Mathematical Productions with order of operations and avoiding left tail recursion

productions.go

func addMathProductions() {
	// expr -> expr + term
	//       | expr - term
	//       | term
	//
	// rewritten:
	// expr -> term restAdd
	addProduction(expr,
		rules{
			{term, restAdd},
		})

	// restAdd -> + term restAdd
	//          | - term restAdd
	//          | ε
	addProduction(restAdd,
		rules{
			{ItemOpPlus, term, restAdd},
			{ItemOpMinus, term, restAdd},
			{empty},
		})

	// term -> term * factor
	//       | term / factor
	//       | factor
	//
	// rewritten:
	// term -> factor restMul
	addProduction(term,
		rules{
			{factor, restMul},
		})

	// restMul -> * factor restMul
	//          | / factor restMul
	//          | ε
	addProduction(restMul,
		rules{
			{ItemStar, factor, restMul},
			{ItemOpDivide, factor, restMul},
			{ItemOpModulo, factor, restMul},
			{empty},
		})

	// factor -> num
	//         | ( expr )
	addProduction(factor,
		rules{
			{ItemNumber},
			{ItemLeftParen, expr, ItemRightParen},
			{ItemOpMinus, factor},
		})
}

func addProduction(id NonTerminal, rules rules) {
	p := production{id: id, rules: rules}
	productions = append(productions, p)
}