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Types

Type-promoted-arithmeticp

Check if a type is a promoted arithmetic type.

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

That is, an arithmetic type that is promoted, in the sense that applying integer promotions [C:6.3.1.1/2] to it would leave the type unchanged. This means that the type is not a (signed, unsigned, or plain) char type or a (signed or unsigned) short type.

Definitions and Theorems

Function: type-promoted-arithmeticp

(defun type-promoted-arithmeticp (type)
  (declare (xargs :guard (typep type)))
  (let ((__function__ 'type-promoted-arithmeticp))
    (declare (ignorable __function__))
    (and (type-arithmeticp type)
         (not (type-case type :char))
         (not (type-case type :schar))
         (not (type-case type :uchar))
         (not (type-case type :sshort))
         (not (type-case type :ushort)))))

Theorem: booleanp-of-type-promoted-arithmeticp

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

Theorem: type-promoted-arithmeticp-of-type-fix-type

(defthm type-promoted-arithmeticp-of-type-fix-type
  (equal (type-promoted-arithmeticp (type-fix type))
         (type-promoted-arithmeticp type)))

Theorem: type-promoted-arithmeticp-type-equiv-congruence-on-type

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