• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
    • Theories
    • Rule-classes
    • Proof-builder
    • Recursion-and-induction
    • Hons-and-memoization
    • Events
    • Parallelism
    • History
    • Programming
      • Defun
      • Declare
      • System-utilities
      • Stobj
      • State
      • Mutual-recursion
      • Memoize
      • Mbe
      • Io
      • Defpkg
      • Apply$
      • Loop$
      • Programming-with-state
      • Arrays
      • Characters
      • Time$
      • Defmacro
      • Loop$-primer
      • Fast-alists
      • Defconst
      • Evaluation
      • Guard
      • Equality-variants
      • Compilation
      • Hons
      • ACL2-built-ins
      • Developers-guide
      • System-attachments
      • Advanced-features
      • Set-check-invariant-risk
      • Numbers
      • Efficiency
      • Irrelevant-formals
      • Introduction-to-programming-in-ACL2-for-those-who-know-lisp
      • Redefining-programs
      • Lists
      • Invariant-risk
      • Errors
      • Defabbrev
      • Conses
      • Alists
      • Set-register-invariant-risk
      • Strings
        • Std/strings
          • Pretty-printing
          • Printtree
          • Base64
          • Charset-p
            • Defcharset
            • Count-leading-charset
            • Str-count-leading-charset-fast
            • Str-count-leading-charset
            • Chars-in-charset-p
            • Code-in-charset-p
            • Char-in-charset-p
          • Strtok!
          • Cases
          • Concatenation
          • Html-encoding
          • Character-kinds
          • Substrings
          • Strtok
          • Equivalences
          • Url-encoding
          • Lines
          • Explode-implode-equalities
          • Ordering
          • Numbers
          • Pad-trim
          • Coercion
          • Std/strings/digit-to-char
          • Substitution
          • Symbols
        • String-listp
        • Stringp
        • Length
        • Search
        • Remove-duplicates
        • Position
        • Coerce
        • Concatenate
        • Reverse
        • String
        • Subseq
        • Substitute
        • String-upcase
        • String-downcase
        • Count
        • Char
        • String<
        • String-equal
        • String-utilities
        • String-append
        • String>=
        • String<=
        • String>
        • Hex-digit-char-theorems
        • String-downcase-gen
        • String-upcase-gen
      • Program-wrapper
      • Get-internal-time
      • Basics
      • Packages
      • Oracle-eval
      • Defmacro-untouchable
      • <<
      • Primitive
      • Revert-world
      • Unmemoize
      • Set-duplicate-keys-action
      • Symbols
      • Def-list-constructor
      • Easy-simplify-term
      • Defiteration
      • Fake-oracle-eval
      • Defopen
      • Sleep
    • Operational-semantics
    • Real
    • Start-here
    • Debugging
    • Miscellaneous
    • Output-controls
    • Macros
    • Interfacing-tools
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Charset-p

Count-leading-charset

Count how many characters at the start of a list are members of a particular character set.

Signature

(count-leading-charset x set) → num

Arguments

x — Guard (character-listp x).

set — Guard (charset-p set).

Returns

num — Type (natp num).

Definitions and Theorems

Function: count-leading-charset

(defun count-leading-charset (x set)
  (declare (xargs :guard (and (character-listp x)
                              (charset-p set))))
  (let ((acl2::__function__ 'count-leading-charset))
    (declare (ignorable acl2::__function__))
    (cond ((atom x) 0)
          ((char-in-charset-p (car x) set)
           (+ 1 (count-leading-charset (cdr x) set)))
          (t 0))))

Theorem: natp-of-count-leading-charset

(defthm natp-of-count-leading-charset
  (b* ((num (count-leading-charset x set)))
    (natp num))
  :rule-classes :type-prescription)

Theorem: upper-bound-of-count-leading-charset

(defthm upper-bound-of-count-leading-charset
  (<= (count-leading-charset x set)
      (len x))
  :rule-classes ((:rewrite) (:linear)))

Theorem: count-leading-charset-len

(defthm count-leading-charset-len
  (equal (equal (len x)
                (count-leading-charset x set))
         (chars-in-charset-p x set))
  :rule-classes
  ((:rewrite)
   (:rewrite :corollary (equal (< (count-leading-charset x set)
                                  (len x))
                               (not (chars-in-charset-p x set))))
   (:linear :corollary (implies (not (chars-in-charset-p x set))
                                (< (count-leading-charset x set)
                                   (len x))))))

Theorem: count-leading-charset-zero

(defthm count-leading-charset-zero
  (equal (equal 0 (count-leading-charset x set))
         (not (char-in-charset-p (car x) set)))
  :rule-classes
  ((:rewrite)
   (:rewrite :corollary (equal (< 0 (count-leading-charset x set))
                               (char-in-charset-p (car x) set)))
   (:linear
        :corollary (implies (char-in-charset-p (car x) set)
                            (< 0 (count-leading-charset x set))))))

Theorem: count-leading-charset-sound

(defthm count-leading-charset-sound
  (let ((n (count-leading-charset x set)))
    (chars-in-charset-p (take n x) set)))

Theorem: count-leading-charset-complete

(defthm count-leading-charset-complete
  (b* ((n (count-leading-charset x set))
       (next-char (nth n x)))
    (not (char-in-charset-p next-char set))))