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• Vttree

Vttree-count

Measure for recurring over vttree structures.

Signature

(vttree-count x) → count

Arguments

x — Guard (vttree-p x).

Returns

count — Type (natp count).

Definitions and Theorems

Function: vttree-count

(defun vttree-count (x)
  (declare (xargs :guard (vttree-p x)))
  (let ((__function__ 'vttree-count))
    (declare (ignorable __function__))
    (common-lisp::case (vttree-kind x)
      (:none 1)
      (:warnings 1)
      (:constraints 1)
      (:context (+ 3
                   (vttree-count (vttree-context->subtree x))))
      (:branch (+ 3 (vttree-count (vttree-branch->left x))
                  (vttree-count (vttree-branch->right x)))))))

Theorem: natp-of-vttree-count

(defthm natp-of-vttree-count
  (b* ((count (vttree-count x)))
    (natp count))
  :rule-classes :type-prescription)

Theorem: vttree-count-of-vttree-fix-x

(defthm vttree-count-of-vttree-fix-x
  (equal (vttree-count (vttree-fix x))
         (vttree-count x)))

Theorem: vttree-count-vttree-equiv-congruence-on-x

(defthm vttree-count-vttree-equiv-congruence-on-x
  (implies (vttree-equiv x x-equiv)
           (equal (vttree-count x)
                  (vttree-count x-equiv)))
  :rule-classes :congruence)

Theorem: vttree-count-of-vttree-context

(defthm vttree-count-of-vttree-context
  (implies t
           (< (+ (vttree-count subtree))
              (vttree-count (vttree-context ctx subtree))))
  :rule-classes :linear)

Theorem: vttree-count-of-vttree-context->subtree

(defthm vttree-count-of-vttree-context->subtree
  (implies (equal (vttree-kind x) :context)
           (< (vttree-count (vttree-context->subtree x))
              (vttree-count x)))
  :rule-classes :linear)

Theorem: vttree-count-of-vttree-branch

(defthm vttree-count-of-vttree-branch
  (implies t
           (< (+ (vttree-count left)
                 (vttree-count right))
              (vttree-count (vttree-branch left right))))
  :rule-classes :linear)

Theorem: vttree-count-of-vttree-branch->left

(defthm vttree-count-of-vttree-branch->left
  (implies (equal (vttree-kind x) :branch)
           (< (vttree-count (vttree-branch->left x))
              (vttree-count x)))
  :rule-classes :linear)

Theorem: vttree-count-of-vttree-branch->right

(defthm vttree-count-of-vttree-branch->right
  (implies (equal (vttree-kind x) :branch)
           (< (vttree-count (vttree-branch->right x))
              (vttree-count x)))
  :rule-classes :linear)