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Types

Type-arithmeticp

Check if a type is an arithmetic type.

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

Definitions and Theorems

Function: type-arithmeticp

(defun type-arithmeticp (type)
  (declare (xargs :guard (typep type)))
  (let ((__function__ 'type-arithmeticp))
    (declare (ignorable __function__))
    (or (type-integerp type)
        (type-case type :field)
        (type-case type :group)
        (type-case type :scalar))))

Theorem: booleanp-of-type-arithmeticp

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

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

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

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

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