Hi,
The half cock notch was a key feature of the original French "true" flintlock developed during the 1st quarter of the 17th century. Some early type 1 English locks, which were basically reworked snaphaunces, had half cock notches. However, recent scholarship indicates the early English locks were a response to the French flintlock not a predecessor. The English carried on with later locks that had no half cock but did have the dog catch. Those locks had lateral sears early on and then "French" vertical sears later with no half cock notch. Some very inexpensive trade guns may have eliminated the dog catch to cut costs. As Richard mentioned, there also were dog locks with half cock notches as well.
dave