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Operations

Add-values

Apply binary + to values [C:6.5.5/2] [C:6.5.5/5].

Signature
(add-values val1 val2) → resval
Arguments: val1 — Guard (valuep val1).; val2 — Guard (valuep val2).
Returns: resval — Type (value-resultp resval).

We only support arithmetic values for now (no pointer arithmetic).

Definitions and Theorems

Function: add-values

(defun add-values (val1 val2)
  (declare (xargs :guard (and (valuep val1) (valuep val2))))
  (let ((__function__ 'add-values))
    (declare (ignorable __function__))
    (if (and (value-arithmeticp val1)
             (value-arithmeticp val2))
        (add-arithmetic-values val1 val2)
      (error (list :add-mistype :required :arithmetic
                   :arithmetic :supplied (value-fix val1)
                   (value-fix val2))))))

Theorem: value-resultp-of-add-values

(defthm value-resultp-of-add-values
  (b* ((resval (add-values val1 val2)))
    (value-resultp resval))
  :rule-classes :rewrite)

Theorem: add-values-of-value-fix-val1

(defthm add-values-of-value-fix-val1
  (equal (add-values (value-fix val1) val2)
         (add-values val1 val2)))

Theorem: add-values-value-equiv-congruence-on-val1

(defthm add-values-value-equiv-congruence-on-val1
  (implies (value-equiv val1 val1-equiv)
           (equal (add-values val1 val2)
                  (add-values val1-equiv val2)))
  :rule-classes :congruence)

Theorem: add-values-of-value-fix-val2

(defthm add-values-of-value-fix-val2
  (equal (add-values val1 (value-fix val2))
         (add-values val1 val2)))

Theorem: add-values-value-equiv-congruence-on-val2

(defthm add-values-value-equiv-congruence-on-val2
  (implies (value-equiv val2 val2-equiv)
           (equal (add-values val1 val2)
                  (add-values val1 val2-equiv)))
  :rule-classes :congruence)