Question

Design a language description for which a BNF/EBNF based grammar cannot be written. Prove that the grammar cannot be written for the description.

Answer 1

The EBNF is the most commonly used formalism to describe the structure of languages.

What is the EBNF?
The EBNF is a way to specify a formal language grammar. It can be considered a metalanguage because it is a language to describe other languages.
A formal language is a language with a precise structure, like programming languages, data languages, or Domain Specific Languages (DSLs). Java, XML, and CSS are all examples of formal languages.
A grammar can be used to define two opposite things:
how to recognize the different portions in a piece of code written in the formal language
the possible ways to build a valid piece of code in the formal language
For example, a simple grammar could tell us that a document in our language is composed by a list of declarations, and declarations are defined by the sequence of a keyword Xyz and a a name.
Based on this we could:
recognize in the code sequences of the keyword Xyz and a name as instances of these declarations we have considered
we could generate valid documents in our language by writing a list of declarations, each time inserting a keyword Xyz and a name
While there are two possible usages for a grammar, we are typically interested only in the first one: recognizing if a piece of code is valid for a given language and identifying the different structures typical of the language (like functions, methods, classes, etc.).