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Syntax-abstraction

Abs-lowercaseletter/decimaldigit

Abstract a ( lowercase-letter / decimal-digit ) to an ACL2 character.

Signature
(abs-lowercaseletter/decimaldigit tree) → char
Arguments: tree — Guard (abnf::treep tree).
Returns: char — Type (character-resultp char).

Definitions and Theorems

Function: abs-lowercaseletter/decimaldigit

(defun abs-lowercaseletter/decimaldigit (tree)
 (declare (xargs :guard (abnf::treep tree)))
 (let ((__function__ 'abs-lowercaseletter/decimaldigit))
   (declare (ignorable __function__))
   (b* (((okf tree)
         (abnf::check-tree-nonleaf-1-1 tree nil))
        (char (abs-lowercase-letter tree))
        ((when (not (reserrp char))) char)
        (char (abs-decimal-digit-to-char tree))
        ((when (not (reserrp char))) char))
     (reserrf
          (list :found-subtree (abnf::tree-info-for-error tree))))))

Theorem: character-resultp-of-abs-lowercaseletter/decimaldigit

(defthm character-resultp-of-abs-lowercaseletter/decimaldigit
  (b* ((char (abs-lowercaseletter/decimaldigit tree)))
    (character-resultp char))
  :rule-classes :rewrite)

Theorem: loletter/digit-char-p-of-abs-lowercaseletter/decimaldigit

(defthm loletter/digit-char-p-of-abs-lowercaseletter/decimaldigit
  (b* ((?char (abs-lowercaseletter/decimaldigit tree)))
    (implies (not (reserrp char))
             (str::lcletter/digit-char-p char))))

Theorem: abs-lowercaseletter/decimaldigit-of-tree-fix-tree

(defthm abs-lowercaseletter/decimaldigit-of-tree-fix-tree
  (equal (abs-lowercaseletter/decimaldigit (abnf::tree-fix tree))
         (abs-lowercaseletter/decimaldigit tree)))

Theorem: abs-lowercaseletter/decimaldigit-tree-equiv-congruence-on-tree

(defthm
     abs-lowercaseletter/decimaldigit-tree-equiv-congruence-on-tree
  (implies (abnf::tree-equiv tree tree-equiv)
           (equal (abs-lowercaseletter/decimaldigit tree)
                  (abs-lowercaseletter/decimaldigit tree-equiv)))
  :rule-classes :congruence)