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Match-string-at

Signature

(match-string-at target x index) → (mv matchedp new-index)

Arguments

target — Guard (stringp target).

x — Guard (stringp x).

index — Guard (natp index).

Returns

matchedp — Type (booleanp matchedp).

new-index — Type (natp new-index).

Definitions and Theorems

Function: match-string-at

(defun match-string-at (target x index)
  (declare (xargs :guard (and (stringp target)
                              (stringp x)
                              (natp index))))
  (declare (xargs :guard (<= index (strlen x))))
  (let ((__function__ 'match-string-at))
    (declare (ignorable __function__))
    (b* ((match (str::strprefixp-impl (lstrfix target)
                                      (lstrfix x)
                                      0 (lnfix index)
                                      (strlen target)
                                      (strlen x))))
      (if match (mv t (+ (strlen target) (lnfix index)))
        (mv nil (lnfix index))))))

Theorem: booleanp-of-match-string-at.matchedp

(defthm booleanp-of-match-string-at.matchedp
  (b* (((mv ?matchedp ?new-index)
        (match-string-at target x index)))
    (booleanp matchedp))
  :rule-classes :type-prescription)

Theorem: natp-of-match-string-at.new-index

(defthm natp-of-match-string-at.new-index
  (b* (((mv ?matchedp ?new-index)
        (match-string-at target x index)))
    (natp new-index))
  :rule-classes :type-prescription)

Theorem: new-index-less-than-length-of-match-string-at

(defthm new-index-less-than-length-of-match-string-at
  (b* (((mv ?matchedp ?new-index)
        (match-string-at target x index)))
    (implies (<= (nfix index)
                 (len (acl2::explode x)))
             (<= new-index (len (acl2::explode x)))))
  :rule-classes :linear)

Theorem: new-index-increasing-of-match-string-at

(defthm new-index-increasing-of-match-string-at
  (b* (((mv ?matchedp ?new-index)
        (match-string-at target x index)))
    (<= (nfix index) new-index))
  :rule-classes :linear)

Theorem: new-index-increasing-strong-of-match-string-at

(defthm new-index-increasing-strong-of-match-string-at
  (b* (((mv ?matchedp ?new-index)
        (match-string-at target x index)))
    (implies (and matchedp
                  (not (equal 0 (strlen target))))
             (< (nfix index) new-index)))
  :rule-classes :linear)

Theorem: no-change-of-match-string-at

(defthm no-change-of-match-string-at
  (b* (((mv ?matchedp ?new-index)
        (match-string-at target x index)))
    (implies (not matchedp)
             (equal new-index (lnfix index)))))

Theorem: measure-decr-of-match-string-at

(defthm measure-decr-of-match-string-at
  (b* (((mv ?matchedp ?new-index)
        (match-string-at target x index)))
    (<= (nfix (+ (len (acl2::explode x))
                 (- new-index)))
        (nfix (+ (- (nfix index))
                 (len (acl2::explode x))))))
  :rule-classes :linear)

Theorem: index-lte-len-when-match-string-at-nonempty

(defthm index-lte-len-when-match-string-at-nonempty
  (b* (((mv ?matchedp ?new-index)
        (match-string-at target x index)))
    (implies (and matchedp
                  (not (equal 0 (strlen target))))
             (<= (nfix index)
                 (len (acl2::explode x)))))
  :rule-classes :forward-chaining)

Theorem: new-index-less-than-length-of-match-string-at-when-matched-nonempty

(defthm
 new-index-less-than-length-of-match-string-at-when-matched-nonempty
 (b* (((mv ?matchedp ?new-index)
       (match-string-at target x index)))
   (implies (and matchedp
                 (not (equal 0 (strlen target))))
            (<= new-index (len (acl2::explode x)))))
 :rule-classes :linear)

Theorem: measure-decr-of-match-string-at-strong

(defthm measure-decr-of-match-string-at-strong
  (b* (((mv ?matchedp ?new-index)
        (match-string-at target x index)))
    (implies (and matchedp
                  (not (equal 0 (strlen target))))
             (< (nfix (+ (len (acl2::explode x))
                         (- new-index)))
                (nfix (+ (- (nfix index))
                         (len (acl2::explode x)))))))
  :rule-classes :linear)

Theorem: match-string-at-of-str-fix-target

(defthm match-string-at-of-str-fix-target
  (equal (match-string-at (acl2::str-fix target)
                          x index)
         (match-string-at target x index)))

Theorem: match-string-at-streqv-congruence-on-target

(defthm match-string-at-streqv-congruence-on-target
  (implies (acl2::streqv target target-equiv)
           (equal (match-string-at target x index)
                  (match-string-at target-equiv x index)))
  :rule-classes :congruence)

Theorem: match-string-at-of-str-fix-x

(defthm match-string-at-of-str-fix-x
  (equal (match-string-at target (acl2::str-fix x)
                          index)
         (match-string-at target x index)))

Theorem: match-string-at-streqv-congruence-on-x

(defthm match-string-at-streqv-congruence-on-x
  (implies (acl2::streqv x x-equiv)
           (equal (match-string-at target x index)
                  (match-string-at target x-equiv index)))
  :rule-classes :congruence)

Theorem: match-string-at-of-nfix-index

(defthm match-string-at-of-nfix-index
  (equal (match-string-at target x (nfix index))
         (match-string-at target x index)))

Theorem: match-string-at-nat-equiv-congruence-on-index

(defthm match-string-at-nat-equiv-congruence-on-index
  (implies (acl2::nat-equiv index index-equiv)
           (equal (match-string-at target x index)
                  (match-string-at target x index-equiv)))
  :rule-classes :congruence)