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Operations

Eq-values

Apply == to values [C:6.5.9/2] [C:6.5.9/3] [C:6.5.9/4].

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

For now we only support arithmetic types.

Definitions and Theorems

Function: eq-values

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

Theorem: value-resultp-of-eq-values

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

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

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

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

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

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

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

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

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