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• Semantics

Tree-match-char-val-p

Semantics of character value notations.

Signature

(tree-match-char-val-p tree char-val) → yes/no

Arguments

tree — Guard (treep tree).

char-val — Guard (char-val-p char-val).

Returns

yes/no — Type (booleanp yes/no).

A tree matches a character value notation iff the tree is a leaf consisting of a list of natural numbers that match the corresponding characters, case-sensitively or case-insensitively (depending on the kind of character value notation).

Definitions and Theorems

Function: tree-match-char-val-p

(defun tree-match-char-val-p (tree char-val)
 (declare (xargs :guard (and (treep tree)
                             (char-val-p char-val))))
 (and
  (tree-case tree :leafterm)
  (let ((nats (tree-leafterm->get tree)))
   (char-val-case
    char-val
    :sensitive
    (nats-match-sensitive-chars-p nats (explode char-val.get))
    :insensitive
    (nats-match-insensitive-chars-p nats (explode char-val.get))))))

Theorem: booleanp-of-tree-match-char-val-p

(defthm booleanp-of-tree-match-char-val-p
  (b* ((yes/no (tree-match-char-val-p tree char-val)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: tree-match-char-val-p-of-tree-fix-tree

(defthm tree-match-char-val-p-of-tree-fix-tree
  (equal (tree-match-char-val-p (tree-fix tree)
                                char-val)
         (tree-match-char-val-p tree char-val)))

Theorem: tree-match-char-val-p-tree-equiv-congruence-on-tree

(defthm tree-match-char-val-p-tree-equiv-congruence-on-tree
  (implies (tree-equiv tree tree-equiv)
           (equal (tree-match-char-val-p tree char-val)
                  (tree-match-char-val-p tree-equiv char-val)))
  :rule-classes :congruence)

Theorem: tree-match-char-val-p-of-char-val-fix-char-val

(defthm tree-match-char-val-p-of-char-val-fix-char-val
  (equal (tree-match-char-val-p tree (char-val-fix char-val))
         (tree-match-char-val-p tree char-val)))

Theorem: tree-match-char-val-p-char-val-equiv-congruence-on-char-val

(defthm tree-match-char-val-p-char-val-equiv-congruence-on-char-val
  (implies (char-val-equiv char-val char-val-equiv)
           (equal (tree-match-char-val-p tree char-val)
                  (tree-match-char-val-p tree char-val-equiv)))
  :rule-classes :congruence)