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Primitive-functions

Eval-coerce

Evaluation semantics of coerce.

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

Definitions and Theorems

Theorem: verify-guards-lemma

(defthm verify-guards-lemma
  (implies (character-listp x)
           (good-valuep x)))

Function: eval-coerce

(defun eval-coerce (x y)
 (declare (xargs :guard (and (valuep x) (valuep y))))
 (let ((__function__ 'eval-coerce))
  (declare (ignorable __function__))
  (cond
      ((value-equiv y (value-symbol (lift-symbol 'list)))
       (if (value-case x :string)
           (lift-value (coerce (value-string->get x) 'list))
         (value-nil)))
      (t (value-string (coerce (make-character-list (lower-value x))
                               'string))))))

Theorem: valuep-of-eval-coerce

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

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

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

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

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

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

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

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

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