		Search-engine friendly clone of the ACL2 documentation.

Types

Type-real-floatingp

Check if a type is a real floating type [C17:6.2.5/10].

Signature
(type-real-floatingp type) → yes/no
Arguments: type — Guard (typep type).
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: type-real-floatingp

(defun type-real-floatingp (type)
  (declare (xargs :guard (typep type)))
  (and (member-eq (type-kind type)
                  '(:float :double :ldouble))
       t))

Theorem: booleanp-of-type-real-floatingp

(defthm booleanp-of-type-real-floatingp
  (b* ((yes/no (type-real-floatingp type)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: type-real-floatingp-when-type-kind-syntaxp

(defthm type-real-floatingp-when-type-kind-syntaxp
 (implies (and (equal (type-kind type) kind)
               (syntaxp (quotep kind)))
          (equal (type-real-floatingp type)
                 (and (member-equal kind '(:float :double :ldouble))
                      t))))

Theorem: type-real-floatingp-of-type-fix-type

(defthm type-real-floatingp-of-type-fix-type
  (equal (type-real-floatingp (type-fix type))
         (type-real-floatingp type)))

Theorem: type-real-floatingp-type-equiv-congruence-on-type

(defthm type-real-floatingp-type-equiv-congruence-on-type
  (implies (type-equiv type type-equiv)
           (equal (type-real-floatingp type)
                  (type-real-floatingp type-equiv)))
  :rule-classes :congruence)