"class A succeeds class B" means in Scala reference?

Question

In the Scala 2.8 reference, section 5.3.3 page 69 (77 in the pdf) the following paragraph appear:

Assume a trait D defines some aspect of an instance x of type C (i.e. D is a base class of C). Then the actual supertype of D in x is the compound type consisting of all the base classes in L(C) that succeed D.

What does the notation L(C) means (in the original text it's a calligraphic capital \ell like symbol)?

What does the phrase "classes... that succeed D" means? I'm not familiar with the notation.

Answer 1

The bottom line is, L(C) consists of all the base classes (the whole inheritance hierarchy of C, including traits) ordered as a chain, with Any at the top, and C at the bottom. Succeeds D means, is higher in the chain then D.

The longer explanation is that we want to know, for each class, its "parent" -- for implementation purposes and general clarity (it's terribly messy in C++, where unbounded multiple inheritance is allowed). In Java it is simple -- you only have a single direct superclass. However, because of the mixin-class composition in Scala, which is a form of multiple inheritance (from one superclass + possibly several traits), the base classes of any class form a directed acyclic graph. L(C) is the linearization of the C's base classes -- starting from the superclass, and adding the traits (and their base classes) such that they form a chain and each class has her own base classes above itself. You can read more about it in Section 6 of the overview of Scala. It's a nice, comprehensive outline of the feature.

Answer 2

L(C) is class linearization. Then "succeeds" regards to the position in the result sequence. Linearization is defined in chapter 5.1.2 of the spec.