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Group-literal

Group-literalp

Recognizer for group-literal structures.

Signature
(group-literalp lit) → *

Definitions and Theorems

Function: group-literalp

(defun group-literalp (lit)
  (declare (xargs :guard t))
  (let ((__function__ 'group-literalp))
    (declare (ignorable __function__))
    (and (consp lit)
         (cond ((or (atom lit) (eq (car lit) :affine))
                (and (true-listp (cdr lit))
                     (eql (len (cdr lit)) 2)
                     (b* ((x (std::da-nth 0 (cdr lit)))
                          (y (std::da-nth 1 (cdr lit))))
                       (and (coordinatep x) (coordinatep y)))))
               (t (and (eq (car lit) :product)
                       (and (true-listp (cdr lit))
                            (eql (len (cdr lit)) 1))
                       (b* ((factor (std::da-nth 0 (cdr lit))))
                         (natp factor))))))))

Theorem: consp-when-group-literalp

(defthm consp-when-group-literalp
  (implies (group-literalp lit)
           (consp lit))
  :rule-classes :compound-recognizer)