C3 linearization

In computing, the C3 superclass linearization is an algorithm used primarily to obtain the order in which methods should be inherited (the "linearization") in the presence of multiple inheritance, and is often termed Method Resolution Order (MRO). The name C3 refers to the three important properties of the resulting linearization: a consistent extended precedence graph, preservation of local precedence order, and fitting the monotonicity criterion. (The name "C3" is not an initialism.) It was first published at the 1996 OOPSLA conference, in a paper entitled "A Monotonic Superclass Linearization for Dylan". It was adapted to the Open Dylan implementation in January 2012 following an enhancement proposal. It has been chosen as the default algorithm for method resolution in Python 2.3 (and newer),Perl 6,Parrot, and Solidity. It is also available as an alternative, non-default MRO in the core of Perl 5 starting with version 5.10.0. An extension implementation for earlier versions of Perl 5 named Class::C3 exists on CPAN.

The C3 superclass linearization of a class is the sum of the class plus a unique merge of the linearizations of its parents and a list of the parents itself. The list of parents as the last argument to the merge process preserves the local precedence order of direct parent classes.

The merge of parents' linearizations and parents list is done by selecting the first head of the lists which does not appear in the tail (all elements of a list except the first) of any of the lists. Note, that a good head may appear as the first element in multiple lists at the same time, but it is forbidden to appear anywhere else. The selected element is removed from all the lists where it appears as a head and appended to the output list. The process of selecting and removing a good head to extend the output list is repeated until all remaining lists are exhausted. If at some point no good head can be selected, because the heads of all remaining lists appear in any one tail of the lists, then the merge is impossible to compute due to cyclic dependencies in the inheritance hierarchy and no linearization of the original class exists.

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