The expressions in the above may not use macros, etc.
There are the same number of expressions in a macro_reference as symbols in the macro_definition.
Examples useful for describing languages (See Ada and C)
It is also possible to include more complex mappings than the context free macros described above. A nice example occurs in most programming languages in the definition of a litteral character string. Coming up with a clear, unambiguous and universal notation is not easier and there have been half-a-dozen solutions proposed [Higman, Chapter ??]. By using the more advanced (non-Chomsky) notations of MATHS many of these can be defined as follows:
There is a designated quote character q and a partial 1-1 map called 'escaping' (E) which associates some of the characters with a unique string. The domain of definition of E are the escapable characters. The image of E are the escape strings. q is one of these escapable character. The escape strings are NOT characters. Therefore q is not one of the escape strings (but may be a character in an escape string. Strings are then defined unambiguously by
In MATHS,
. . . . . . . . . ( end of section Macros) <<Contents | End>>
Proofs follow a natural deduction style that start with assumptions ("Let") and continue to a consequence ("Close Let") and then discard the assumptions and deduce a conclusion. Look here [ Block Structure in logic_25_Proofs ] for more on the structure and rules.
The notation also allows you to create a new network of variables and constraints. A "Net" has a number of variables (including none) and a number of properties (including none) that connect variables. You can give them a name and then reuse them. The schema, formal system, or an elementary piece of documentation starts with "Net" and finishes "End of Net". For more, see [ notn_13_Docn_Syntax.html ] for these ways of defining and reusing pieces of logic and algebra in your documents. A quick example: a circle might be described by Net{radius:Positive Real, center:Point, area:=π*radius^2, ...}.
For a complete listing of pages in this part of my site by topic see [ home.html ]
For a more rigorous description of the standard notations see