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Types

Type-arithmeticp

Check if a type is an arithmetic type [C17:6.2.5/18].

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)))
  (or (type-integerp type)
      (type-floatingp type)))

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-when-type-kind-syntaxp

(defthm type-arithmeticp-when-type-kind-syntaxp
  (implies (and (equal (type-kind type) kind)
                (syntaxp (quotep kind)))
           (equal (type-arithmeticp type)
                  (or (type-integerp type)
                      (type-floatingp type)))))

Theorem: type-arithmeticp-when-type-integerp

(defthm type-arithmeticp-when-type-integerp
  (implies (type-integerp type)
           (type-arithmeticp type)))

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)