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Acre-internals

Parse-charset-elem

Signature
(parse-charset-elem 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-elem

(defun parse-charset-elem (x index)
  (declare (xargs :guard (and (stringp x) (natp index))))
  (declare (xargs :guard (<= index (strlen x))))
  (let ((__function__ 'parse-charset-elem))
    (declare (ignorable __function__))
    (b* (((mv err set new-index)
          (parse-charset-set x index))
         ((unless err) (mv nil set new-index))
         ((mv err char1 index)
          (parse-charset-atom x index))
         ((when err) (mv err nil index))
         ((unless (< index (strlen x)))
          (mv "String ended inside charset"
              nil index))
         (dash (char x index))
         ((unless (eql dash #\-))
          (mv nil (list char1) index))
         ((mv err char2 index)
          (parse-charset-atom x (+ 1 index)))
         ((when err) (mv err nil index))
         ((when (< (char-code char2) (char-code char1)))
          (mv "Invalid range" nil index)))
      (mv nil (charset-range char1 char2)
          index))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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