BNF (Backus Naur Form) is a simplified grammar that is easier to work with when automatically processing grammars using various algorithms. Note that BNF grammars were developed first, then, for human simplicity and use, EBNF grammars were created.

A BNF grammar has productions, variables, and terminal symbols but no meta-character notation.

An EBNF grammar is easily converted (manually or automatically) to BNF form. This is now covered.

A bottom up analysis (more difficult manually or automatically) can convert a BNF grammar to an EBNF grammar. In doing so, some human intervention can help in obtaining meaningful names for certain productions.

In each case, a EBNF part is given a new and unique name for the BNF production. The new production name X is used. The three dots "..." indicate other parts of a grammar.

The transformation is done recursively for each part of a EBNF production.

The process is continued until all EBNF constructs have been converted.

The following is EBNF for conditional.

Convert this to the following BNF.

The following is EBNF for alternatives

Convert this to the following BNF.

The following is EBNF for sequence.

Convert this to the following BNF.

The following is EBNF for grouping.

Convert this to the following BNF.

Note that the parentheses disappear.

The following is EBNF for repetition.

Convert this to the following BNF (right recursive).

The following recursive BNF forms are equivalent.

Right recursive: (LL and LR parsers):

Left recursive: (LL parsers, not LR parsers):

Consider a grammar for a number.

Here is the associated EBNF (Extended Backus Naur Form) grammar.

Here is the associated EBNF syntax diagram(s).


Note: The generated diagram shows an improvement from the straight-forward conversion. Here is the associated EBNF grammar.

Here is an equivalent BNF grammar.

Here is the above syntax diagram and EBNF converted to BNF using "X".

Here is the associated EBNF syntax diagram(s).


Here is the associated EBNF grammar.

Here is the associated BNF grammar (without production compression) as follows.

Consider a grammar for an identifier.

Here is the associated EBNF grammar.

Here is the associated EBNF syntax diagram(s).

Here is the associated EBNF grammar.

Here is an equivalent BNF grammar.

Here is the above syntax diagram and EBNF converted to BNF using "X".

Here is the associated EBNF syntax diagram(s).


Here is the associated EBNF grammar.

Here is the associated BNF grammar (without production compression) as follows.

Here is EBNF in EBNF

Here is the associated EBNF syntax diagram(s).

Here is the associated EBNF grammar.

Let us take the conversion of EBNF in EBNF to BNF in parts.

Here is the associated EBNF syntax diagram(s).


Here is the associated EBNF grammar.

Here is the associated BNF grammar (without production compression) as follows.

With production compression (and renaming), the following is an equivalent BNF grammar.

Here is the associated EBNF syntax diagram(s).


Here is the associated EBNF grammar.

Here is the associated BNF grammar (without production compression) as follows.

Notice that with a sequence (without meta-characters), there is no change

Here is the associated EBNF syntax diagram(s).


Here is the associated EBNF grammar.

Here is the associated BNF grammar (without production compression) as follows.

With production compression (and renaming), the following is an equivalent BNF grammar.

Here is the associated EBNF syntax diagram(s).


Here is the associated EBNF grammar.

Here is the associated BNF grammar (without production compression) as follows.

With production compression (and renaming), the following is an equivalent BNF grammar.

The following improvement can be made (in line with the above syntax diagram), for LR parsers or LL parsers (recursive descent) that take into consideration the common prefix.

Here is the associated EBNF syntax diagram(s).


Here is the associated EBNF grammar.

Here is the associated BNF grammar (without production compression) as follows.

With production compression (and renaming), the following is an equivalent BNF grammar.

Some parsing algorithms are easier to specify and show correct if the grammar is in CNF (Chomsky Normal Form) , developed by and named after the famous linguist Noam Chomsky. In a CNF grammar, each production needs to contain at most two parts of the following form.

A simple form results in a lot of simple productions - difficult for humans but easy for algorithm analysis and implementation involving parsing and grammars.

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