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Acre-internals

Parse-repeatmod

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

Definitions and Theorems

Function: parse-repeatmod

(defun parse-repeatmod (x index)
  (declare (xargs :guard (and (stringp x) (natp index))))
  (declare (xargs :guard (<= index (strlen x))))
  (let ((__function__ 'parse-repeatmod))
    (declare (ignorable __function__))
    (b* ((index (lnfix index))
         ((when (<= (strlen x) index))
          (mv "End of string when parsing repeatmod"
              nil index))
         (char (char x index)))
      (case char
        (#\? (mv nil :? (+ 1 index)))
        (#\+ (mv nil :+ (+ 1 index)))
        (t (mv "Not a repeatmod" nil index))))))

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

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

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

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

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

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

Theorem: new-index-of-parse-repeatmod

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

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

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

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

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

Theorem: no-change-of-parse-repeatmod

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

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

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

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

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

Theorem: parse-repeatmod-of-nfix-index

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

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

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