org-element: Move archived tree handling out of org-element-map

* contrib/lisp/org-element.el: Move archived tree handling out of
  org-element-map.
* contrib/lisp/org-export.el (org-export-get-ignore-list): Properly
  ignore archived with `org-export-with-archived-trees' set to
  `headline'.
* testing/contrib/lisp/test-org-export.el (test-org-export/handle-options):
  Add a test for that.

contrib/lisp/org-element.el

@@ -3009,8 +3009,7 @@ information.
 
 When optional argument INFO is non-nil, it should be a plist
 holding export options.  In that case, parts of the parse tree
-not exportable according to that property list will be skipped
-and files included through a keyword will be visited.
+not exportable according to that property list will be skipped.
 
 When optional argument FIRST-MATCH is non-nil, stop at the first
 match for which FUN doesn't return nil, and return that value.
@@ -3077,18 +3076,7 @@ Nil values returned from FUN are ignored in the result."
 		  ;; possible and allowed.
 		  (cond
 		   ;; Element or object not exportable.
-		   ((member --blob (plist-get info :ignore-list)))
-		   ;; Archived headline: Maybe apply FUN on it, but
-		   ;; ignore contents.
-		   ((and info
-			 (eq --type 'headline)
-			 (eq (plist-get info :with-archived-trees) 'headline)
-			 (org-element-property :archivedp --blob))
-		    (funcall --check-blob
-			     --type types fun
-			     ;; Ensure --BLOB has no contents.
-			     (list --type (nth 1 --blob))
-			     info))
+		   ((and info (member --blob (plist-get info :ignore-list))))
 		   ;; Limiting recursion to greater elements, and --BLOB
 		   ;; isn't one.
 		   ((and (eq --category 'greater-elements)

contrib/lisp/org-export.el

@@ -1414,12 +1414,21 @@ Return elements or objects to ignore as a list."
 	     (lambda (el)
 	       (if (org-export--skip-p el options) (push el ignore-list)
 		 (let ((type (org-element-type el)))
-		   (when (or (eq type 'org-data)
-			     (memq type org-element-greater-elements)
-			     (memq type org-element-recursive-objects)
-			     (eq type 'paragraph))
-		     (funcall walk-data el options)))))
+		   (if (and (eq (plist-get info :with-archived-trees) 'headline)
+			    (eq (org-element-type el) 'headline)
+			    (org-element-property :archivedp el))
+		       ;; If headline is archived but tree below has
+		       ;; to be skipped, add it to ignore list.
+		       (mapc (lambda (e) (push e ignore-list))
+			     (org-element-contents el))
+		     ;; Move into recursive objects/elements.
+		     (when (or (eq type 'org-data)
+			       (memq type org-element-greater-elements)
+			       (memq type org-element-recursive-objects)
+			       (eq type 'paragraph))
+		       (funcall walk-data el options))))))
 	     (org-element-contents data))))))
+    ;; Main call.
     (funcall walk-data data options)
     ;; Return value.
     ignore-list))

testing/contrib/lisp/test-org-export.el

@@ -159,6 +159,14 @@ as Org syntax."
 	(should
 	 (equal (org-export-as 'test nil nil nil '(:with-archived-trees nil))
 		"")))))
+  (org-test-with-temp-text "* Head1 :archive:\nbody\n** Sub-head 2"
+    (let ((org-archive-tag "archive"))
+      (org-test-with-backend "test"
+	(should
+	 (string-match
+	  "\\* Head1[ \t]+:archive:"
+	  (org-export-as 'test nil nil nil
+			 '(:with-archived-trees headline)))))))
   (org-test-with-temp-text "* Head1 :archive:"
     (let ((org-archive-tag "archive"))
       (org-test-with-backend "test"