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Strong copyleft licences go a step further from weak copyleft licences and mandate that any distributed software that links or otherwise incorporates such code be licensed under compatible licences, which are a subset of the available open-source licences. As a result, these licences have been called “viral”.
Examples of strong copyleft licences include:
the GNU General Public License (or GPL for short), which has two common primary versions - version 2 and version 3. The GPL has a complicated language (I read the GPL version 2 once and did not fully understand it) and has some additional restrictions beyond just making sure that code incorporating its code would be under compatible, open-source licences.
Note that there is a difference between the GPL version 2, and the GPL version 3 and that they are mutually incompatible. Some people use the language “Licensed under the GNU General Public Licence, version 2, or at your option any later version” which avoids this problem. However, many projects including the Linux kernel are licensed only under version 2 of the GPL (and not a later version).
The Sleepycat License. This licence was formulated by Sleepycat Software (now part of Oracle) for use in their Berkeley DB database product. The reason this licence was chosen instead of the GPL was because the source for the Berkeley DB was originally written under one of the BSD licences, and it was not clear whether it was possible to sub-license it under the GPL.
The Sleepycat licence is short and has a simple language, and is easy to understand. From my reading of it, it seems that it is both recursive (requires code that originated from it to be licensed under the same licence) and that it mandates releasing the source code of software applications that linked against it, but under a non-specified (and possibly non-free) licence.
Sleepycat has also provided a commercial licence for using Berkeley DB which allows incorporating it into a larger work without the need to release the source. This is a valid business model used by originators of GPL-licensed software and other strong copyleft licences. See Richard Stallman's "Selling Exceptions to the GNU GPL" essay.