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• Acre-internals

Match-add-backref

Signature

(match-add-backref name start-index match) → new-match

Arguments

start-index — Guard (natp start-index).

match — Guard (matchstate-p match).

Returns

new-match — Type (matchstate-p new-match).

Definitions and Theorems

Function: match-add-backref

(defun match-add-backref (name start-index match)
 (declare (xargs :guard (and (natp start-index)
                             (matchstate-p match))))
 (declare (xargs :guard (<= start-index (matchstate->index match))))
 (let ((__function__ 'match-add-backref))
  (declare (ignorable __function__))
  (b* (((matchstate match))
       (start-index (lnfix start-index))
       ((when (assoc-equal name match.backrefs))
        (matchstate-fix match)))
   (change-matchstate
        match
        :backrefs
        (cons (cons name
                    (make-backref :loc start-index
                                  :len (- match.index start-index)))
              match.backrefs)))))

Theorem: matchstate-p-of-match-add-backref

(defthm matchstate-p-of-match-add-backref
  (b* ((new-match (match-add-backref name start-index match)))
    (matchstate-p new-match))
  :rule-classes :rewrite)

Theorem: match-index-of-match-add-backref

(defthm match-index-of-match-add-backref
  (b* ((?new-match (match-add-backref name start-index match)))
    (equal (matchstate->index new-match)
           (matchstate->index match))))

Theorem: match-add-backref-of-nfix-start-index

(defthm match-add-backref-of-nfix-start-index
  (equal (match-add-backref name (nfix start-index)
                            match)
         (match-add-backref name start-index match)))

Theorem: match-add-backref-nat-equiv-congruence-on-start-index

(defthm match-add-backref-nat-equiv-congruence-on-start-index
  (implies (acl2::nat-equiv start-index start-index-equiv)
           (equal (match-add-backref name start-index match)
                  (match-add-backref name start-index-equiv match)))
  :rule-classes :congruence)

Theorem: match-add-backref-of-matchstate-fix-match

(defthm match-add-backref-of-matchstate-fix-match
  (equal (match-add-backref name start-index (matchstate-fix match))
         (match-add-backref name start-index match)))

Theorem: match-add-backref-matchstate-equiv-congruence-on-match

(defthm match-add-backref-matchstate-equiv-congruence-on-match
  (implies (matchstate-equiv match match-equiv)
           (equal (match-add-backref name start-index match)
                  (match-add-backref name start-index match-equiv)))
  :rule-classes :congruence)