Grammars for parsing arithmetic expressions

gistfile1.txt

Grammar with left-recursion (e.g. Expr's derivation contains Expr as first non-terminal).
Not suitable for Recursive Descent parsing.

	Expr   = Expr "+" Term | Expr "-" Term | Term
	Term   = Term "*" Factor | Term "/" Factor | Factor
	Factor = "(" Expr ")" | "-" Factor | Number

gistfile2.txt

Grammar without left-recursion. But not left-factored, that's why it needs arbitrary lookahead,
e.g. Expr's derivation will need to look ahead Term to see which derivation to go with.
Suitable for R.D. parsing but needs backtracking.

	Expr   = Term "+" Expr | Term "-" Expr | Term
	Term   = Factor "*" Term | Factor "/" Term | Factor
	Factor = "(" Expr ")" | "-" Factor | Number

gistfile3.txt

Grammar without left-recursion. Left-factored. Needs single lookahead.
Suitable for R.D. parsing. Does not need backtracking.

	Expr   = Term Expr'
	Expr'  = "+" Expr | "-" Expr | ε
	Term   = Factor Term'
	Term'  = "*" Term | "/" Term | ε
	Factor = "(" Expr ")" | "-" Factor | Number