Hints.

An automaton type is needed. This could be made of

• a list of the letters of the alphabet of the automaton,
• a list of its states,
• its initial state,
• its final states,
• a transition table.

A symbol table is also needed. An entry of the symbol table may consist of

• the name of a defined language,
• a pointer toward an automaton recognizing the language.

To make thinks simple you may design your desk calculator is two steps

Low-level.

At this level you restrict the regular expressions between { and } to letters of the alphabet $\Sigma$. So, the user needs to replace

? L1 := {a(a|b)*}

by the following sequence of commands

? A := {a}
= defined A
? B := {b}
= defined B
? C0 := A | B
= defined C0
? C1 := C0*
= defined C1
? L1 := A.C1
= defined L1

High-level.

Now the user can use any regular expressions between { and }.