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• Obj-adeclor

Obj-adeclor-count

Measure for recurring over obj-adeclor structures.

Signature

(obj-adeclor-count x) → count

Arguments

x — Guard (obj-adeclorp x).

Returns

count — Type (natp count).

Definitions and Theorems

Function: obj-adeclor-count

(defun obj-adeclor-count (x)
 (declare (xargs :guard (obj-adeclorp x)))
 (let ((__function__ 'obj-adeclor-count))
  (declare (ignorable __function__))
  (case (obj-adeclor-kind x)
    (:none 1)
    (:pointer (+ 2
                 (obj-adeclor-count (obj-adeclor-pointer->decl x))))
    (:array (+ 3
               (obj-adeclor-count (obj-adeclor-array->decl x)))))))

Theorem: natp-of-obj-adeclor-count

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

Theorem: obj-adeclor-count-of-obj-adeclor-fix-x

(defthm obj-adeclor-count-of-obj-adeclor-fix-x
  (equal (obj-adeclor-count (obj-adeclor-fix x))
         (obj-adeclor-count x)))

Theorem: obj-adeclor-count-obj-adeclor-equiv-congruence-on-x

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

Theorem: obj-adeclor-count-of-obj-adeclor-pointer

(defthm obj-adeclor-count-of-obj-adeclor-pointer
  (implies t
           (< (+ (obj-adeclor-count decl))
              (obj-adeclor-count (obj-adeclor-pointer decl))))
  :rule-classes :linear)

Theorem: obj-adeclor-count-of-obj-adeclor-pointer->decl

(defthm obj-adeclor-count-of-obj-adeclor-pointer->decl
  (implies (equal (obj-adeclor-kind x) :pointer)
           (< (obj-adeclor-count (obj-adeclor-pointer->decl x))
              (obj-adeclor-count x)))
  :rule-classes :linear)

Theorem: obj-adeclor-count-of-obj-adeclor-array

(defthm obj-adeclor-count-of-obj-adeclor-array
  (implies t
           (< (+ (obj-adeclor-count decl))
              (obj-adeclor-count (obj-adeclor-array decl size))))
  :rule-classes :linear)

Theorem: obj-adeclor-count-of-obj-adeclor-array->decl

(defthm obj-adeclor-count-of-obj-adeclor-array->decl
  (implies (equal (obj-adeclor-kind x) :array)
           (< (obj-adeclor-count (obj-adeclor-array->decl x))
              (obj-adeclor-count x)))
  :rule-classes :linear)