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Value-cons

Value-cons->car

Get the car field from a value-cons.

Signature
(value-cons->car x) → car
Arguments: x — Guard (valuep x).
Returns: car — Type (valuep car).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: value-cons->car$inline

(defun value-cons->car$inline (x)
  (declare (xargs :guard (valuep x)))
  (declare (xargs :guard (equal (value-kind x) :cons)))
  (let ((__function__ 'value-cons->car))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (value-kind x) :cons) x)))
           (value-fix (std::da-nth 0 (cdr x))))
         :exec (std::da-nth 0 (cdr x)))))

Theorem: valuep-of-value-cons->car

(defthm valuep-of-value-cons->car
  (b* ((car (value-cons->car$inline x)))
    (valuep car))
  :rule-classes :rewrite)

Theorem: value-cons->car$inline-of-value-fix-x

(defthm value-cons->car$inline-of-value-fix-x
  (equal (value-cons->car$inline (value-fix x))
         (value-cons->car$inline x)))

Theorem: value-cons->car$inline-value-equiv-congruence-on-x

(defthm value-cons->car$inline-value-equiv-congruence-on-x
  (implies (value-equiv x x-equiv)
           (equal (value-cons->car$inline x)
                  (value-cons->car$inline x-equiv)))
  :rule-classes :congruence)

Theorem: value-cons->car-when-wrong-kind

(defthm value-cons->car-when-wrong-kind
  (implies (not (equal (value-kind x) :cons))
           (equal (value-cons->car x)
                  (value-fix nil))))