Zapišite rekurzivni navzdolni razpoznavalnik za programski jezik iz naloge 4 z naslednjo gramatiko:

\[\newcommand\Seq{\mathrel{}} \newcommand\Union{\mathrel{|}} \begin{alignedat}{3} \text{Expr}_{start} &&{}\Coloneqq{} &\text{Additive}\cr \text{Additive} &&{}\Coloneqq{} &\text{Multiplicative} \Seq \text{Additive'}\cr \text{Additive'} &&{}\Coloneqq{} &\text{plus} \Seq \text{Multiplicative} \Seq \text{Additive'}\cr &&{}\Union{}& \text{minus} \Seq \text{Multiplicative} \Seq \text{Additive'}\cr &&{}\Union{}& \epsilon\cr \text{Multiplicative} &&{}\Coloneqq{} &\text{Exponential} \Seq \text{Multiplicative'}\cr \text{Multiplicative'} &&{}\Coloneqq{} &\text{times} \Seq \text{Exponential} \Seq \text{Multiplicative'} \cr &&{}\Union{}& \text{divide} \Seq \text{Exponential} \Seq \text{Multiplicative'}\cr &&{}\Union{}& \text{integer-divide} \Seq \text{Exponential} \Seq \text{Multiplicative'}\cr &&{}\Union{}& \epsilon\cr \text{Exponential} &&{}\Coloneqq{} &\text{Unary} \Seq \text{Exponential'}\cr \text{Exponential'} &&{}\Coloneqq{} &\text{pow} \Seq \text{Unary} \Seq \text{Exponential'}\cr &&{}\Union{}& \epsilon\cr \text{Unary} &&{}\Coloneqq{} &\text{plus} \Seq \text{Primary} \Union \text{minus} \Seq \text{Primary} \Union \text{Primary}\cr \text{Primary} &&{}\Coloneqq{} &\text{real} \Union \text{variable} \Union \text{lparen} \Seq \text{Additive} \Seq \text{rparen} \end{alignedat}\]

Program naj loči med sintaktično veljavnimi: 5 * 6 + ( 3 * 4 + var123), in sintaktično nevaljavnimi programi: 5 * 6 + 7 8.

Program naj iz vhodne datoteke prebere izvorni program in v izhodno datoteko izpiše accept, če je primer veljaven in reject, če je primer neveljaven. Imeni datotek bo program dobil kot konzolna argumenta.

Nalogo oddajte na GitHub, link.