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Acre-internals

Parse-range

Signature
(parse-range x index) → (mv err min max new-index)
Arguments: x — Guard (stringp x).; index — Guard (natp index).
Returns: err — Type (acl2::maybe-stringp err).; min — Type (natp min).; max — Type (maybe-natp max).; new-index — Type (natp new-index).

Definitions and Theorems

Function: parse-range

(defun parse-range (x index)
 (declare (xargs :guard (and (stringp x) (natp index))))
 (declare (xargs :guard (<= index (strlen x))))
 (let ((__function__ 'parse-range))
  (declare (ignorable __function__))
  (b* ((x (lstrfix x))
       (index (lnfix index))
       ((when (eql index (strlen x)))
        (mv "String ended inside range expression (start)"
            0 0 index))
       ((mv min len1)
        (str::parse-nat-from-string x 0 0 index (strlen x)))
       (index (+ len1 index))
       ((when (eql index (strlen x)))
        (mv "String ended inside range expression (after min index)"
            0 0 index))
       (nextchar (char x index))
       ((when (eql nextchar #\}))
        (mv nil min min (+ 1 index)))
       ((unless (eql nextchar #\,))
        (mv "Malformed range -- expecting comma"
            0 0 index))
       (index (+ 1 index))
       ((when (eql index (strlen x)))
        (mv "String ended inside range expression (after comma)"
            0 0 index))
       ((mv val2 len2)
        (str::parse-nat-from-string x 0 0 index (strlen x)))
       (max (and (not (eql len2 0)) val2))
       (index (+ len2 index))
       ((when (eql index (strlen x)))
        (mv "String ended inside range expression (after max index)"
            0 0 index))
       (nextchar (char x index))
       ((unless (eql nextchar #\}))
        (mv "Malformed range -- expecting close brace"
            0 0 index)))
    (mv nil min max (+ 1 index)))))

Theorem: maybe-stringp-of-parse-range.err

(defthm maybe-stringp-of-parse-range.err
  (b* (((mv ?err common-lisp::?min
            common-lisp::?max ?new-index)
        (parse-range x index)))
    (acl2::maybe-stringp err))
  :rule-classes :type-prescription)

Theorem: natp-of-parse-range.min

(defthm natp-of-parse-range.min
  (b* (((mv ?err common-lisp::?min
            common-lisp::?max ?new-index)
        (parse-range x index)))
    (natp min))
  :rule-classes :type-prescription)

Theorem: maybe-natp-of-parse-range.max

(defthm maybe-natp-of-parse-range.max
  (b* (((mv ?err common-lisp::?min
            common-lisp::?max ?new-index)
        (parse-range x index)))
    (maybe-natp max))
  :rule-classes :type-prescription)

Theorem: natp-of-parse-range.new-index

(defthm natp-of-parse-range.new-index
  (b* (((mv ?err common-lisp::?min
            common-lisp::?max ?new-index)
        (parse-range x index)))
    (natp new-index))
  :rule-classes :type-prescription)

Theorem: new-index-of-parse-range

(defthm new-index-of-parse-range
  (b* (((mv ?err common-lisp::?min
            common-lisp::?max ?new-index)
        (parse-range x index)))
    (<= (nfix index) new-index))
  :rule-classes :linear)

Theorem: new-index-of-parse-range-strong

(defthm new-index-of-parse-range-strong
  (b* (((mv ?err common-lisp::?min
            common-lisp::?max ?new-index)
        (parse-range x index)))
    (implies (not err)
             (< (nfix index) new-index)))
  :rule-classes :linear)

Theorem: new-index-of-parse-range-less-than-length

(defthm new-index-of-parse-range-less-than-length
  (b* (((mv ?err common-lisp::?min
            common-lisp::?max ?new-index)
        (parse-range x index)))
    (implies (<= (nfix index)
                 (len (acl2::explode x)))
             (<= new-index (len (acl2::explode x)))))
  :rule-classes :linear)

Theorem: parse-range-of-str-fix-x

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

Theorem: parse-range-streqv-congruence-on-x

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

Theorem: parse-range-of-nfix-index

(defthm parse-range-of-nfix-index
  (equal (parse-range x (nfix index))
         (parse-range x index)))

Theorem: parse-range-nat-equiv-congruence-on-index

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