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Types

Type-complexp

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

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

Definitions and Theorems

Function: type-complexp

(defun type-complexp (type)
  (declare (xargs :guard (typep type)))
  (and (member-eq (type-kind type)
                  '(:floatc :doublec :ldoublec))
       t))

Theorem: booleanp-of-type-complexp

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

Theorem: type-complexp-when-type-kind-syntaxp

(defthm type-complexp-when-type-kind-syntaxp
  (implies
       (and (equal (type-kind type) kind)
            (syntaxp (quotep kind)))
       (equal (type-complexp type)
              (and (member-equal kind '(:floatc :doublec :ldoublec))
                   t))))

Theorem: type-complexp-of-type-fix-type

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

Theorem: type-complexp-type-equiv-congruence-on-type

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