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Input-syntax-abstraction

Abs-input-title

Abstract an input-title to an input title.

Signature
(abs-input-title tree) → intitle
Arguments: tree — Guard (abnf::treep tree).
Returns: intitle — Type (input-title-option-resultp intitle).

Definitions and Theorems

Function: abs-input-title

(defun abs-input-title (tree)
  (declare (xargs :guard (abnf::treep tree)))
  (let ((__function__ 'abs-input-title))
    (declare (ignorable __function__))
    (b* (((okf (abnf::tree-list-tuple3 sub))
          (abnf::check-tree-nonleaf-3 tree "input-title"))
         ((okf tree)
          (abnf::check-tree-list-1 sub.1st))
         ((okf &)
          (abnf::check-tree-ichars tree "["))
         ((okf tree)
          (abnf::check-tree-list-1 sub.2nd))
         ((okf intitle)
          (abs-public/private/constants/constant/const/main/registers
               tree))
         ((okf tree)
          (abnf::check-tree-list-1 sub.3rd))
         ((okf &)
          (abnf::check-tree-ichars tree "]")))
      intitle)))

Theorem: input-title-option-resultp-of-abs-input-title

(defthm input-title-option-resultp-of-abs-input-title
  (b* ((intitle (abs-input-title tree)))
    (input-title-option-resultp intitle))
  :rule-classes :rewrite)

Theorem: abs-input-title-of-tree-fix-tree

(defthm abs-input-title-of-tree-fix-tree
  (equal (abs-input-title (abnf::tree-fix tree))
         (abs-input-title tree)))

Theorem: abs-input-title-tree-equiv-congruence-on-tree

(defthm abs-input-title-tree-equiv-congruence-on-tree
  (implies (abnf::tree-equiv tree tree-equiv)
           (equal (abs-input-title tree)
                  (abs-input-title tree-equiv)))
  :rule-classes :congruence)