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Acre-internals

Parse-repeatop

Signature
(parse-repeatop x index) → (mv err min max repeatmod 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).; repeatmod — Type (repeatmod-p repeatmod).; new-index — Type (natp new-index).

Definitions and Theorems

Function: parse-repeatop

(defun parse-repeatop (x index)
  (declare (xargs :guard (and (stringp x) (natp index))))
  (declare (xargs :guard (<= index (strlen x))))
  (let ((__function__ 'parse-repeatop))
    (declare (ignorable __function__))
    (b* (((mv err min max index)
          (parse-repeatbase x index))
         ((when err) (mv err 0 0 nil index))
         ((mv err repeatmod index)
          (parse-repeatmod x index))
         ((when err) (mv nil min max nil index)))
      (mv nil min max repeatmod index))))

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

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

Theorem: natp-of-parse-repeatop.min

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

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

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

Theorem: repeatmod-p-of-parse-repeatop.repeatmod

(defthm repeatmod-p-of-parse-repeatop.repeatmod
  (b* (((mv ?err common-lisp::?min
            common-lisp::?max ?repeatmod ?new-index)
        (parse-repeatop x index)))
    (repeatmod-p repeatmod))
  :rule-classes :rewrite)

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

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

Theorem: new-index-of-parse-repeatop

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

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

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

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

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

Theorem: no-change-of-parse-repeatop

(defthm no-change-of-parse-repeatop
  (b* (((mv ?err common-lisp::?min
            common-lisp::?max ?repeatmod ?new-index)
        (parse-repeatop x index)))
    (implies err (equal new-index (nfix index)))))

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

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

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

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

Theorem: parse-repeatop-of-nfix-index

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

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

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