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Primitive-functions

Eval-cdr

Evaluation semantics of cdr.

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

Definitions and Theorems

Function: eval-cdr

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

Theorem: valuep-of-eval-cdr

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

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

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

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

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