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Primitive-functions

Eval-if

Evaluation semantics of if.

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

The function if is non-strict in the evaluation semantics. So we may not need this eval-if function. Nonetheless, we have it return the prescribed value, given the argument values.

Definitions and Theorems

Function: eval-if

(defun eval-if (x y z)
  (declare (xargs :guard (and (valuep x) (valuep y) (valuep z))))
  (let ((__function__ 'eval-if))
    (declare (ignorable __function__))
    (if (value-equiv x (value-nil))
        (value-fix z)
      (value-fix y))))

Theorem: valuep-of-eval-if

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

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

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

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

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

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

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

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

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

Theorem: eval-if-of-value-fix-z

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

Theorem: eval-if-value-equiv-congruence-on-z

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