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Implementation-environments

Sint-rangep

Check if a mathematical integer is in the range of (i.e. representable in) type signed int.

Signature
(sint-rangep val ienv) → yes/no
Arguments: val — Guard (integerp val).; ienv — Guard (ienvp ienv).
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: sint-rangep

(defun sint-rangep (val ienv)
  (declare (xargs :guard (and (integerp val) (ienvp ienv))))
  (let ((__function__ 'sint-rangep))
    (declare (ignorable __function__))
    (and (<= (sint-min ienv) (ifix val))
         (<= (ifix val) (sint-max ienv)))))

Theorem: booleanp-of-sint-rangep

(defthm booleanp-of-sint-rangep
  (b* ((yes/no (sint-rangep val ienv)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: sint-rangep-of-ifix-val

(defthm sint-rangep-of-ifix-val
  (equal (sint-rangep (ifix val) ienv)
         (sint-rangep val ienv)))

Theorem: sint-rangep-int-equiv-congruence-on-val

(defthm sint-rangep-int-equiv-congruence-on-val
  (implies (acl2::int-equiv val val-equiv)
           (equal (sint-rangep val ienv)
                  (sint-rangep val-equiv ienv)))
  :rule-classes :congruence)

Theorem: sint-rangep-of-ienv-fix-ienv

(defthm sint-rangep-of-ienv-fix-ienv
  (equal (sint-rangep val (ienv-fix ienv))
         (sint-rangep val ienv)))

Theorem: sint-rangep-ienv-equiv-congruence-on-ienv

(defthm sint-rangep-ienv-equiv-congruence-on-ienv
  (implies (ienv-equiv ienv ienv-equiv)
           (equal (sint-rangep val ienv)
                  (sint-rangep val ienv-equiv)))
  :rule-classes :congruence)