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Path

Path-count

Measure for recurring over path structures.

Signature
(path-count x) → count
Arguments: x — Guard (path-p x).
Returns: count — Type (natp count).

Definitions and Theorems

Function: path-count

(defun path-count (x)
  (declare (xargs :guard (path-p x)))
  (let ((__function__ 'path-count))
    (declare (ignorable __function__))
    (case (path-kind x)
      (:wire 1)
      (:scope (+ 3
                 (path-count (path-scope->subpath x)))))))

Theorem: natp-of-path-count

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

Theorem: path-count-of-path-fix-x

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

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

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

Theorem: path-count-of-path-scope

(defthm path-count-of-path-scope
  (implies t
           (< (+ (path-count subpath))
              (path-count (path-scope subpath namespace))))
  :rule-classes :linear)

Theorem: path-count-of-path-scope->subpath

(defthm path-count-of-path-scope->subpath
  (implies (equal (path-kind x) :scope)
           (< (path-count (path-scope->subpath x))
              (path-count x)))
  :rule-classes :linear)