====== Context Free Languages ======

=== Pumping Lemma ===


**1.** Pumping Lemma

Prove that the following languages are **not** context-free.

//1.1.// $ L=\{a^nb^{2n}c^n \ | \ n \geq 0\} $

//1.2.// $ L=\{a^n \ | \ n \text{ is a prime number}\} $

//1.3.// $ L=\{ww \ | \ w \in \{0,1\}^*\} $


**2.** Simple parser based on PDAs.

//2.1.// Write a PDA which accepts the language described below:

<code python>
<expr> ::= <expr> + <expr> | <expr> * <expr> | (<expr>) | <number>
<number> ::= [0-9]+
</code>

//2.2.// Define classes: $\texttt{Expr}$, as well as the following classes which extend expressions:  $\texttt{Plus}$,  $\texttt{Mult}$,  $\texttt{Par}$,  $\texttt{Number}$. Add the $\texttt{__str__()}$ function for each class.

//2.3.// Based on the written PDA, implement a parser in Python for expressions. The parser should return an $\texttt{Expr}$ object.

//2.4.// Write a procedure which evaluates expressions. What is the natural way to implement it?