I think the below is actually LL(1) but I am not 100% sure. are we able to prove that this iss LL(1) grammar and then also, is the first and follow sets given correct? I dont really understand for sure how to actually get the follow sets.
Grammar
expr ::= term {addop term}
term ::= factor {mulop factor}
factor ::= variable| unsigned-number| ( expr)
variable ::= identifier
addop ::= + | -
mulop ::= * | /
First Sets
First(expr) = identifier, unsigned number, (
First(Term) = identifier, unsigned number, (
First(Factor) = identifier, unsigned number, (
First(Variable) = Identifier
First(addop) = +, -
First(mulop) = *, /
Follow Sets
Follow(Expr) = First(term)
Follow(Term) = First(Factor)
Do not understand how to do the Follow sets of the below sets
Follow(Factor) = First( ")" ) = )
Follow(Variable) Follow(addop) Follow(mulop)
FIRST sets are correct.
FOLLOW sets:
FOLLOW(A) of non-terminal A is the set of terminal symbols that can follow in the derivation sequence
FOLLOW(expr): check where it appeared in the right-hand side of production. It is there is factor:=(expr), when we take this production in the derivation what follows expr is ) and expr is a start symbol.
FOLLOW(expr)={),$}
similarly,
FOLLOW(term) = FIRST(addop) U FOLLOW(expr) = {+,-,),$}
FOLLOW(factor) = FIRST(mulop) U FOLLOW(trem) = {*,/,+,-,),$}
FOLLOW(addop) = FIRST(term) = {identifier,unsigned number,(}
FOLLOW(multop) = FIRST(factor) = {identifier,unsigned number,(}
FOLLOW(Variable)= FOLLOW(factor) = {*,/,+,-,),$}
where $ is the end of the input.
Given grammar is LL(1). FIRST sets of factor are disjoint and we don't need check the FOLLOW sets as there are no epsilon productions.