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Types

Type-primitivep

Check if a type is a primitive type.

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

Definitions and Theorems

Function: type-primitivep

(defun type-primitivep (type)
  (declare (xargs :guard (typep type)))
  (let ((__function__ 'type-primitivep))
    (declare (ignorable __function__))
    (or (type-arithmeticp type)
        (type-case type :bool)
        (type-case type :address)
        (type-case type :string))))

Theorem: booleanp-of-type-primitivep

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

Theorem: type-primitivep-of-type-fix-type

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

Theorem: type-primitivep-type-equiv-congruence-on-type

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