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Std/system/term-queries

Lambda-closedp

Check if a lambda expression is closed, i.e. it has no free variables.

Signature
(lambda-closedp lambd) → yes/no
Arguments: lambd — Guard (pseudo-lambdap lambd).
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: lambda-closedp

(defun lambda-closedp (lambd)
  (declare (xargs :guard (pseudo-lambdap lambd)))
  (let ((__function__ 'lambda-closedp))
    (declare (ignorable __function__))
    (subsetp-eq (all-vars (lambda-body lambd))
                (lambda-formals lambd))))

Theorem: booleanp-of-lambda-closedp

(defthm booleanp-of-lambda-closedp
  (b* ((yes/no (lambda-closedp lambd)))
    (booleanp yes/no))
  :rule-classes :rewrite)