L-attributed definitions include all syntax-directed definitions based on LL(1) grammars

Question

I was going through the text Compilers: Principles, Techniques and Tools by Ullman et. al where I came across the following claim:

L-attributed definitions include all syntax-directed definitions based on LL(1) grammars.

What is the intuition or logic behind this statement?

In the later sections they show that L attributed grammars can be easily implemented by a DFS search algorithm of the parse tree (and hence easily by a predictive parser [recursive/non recursive]). $^\dagger$

Is it so that since LL(1) grammars can also be parsed by predictive parser and by the logic of $\dagger$, the authors make the claim?

Answer 1

L-attributed definitions are definition whose attributes can be evaluated in depth-first order (as they say in the first sentence).

The statement "L-attributed definitions include all syntax-directed definitions based on LL(1) grammars" is perhaps a bit subtle. It's not saying that the two sets of definitions are the same; rather, that syntax-directed definitions "based on LL(1) grammars" are a subset of L-attributed definitions.

That's true because the predictive parser based on the LL(1) grammar visits the parse tree in strictly depth-first order. This was already noted in Designing a Predictive Parser in Section 2.4 of the text book, which goes on to build a recursive-descent parser illustrating how this works.