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Types

Type-integer-promotedp

Check if an arithmetic type is a promoted one.

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

That is, check if it is a possible result of type-integer-promote. This holds for all types except the integer ones with rank below int.

Definitions and Theorems

Function: type-integer-promotedp

(defun type-integer-promotedp (type)
  (declare (xargs :guard (typep type)))
  (declare (xargs :guard (type-arithmeticp type)))
  (not (member-eq (type-kind type)
                  '(:bool :char :schar
                          :uchar :sshort
                          :ushort :enum))))

Theorem: booleanp-of-type-integer-promotedp

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

Theorem: type-integer-promotedp-when-type-kind-syntaxp

(defthm type-integer-promotedp-when-type-kind-syntaxp
  (implies (and (equal (type-kind type) kind)
                (syntaxp (quotep kind)))
           (equal (type-integer-promotedp type)
                  (not (member-equal kind
                                     '(:bool :char :schar
                                             :uchar :sshort
                                             :ushort :enum))))))

Theorem: type-integer-promotedp-of-type-fix-type

(defthm type-integer-promotedp-of-type-fix-type
  (equal (type-integer-promotedp (type-fix type))
         (type-integer-promotedp type)))

Theorem: type-integer-promotedp-type-equiv-congruence-on-type

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