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Abstract-syntax-operations

Label-nocallsp

Check if a label does not contain any function calls.

Signature
(label-nocallsp label) → yes/no
Arguments: label — Guard (labelp label).
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: label-nocallsp

(defun label-nocallsp (label)
  (declare (xargs :guard (labelp label)))
  (let ((__function__ 'label-nocallsp))
    (declare (ignorable __function__))
    (label-case label
                :name t
                :cas (expr-nocallsp label.get)
                :default t)))

Theorem: booleanp-of-label-nocallsp

(defthm booleanp-of-label-nocallsp
  (b* ((yes/no (label-nocallsp label)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: label-nocallsp-of-label-fix-label

(defthm label-nocallsp-of-label-fix-label
  (equal (label-nocallsp (label-fix label))
         (label-nocallsp label)))

Theorem: label-nocallsp-label-equiv-congruence-on-label

(defthm label-nocallsp-label-equiv-congruence-on-label
  (implies (label-equiv label label-equiv)
           (equal (label-nocallsp label)
                  (label-nocallsp label-equiv)))
  :rule-classes :congruence)