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Lexer

Lex-repetition-4-hex-digits

Lex exactly 4 hexadecimal digits.

Signature
(lex-repetition-4-hex-digits input) → (mv trees rest-input)
Arguments: input — Guard (nat-listp input).
Returns: trees — Type (abnf::tree-list-resultp trees).; rest-input — Type (nat-listp rest-input).

This is used to lex a 16-bit number expressed in hex.

Definitions and Theorems

Function: lex-repetition-4-hex-digits

(defun lex-repetition-4-hex-digits (input)
  (declare (xargs :guard (nat-listp input)))
  (let ((__function__ 'lex-repetition-4-hex-digits))
    (declare (ignorable __function__))
    (b* (((mv tree-digit1 input-after-digit1)
          (lex-hex-digit input))
         ((when (reserrp tree-digit1))
          (mv tree-digit1 (acl2::nat-list-fix input)))
         ((mv tree-digit2 input-after-digit2)
          (lex-hex-digit input-after-digit1))
         ((when (reserrp tree-digit2))
          (mv tree-digit2 (acl2::nat-list-fix input)))
         ((mv tree-digit3 input-after-digit3)
          (lex-hex-digit input-after-digit2))
         ((when (reserrp tree-digit3))
          (mv tree-digit3 (acl2::nat-list-fix input)))
         ((mv tree-digit4 input-after-digit4)
          (lex-hex-digit input-after-digit3))
         ((when (reserrp tree-digit4))
          (mv tree-digit4
              (acl2::nat-list-fix input))))
      (mv (list tree-digit1
                tree-digit2 tree-digit3 tree-digit4)
          input-after-digit4))))

Theorem: tree-list-resultp-of-lex-repetition-4-hex-digits.trees

(defthm tree-list-resultp-of-lex-repetition-4-hex-digits.trees
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-4-hex-digits input)))
    (abnf::tree-list-resultp trees))
  :rule-classes :rewrite)

Theorem: nat-listp-of-lex-repetition-4-hex-digits.rest-input

(defthm nat-listp-of-lex-repetition-4-hex-digits.rest-input
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-4-hex-digits input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-lex-repetition-4-hex-digits-<

(defthm len-of-lex-repetition-4-hex-digits-<
  (b* (((mv ?trees ?rest-input)
        (lex-repetition-4-hex-digits input)))
    (implies (not (reserrp trees))
             (< (len rest-input) (len input))))
  :rule-classes :linear)

Theorem: lex-repetition-4-hex-digits-of-nat-list-fix-input

(defthm lex-repetition-4-hex-digits-of-nat-list-fix-input
  (equal (lex-repetition-4-hex-digits (acl2::nat-list-fix input))
         (lex-repetition-4-hex-digits input)))

Theorem: lex-repetition-4-hex-digits-nat-list-equiv-congruence-on-input

(defthm
     lex-repetition-4-hex-digits-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv input input-equiv)
           (equal (lex-repetition-4-hex-digits input)
                  (lex-repetition-4-hex-digits input-equiv)))
  :rule-classes :congruence)