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Acre-internals

Match-regex-locs

Signature
(match-regex-locs pat x index mode) → match
Arguments: pat — Guard (regex-p pat).; x — Guard (stringp x).; index — Guard (natp index).; mode — Guard (matchmode-p mode).
Returns: match — Type (matchresult-p match).

Definitions and Theorems

Function: match-regex-locs

(defun match-regex-locs (pat x index mode)
 (declare (xargs :guard (and (regex-p pat)
                             (stringp x)
                             (natp index)
                             (matchmode-p mode))))
 (declare (xargs :guard (<= index (strlen x))))
 (let ((__function__ 'match-regex-locs))
   (declare (ignorable __function__))
   (b*
    ((matches1 (match-regex-rec pat x (make-matchstate :index index)
                                mode))
     ((when matches1)
      (b* (((matchstate m1) (car matches1)))
        (make-matchresult :loc (lnfix index)
                          :len (- m1.index (lnfix index))
                          :str x
                          :backrefs m1.backrefs)))
     ((when (mbe :logic (zp (- (strlen x) (nfix index)))
                 :exec (eql (strlen x) (lnfix index))))
      (make-matchresult :loc nil
                        :len 0
                        :str x
                        :backrefs nil)))
    (match-regex-locs pat x (+ 1 (lnfix index))
                      mode))))

Theorem: matchresult-p-of-match-regex-locs

(defthm matchresult-p-of-match-regex-locs
  (b* ((match (match-regex-locs pat x index mode)))
    (matchresult-p match))
  :rule-classes :rewrite)

Theorem: matchresult-in-bounds-of-match-regex-locs

(defthm matchresult-in-bounds-of-match-regex-locs
  (b* ((?match (match-regex-locs pat x index mode)))
    (implies (<= (nfix index) (strlen x))
             (matchresult-in-bounds match))))

Theorem: matchresult->str-of-match-regex-locs

(defthm matchresult->str-of-match-regex-locs
  (b* ((?match (match-regex-locs pat x index mode)))
    (equal (matchresult->str match)
           (lstrfix x))))

Theorem: match-regex-locs-of-regex-fix-pat

(defthm match-regex-locs-of-regex-fix-pat
  (equal (match-regex-locs (regex-fix pat)
                           x index mode)
         (match-regex-locs pat x index mode)))

Theorem: match-regex-locs-regex-equiv-congruence-on-pat

(defthm match-regex-locs-regex-equiv-congruence-on-pat
  (implies (regex-equiv pat pat-equiv)
           (equal (match-regex-locs pat x index mode)
                  (match-regex-locs pat-equiv x index mode)))
  :rule-classes :congruence)

Theorem: match-regex-locs-of-str-fix-x

(defthm match-regex-locs-of-str-fix-x
  (equal (match-regex-locs pat (acl2::str-fix x)
                           index mode)
         (match-regex-locs pat x index mode)))

Theorem: match-regex-locs-streqv-congruence-on-x

(defthm match-regex-locs-streqv-congruence-on-x
  (implies (acl2::streqv x x-equiv)
           (equal (match-regex-locs pat x index mode)
                  (match-regex-locs pat x-equiv index mode)))
  :rule-classes :congruence)

Theorem: match-regex-locs-of-nfix-index

(defthm match-regex-locs-of-nfix-index
  (equal (match-regex-locs pat x (nfix index)
                           mode)
         (match-regex-locs pat x index mode)))

Theorem: match-regex-locs-nat-equiv-congruence-on-index

(defthm match-regex-locs-nat-equiv-congruence-on-index
  (implies (acl2::nat-equiv index index-equiv)
           (equal (match-regex-locs pat x index mode)
                  (match-regex-locs pat x index-equiv mode)))
  :rule-classes :congruence)

Theorem: match-regex-locs-of-matchmode-fix-mode

(defthm match-regex-locs-of-matchmode-fix-mode
  (equal (match-regex-locs pat x index (matchmode-fix mode))
         (match-regex-locs pat x index mode)))

Theorem: match-regex-locs-matchmode-equiv-congruence-on-mode

(defthm match-regex-locs-matchmode-equiv-congruence-on-mode
  (implies (matchmode-equiv mode mode-equiv)
           (equal (match-regex-locs pat x index mode)
                  (match-regex-locs pat x index mode-equiv)))
  :rule-classes :congruence)