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Primitive-functions

Eval-car

Evaluation semantics of car.

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

Definitions and Theorems

Function: eval-car

(defun eval-car (x)
  (declare (xargs :guard (valuep x)))
  (let ((__function__ 'eval-car))
    (declare (ignorable __function__))
    (cond ((value-case x :cons)
           (value-cons->car x))
          (t (value-nil)))))

Theorem: valuep-of-eval-car

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

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

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

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

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