CS606 Short Notes Lecture 17

Lecture 17

Note that productions output are tracing out a lefmost derivation. The grammar symbols on the stack make up left-sentential forms.

LL(1) Table Construction

Top-down parsing expands a parse tree from the start symbol to the leaves. It always expand the leftmost non-terminal. Consider the state

S ? ∗ β Aγ

with b the next token and we are trying to match β bγ. There are two possibilities

1. b belongs to an expansion of A. Any A ? α can be used if b can start a string derived from α. In this case we say that b ∈ FIRST(α )

Q2. b does not belong to an expansion of A . Expansion of A is empty, i.e., A ? ε and b belongs an expansion of γ , e.g., bω. which means that b can appear after A in a derivation of the form S ?

∗ β Abω. We say that b ∈ FOLLOW(A).

Any A ? α can be used if α expands to ε. We say that ε ∈ FIRST(A) in this case.

Definition

FIRST(X) = { b | X ? ∗ ba } ∪ { ε | X ? ∗ ε }