• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
    • Std/lists
    • Std/alists
    • Obags
    • Std/util
    • Std/strings
      • Pretty-printing
      • Printtree
      • Base64
      • Charset-p
      • Strtok!
      • Cases
      • Concatenation
      • Html-encoding
      • Character-kinds
      • Substrings
        • Istrpos
        • Strrpos
        • Strpos
        • Collect-syms-with-isubstr
        • Istrprefixp
        • Collect-strs-with-isubstr
        • Iprefixp
        • Strsuffixp
        • Firstn-chars
        • Strprefixp
        • Isubstrp
        • Substrp
      • Strtok
      • Equivalences
      • Url-encoding
      • Lines
      • Explode-implode-equalities
      • Ordering
      • Numbers
      • Pad-trim
      • Coercion
      • Std/strings/digit-to-char
      • Substitution
      • Symbols
    • Std/io
    • Std/osets
    • Std/basic
    • Std/system
    • Std/typed-lists
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Substrings

Firstn-chars

Efficient way to take leading characters from a string.

(firstn-chars n x) is logically equal to:

(take (min n (length x)) (explode x))

But it is implemented more efficiently, via char.

Definitions and Theorems

Function: firstn-chars-aux

(defun firstn-chars-aux (x n acc)
  (declare (xargs :guard (and (stringp x)
                              (natp n)
                              (< n (length x))))
           (type string x)
           (type (integer 0 *) n))
  (if (zp n)
      (cons (char x 0) acc)
    (firstn-chars-aux x (the (integer 0 *) (- n 1))
                      (cons (char x n) acc))))

Function: firstn-chars

(defun firstn-chars (n x)
  (declare (xargs :guard (and (stringp x) (natp n)))
           (type string x)
           (type (integer 0 *) n))
  (mbe :logic
       (take (min (nfix n) (len (explode x)))
             (explode x))
       :exec
       (let ((n (min n (length x))))
         (if (zp n)
             nil
           (firstn-chars-aux x (the (integer 0 *) (- n 1))
                             nil)))))

Theorem: firstn-chars-aux-removal

(defthm firstn-chars-aux-removal
  (implies (and (stringp x)
                (natp n)
                (< n (length x)))
           (equal (firstn-chars-aux x n acc)
                  (append (take (+ n 1) (coerce x 'list))
                          acc))))

Theorem: character-listp-of-firstn-chars

(defthm character-listp-of-firstn-chars
  (character-listp (firstn-chars n x)))

Theorem: streqv-implies-equal-firstn-chars-2

(defthm streqv-implies-equal-firstn-chars-2
  (implies (streqv x x-equiv)
           (equal (firstn-chars n x)
                  (firstn-chars n x-equiv)))
  :rule-classes (:congruence))

Theorem: istreqv-implies-icharlisteqv-firstn-chars-2

(defthm istreqv-implies-icharlisteqv-firstn-chars-2
  (implies (istreqv x x-equiv)
           (icharlisteqv (firstn-chars n x)
                         (firstn-chars n x-equiv)))
  :rule-classes (:congruence))