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Primitive-functions

Eval-equal

Evaluation semantics of equal.

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

Definitions and Theorems

Function: eval-equal

(defun eval-equal (x y)
  (declare (xargs :guard (and (valuep x) (valuep y))))
  (let ((__function__ 'eval-equal))
    (declare (ignorable __function__))
    (lift-value (value-equiv x y))))

Theorem: valuep-of-eval-equal

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

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

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

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

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

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

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

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

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