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Types

Type-floatingp

Check if a type is a floating type [C17:6.2.5/11].

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

Definitions and Theorems

Function: type-floatingp

(defun type-floatingp (type)
  (declare (xargs :guard (typep type)))
  (or (type-real-floatingp type)
      (type-complexp type)))

Theorem: booleanp-of-type-floatingp

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

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

(defthm type-floatingp-when-type-kind-syntaxp
  (implies (and (equal (type-kind type) kind)
                (syntaxp (quotep kind)))
           (equal (type-floatingp type)
                  (or (type-real-floatingp type)
                      (type-complexp type)))))

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

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

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

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