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Syntax-abstraction

Abs-lowercase-letter

Abstract a lowercase-letter to an ACL2 character.

Signature
(abs-lowercase-letter tree) → char
Arguments: tree — Guard (abnf::treep tree).
Returns: char — Type (character-resultp char).

Definitions and Theorems

Function: abs-lowercase-letter

(defun abs-lowercase-letter (tree)
 (declare (xargs :guard (abnf::treep tree)))
 (let ((__function__ 'abs-lowercase-letter))
  (declare (ignorable __function__))
  (b*
   (((okf nat)
     (check-tree-nonleaf-num-range tree "lowercase-letter" 97 122)))
   (code-char nat))))

Theorem: character-resultp-of-abs-lowercase-letter

(defthm character-resultp-of-abs-lowercase-letter
  (b* ((char (abs-lowercase-letter tree)))
    (character-resultp char))
  :rule-classes :rewrite)

Theorem: lcletter-char-p-of-abs-lowercase-letter

(defthm lcletter-char-p-of-abs-lowercase-letter
  (b* ((common-lisp::?char (abs-lowercase-letter tree)))
    (implies (not (reserrp char))
             (str::lcletter-char-p char))))

Theorem: abs-lowercase-letter-of-tree-fix-tree

(defthm abs-lowercase-letter-of-tree-fix-tree
  (equal (abs-lowercase-letter (abnf::tree-fix tree))
         (abs-lowercase-letter tree)))

Theorem: abs-lowercase-letter-tree-equiv-congruence-on-tree

(defthm abs-lowercase-letter-tree-equiv-congruence-on-tree
  (implies (abnf::tree-equiv tree tree-equiv)
           (equal (abs-lowercase-letter tree)
                  (abs-lowercase-letter tree-equiv)))
  :rule-classes :congruence)