "String ended inside charset"
              nil (lnfix index)))
         (x (lstrfix x))
         (index (lnfix index))
         (char1 (char x index))
         ((when (eql char1 #\]))
          (mv nil nil (+ 1 index)))
         ((mv err chars index)
          (parse-charset-elem x index))
         ((when err) (mv err nil index))
         ((mv err rest index)
          (parse-charset-aux x index))
         ((when err) (mv err nil index)))
      (mv nil (append chars rest) index))))

Theorem: maybe-stringp-of-parse-charset-aux.err

(defthm maybe-stringp-of-parse-charset-aux.err
  (b* (((mv ?err ?chars ?new-index)
        (parse-charset-aux x index)))
    (acl2::maybe-stringp err))
  :rule-classes :type-prescription)

Theorem: character-listp-of-parse-charset-aux.chars

(defthm character-listp-of-parse-charset-aux.chars
  (b* (((mv ?err ?chars ?new-index)
        (parse-charset-aux x index)))
    (character-listp chars))
  :rule-classes :rewrite)

Theorem: natp-of-parse-charset-aux.new-index

(defthm natp-of-parse-charset-aux.new-index
  (b* (((mv ?err ?chars ?new-index)
        (parse-charset-aux x index)))
    (natp new-index))
  :rule-classes :type-prescription)

Theorem: new-index-of-parse-charset-aux

(defthm new-index-of-parse-charset-aux
  (b* (((mv ?err ?chars ?new-index)
        (parse-charset-aux x index)))
    (<= (nfix index) new-index))
  :rule-classes :linear)

Theorem: new-index-of-parse-charset-aux-strong

(defthm new-index-of-parse-charset-aux-strong
  (b* (((mv ?err ?chars ?new-index)
        (parse-charset-aux x index)))
    (implies (not err)
             (< (nfix index) new-index)))
  :rule-classes :linear)

Theorem: new-index-of-parse-charset-aux-less-than-length

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

Theorem: parse-charset-aux-of-str-fix-x

(defthm parse-charset-aux-of-str-fix-x
  (equal (parse-charset-aux (acl2::str-fix x)
                            index)
         (parse-charset-aux x index)))

Theorem: parse-charset-aux-streqv-congruence-on-x

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

Theorem: parse-charset-aux-of-nfix-index

(defthm parse-charset-aux-of-nfix-index
  (equal (parse-charset-aux x (nfix index))
         (parse-charset-aux x index)))

Theorem: parse-charset-aux-nat-equiv-congruence-on-index

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