Re: First And Follow

"Mr.E" <mr.waverlye@verizon.net> writes:


> ... I wondered is it possible to derive the first and follow sets
> of a grammar by building a tree (or graphs) of the grammar. ...


I realized belatedly that my first response addressed this question
only for FIRST sets, not for FOLLOW sets. Perhaps that was because
the directed graph construcion is more complicated for FOLLOW sets.
Nonetheless, here it is, once again using the simplifying assmption of
no empty right-hand sides (epsilon productions):


(1) Make a directed graph with one vertex for each nonterminal or
terminal symbol, as well as one for the special end-of-input marker,
which is conventionally written as $.


(2) Add a directed edge from the grammar's start symbol to $.


(3) For each production in the grammar, consider in turn each of the
symbols on the right-hand side with the exception of the rightmost
one. If the symbol is a terminal, nothing needs doing. But if it is
a nonterminal (let's say A), then look at the symbol that is
immediately after it in the production's right-hand side; let's call
that symbol x. Note that x could be either a terminal or a
nonterminal symbol. Consider in turn each element of FIRST(x); each
of these will be a terminal symbol, let's say b. For each one, add a
directed edge from A to b.


(4) Consider in turn each production in the grammar that has a
nonterminal symbol as the rightmost symbol of its right-hand side.
Call that rightmost symbol A and the production's left-hand side B.
In each of these cases, add a directed edge from A to B.


Having built the directed graph in this way, then the FOLLOW set of
any nonterminal symbol consists of those terminal or end-of-input
symbols that are reachable from it.

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