• Top
    • Documentation
    • Books
    • Boolean-reasoning
    • Projects
    • Debugging
    • Std
    • Community
    • Proof-automation
    • Macro-libraries
    • ACL2
    • Interfacing-tools
    • Hardware-verification
    • Software-verification
      • Kestrel-books
        • Crypto-hdwallet
        • Apt
        • Error-checking
        • Fty-extensions
        • Isar
        • Kestrel-utilities
          • Omaps
          • Directed-untranslate
          • Include-book-paths
          • Ubi
          • Numbered-names
          • Digits-any-base
          • Context-message-pair
          • With-auto-termination
          • Make-termination-theorem
          • Theorems-about-true-list-lists
          • Checkpoint-list
          • Sublis-expr+
          • Integers-from-to
          • Prove$
          • Defthm<w
          • System-utilities-non-built-in
          • Integer-range-fix
          • Minimize-ruler-extenders
          • Add-const-to-untranslate-preprocess
          • Unsigned-byte-fix
          • Signed-byte-fix
          • Defthmr
          • Paired-names
          • Unsigned-byte-list-fix
          • Signed-byte-list-fix
          • Show-books
          • Skip-in-book
          • Typed-tuplep
          • List-utilities
          • Checkpoint-list-pretty
          • Defunt
          • Keyword-value-list-to-alist
          • Magic-macroexpand
          • Top-command-number-fn
          • Bits-as-digits-in-base-2
          • Show-checkpoint-list
          • Ubyte11s-as-digits-in-base-2048
          • Named-formulas
          • Bytes-as-digits-in-base-256
          • String-utilities
            • Code-char-injectivity-theorem
            • 8bitbytes-hexchars-conversions
            • Code-char-inverses-theorems
            • String-kinds
            • String-codelist-conversions
              • String=>nats
                • Nats<=>string-inverses-theorems
              • Nats=>string
            • Charlist-codelist-conversions
            • 8bitbytes-hexstrings-conversions
          • Make-keyword-value-list-from-keys-and-value
          • Defmacroq
          • Integer-range-listp
          • Apply-fn-if-known
          • Trans-eval-error-triple
          • Checkpoint-info-list
          • Previous-subsumer-hints
          • Fms!-lst
          • Zp-listp
          • Trans-eval-state
          • Injections
          • Doublets-to-alist
          • Theorems-about-osets
          • Typed-list-utilities
          • Book-runes-alist
          • User-interface
          • Bits/ubyte11s-digit-grouping
          • Bits/bytes-digit-grouping
          • Message-utilities
          • Subsetp-eq-linear
          • Oset-utilities
          • Strict-merge-sort-<
          • Miscellaneous-enumerations
          • Maybe-unquote
          • Thm<w
          • Defthmd<w
          • Io-utilities
        • Set
        • Soft
        • C
        • Bv
        • Imp-language
        • Event-macros
        • Java
        • Bitcoin
        • Ethereum
        • Yul
        • Zcash
        • ACL2-programming-language
        • Prime-fields
        • Json
        • Syntheto
        • File-io-light
        • Cryptography
        • Number-theory
        • Lists-light
        • Axe
        • Builtins
        • Solidity
        • Helpers
        • Htclient
        • Typed-lists-light
        • Arithmetic-light
      • X86isa
      • Axe
      • Execloader
    • Math
    • Testing-utilities
  • String-codelist-conversions

String=>nats

Convert a string to the corresponding true list of natural numbers below 256.

Signature
(string=>nats string) → nats
Arguments
string — Guard (stringp string).
Returns
nats — Type (unsigned-byte-listp 8 nats).

Definitions and Theorems

Function: string=>nats

(defun string=>nats (string)
  (declare (xargs :guard (stringp string)))
  (let ((__function__ 'string=>nats))
    (declare (ignorable __function__))
    (chars=>nats (explode string))))

Theorem: return-type-of-string=>nats

(defthm return-type-of-string=>nats
  (b* ((nats (string=>nats string)))
    (unsigned-byte-listp 8 nats))
  :rule-classes :rewrite)

Theorem: nat-listp-of-string=>nats

(defthm nat-listp-of-string=>nats
  (b* ((nats (string=>nats string)))
    (nat-listp nats))
  :rule-classes :rewrite)

Theorem: len-of-string=>nats

(defthm len-of-string=>nats
  (implies (stringp string)
           (equal (len (string=>nats string))
                  (length string))))

Theorem: nth-of-string=>nats

(defthm nth-of-string=>nats
  (equal (nth n (string=>nats string))
         (if (< (nfix n) (len (explode string)))
             (char-code (char string n))
           nil)))

Theorem: consp-of-string=>nats

(defthm consp-of-string=>nats
  (iff (consp (string=>nats string))
       (consp (explode string))))

Theorem: string=>nats-of-implode

(defthm string=>nats-of-implode
  (implies (character-listp chars)
           (equal (string=>nats (implode chars))
                  (chars=>nats chars))))

Theorem: string=>nats-of-str-fix-string

(defthm string=>nats-of-str-fix-string
  (equal (string=>nats (str-fix string))
         (string=>nats string)))

Theorem: string=>nats-streqv-congruence-on-string

(defthm string=>nats-streqv-congruence-on-string
  (implies (streqv string string-equiv)
           (equal (string=>nats string)
                  (string=>nats string-equiv)))
  :rule-classes :congruence)

Subtopics

Nats<=>string-inverses-theorems
nats=>string and string=>nats are mutual inverses.