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Primitive-functions

Eval-complex

Evaluation semantics of complex.

Signature
(eval-complex x y) → result
Arguments: x — Guard (valuep x).; y — Guard (valuep y).
Returns: result — Type (valuep result).

Definitions and Theorems

Function: eval-complex

(defun eval-complex (x y)
  (declare (xargs :guard (and (valuep x) (valuep y))))
  (let ((__function__ 'eval-complex))
    (declare (ignorable __function__))
    (b* ((x-rational (if (value-case-rational x)
                         (value-rational->get x)
                       0))
         (y-rational (if (value-case-rational y)
                         (value-rational->get y)
                       0)))
      (value-number (complex x-rational y-rational)))))

Theorem: valuep-of-eval-complex

(defthm valuep-of-eval-complex
  (b* ((result (eval-complex x y)))
    (valuep result))
  :rule-classes :rewrite)

Theorem: eval-complex-of-value-fix-x

(defthm eval-complex-of-value-fix-x
  (equal (eval-complex (value-fix x) y)
         (eval-complex x y)))

Theorem: eval-complex-value-equiv-congruence-on-x

(defthm eval-complex-value-equiv-congruence-on-x
  (implies (value-equiv x x-equiv)
           (equal (eval-complex x y)
                  (eval-complex x-equiv y)))
  :rule-classes :congruence)

Theorem: eval-complex-of-value-fix-y

(defthm eval-complex-of-value-fix-y
  (equal (eval-complex x (value-fix y))
         (eval-complex x y)))

Theorem: eval-complex-value-equiv-congruence-on-y

(defthm eval-complex-value-equiv-congruence-on-y
  (implies (value-equiv y y-equiv)
           (equal (eval-complex x y)
                  (eval-complex x y-equiv)))
  :rule-classes :congruence)