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Weak Copyleft licences are free software licences that mandate that source code that descended from software licensed under them, will remain under the same, weak copyleft, licence. However, one can still link to weak copyleft code from code under a different licence (including non-open-source code), or otherwise incorporate it in a larger software.
Otherwise, weak copyleft licences allow free distribution, use , selling copies of the code or the binaries (as long as the binaries are accompanied by the (unobfuscated) source code), etc.
Examples of weak copyleft licences include:
The GNU Lesser General Public License (or LGPL for short) - this licence was formulated by the Free Software Foundation based on the GNU General Public License (or GPL). Its text is longer than the GPL, and it is reportedly a more complicated licence. Other than the general “you-can-link-it-against-everything-as-long-as-you-keep-inclusive-code-LGPLed”, it allows an explicit conversion to the GPL, has patent-related clauses, and contains many additional restrictions.
Version 2 of the LGPL was succeeded by version 2.1, and now there’s also version 3 which is based on a short adaptation of the version 3 of the GPL (see below).
The Mozilla Public License (or MPL) was phrased for the public source release of the Mozilla project. It was characterised as a hybridisation of the modified BSD licence and the GPL. Initially, this licence was ruled as GPL-incompatible, which eventually caused the Mozilla project to re-license its code under a triple MPL, GPL and LGPL licence. Version 2.0 of the MPL has GPL and LGPL compatibility.
GPL with an Exemption Clause - the GPL is a strong copy-left licence, but sometimes an additional clause is added that allows it to be linked against code of non-GPL-compatible licences (including non-open-source code). This strategy was chosen by Sun Microsystems when they decided to release the source of the Java programming language under an open-source licence.