Question

I have removed left-recursion from a left-recursive grammar given to me. The original grammar is as follows:

SPRIME::= Expr eof
Expr::= Term | Expr + Term | Expr – Term
Term::= Factor | Term * Factor | Term / Factor | Term mod Factor | Term div factor
Factor::= id | { Expr } | num | Funcall |
Funcall::= id [ Arglist ]
Arglist::= Expr | Expr , Arglist

When removing left-recursion, this is the grammar I produced:

SPRIME::= Expr eof
Expr::= Term Expr’
Expr’::= e | + Term Expr’ | – Term Expr’
Term::= Factor Term’
Term’::= e | * Factor Term’ | / Factor Term’ | mod Factor Term’ | div Factor Term’
Factor::= id | { Expr } | num | Funcall
Funcall::= id [ Arglist ]
Arglist::= Expr Arglist’
Arglist’::= , Arglist | e

My next task is to perform left-factoring on this grammar in order to make it LL(1). Having read the relevant chapter in the Dragon book, I’m unsure if I need to do anything to this grammar. My question is: is this grammar in LL(1) form already? And if not, where do I need to perform left-factoring in order to make it LL(1)?

EDIT: After taking @suddnely_me’s answer into account, I have edited the Arglist non-terminal in order to left-factor it’s productions. Is the grammar I have now an LL(1) grammar?

Answer 1

No, this grammar is not LL(1). At least, the last rules group is not left factored, since FIRST( Expr) and FIRST( Expr, Arglist) do interstect.