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Primitive-functions

Eval-numerator

Evaluation semantics of numerator.

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

Definitions and Theorems

Function: eval-numerator

(defun eval-numerator (x)
  (declare (xargs :guard (valuep x)))
  (let ((__function__ 'eval-numerator))
    (declare (ignorable __function__))
    (value-number (if (value-case-rational x)
                      (value-rational->get x)
                    0))))

Theorem: valuep-of-eval-numerator

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

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

(defthm eval-numerator-of-value-fix-x
  (equal (eval-numerator (value-fix x))
         (eval-numerator x)))

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

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