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Representation-of-integer-conversions

Sint-from-uint-okp

Check if a conversion from type unsigned int to type signed int is well-defined.

Signature
(sint-from-uint-okp x) → yes/no
Arguments: x — Guard (uintp x).
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: sint-from-uint-okp

(defun sint-from-uint-okp (x)
  (declare (xargs :guard (uintp x)))
  (let ((__function__ 'sint-from-uint-okp))
    (declare (ignorable __function__))
    (sint-integerp (integer-from-uint x))))

Theorem: booleanp-of-sint-from-uint-okp

(defthm booleanp-of-sint-from-uint-okp
  (b* ((yes/no (sint-from-uint-okp x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: sint-from-uint-okp-of-uint-fix-x

(defthm sint-from-uint-okp-of-uint-fix-x
  (equal (sint-from-uint-okp (uint-fix x))
         (sint-from-uint-okp x)))

Theorem: sint-from-uint-okp-uint-equiv-congruence-on-x

(defthm sint-from-uint-okp-uint-equiv-congruence-on-x
  (implies (uint-equiv x x-equiv)
           (equal (sint-from-uint-okp x)
                  (sint-from-uint-okp x-equiv)))
  :rule-classes :congruence)