Regular Defination

We may wish to give to regular expression and to define regular expression using these names as if they were symbols.                                                                           

If ∑ is an alphabet of basic symbols, then a regular definition is a sequence of definitions of the form,                                                                                                       

d₁ --> r₁                                                                                                                           

d₂ --> ₂                                                                                                                            

  …….                                                                                                                                 

d_n --> r_n

Where each di is a distinct name, and each ri is a regular expression over the symbols in  ∑ u{d1,d2,….dn}, ie. the basic symbols and the previously defined names. By restricting each ri to symbols of  ∑ and the previously defined names, we can construct a regular expression over ∑  for any r_i by repeatedly replacing regular expression names by the expression they denote. If r_i used dj for some j>=i, then r_i might be recursively defined .and this substitution process would not terminate.                                                                                

To distinguish names from symbols, we print the names in regular definitions in bold face.