Convert the following inductive definition for regular expressions into a grammar first and then into a set of scala classes.

A regular expression is defined inductively as follows:

Any string s is an "atomic" regular expression.

If $1,2$ are regular expressions then so are

The concatenation $1$;$2,$

The disjunction $1|2,$ and

The conjunction $1$&$2.$

If $$ is a regular expression, then its Kleene star $$ is also a regular expression.

Use the constructor symbols:

Atom$()$ to denote an atomic regular expression,

Concat$(1,2)$ for the $"$;$"$ operator,

Or$(1,2)$ for the $"|"$ operator,

And$(1,2)$ for the $"$&$"$ operator and

Star$()$ for the Kleene$-$star operator.

You may use the nonterminal $$ without definition to denote a string of charact