BNF Syntax Checker

Write BNF production rules and test whether strings belong to the language. Edit the grammar, change the start symbol, and add test strings to explore context-free grammars. Spec reference: §4.4.3.

📖 Learn Step-by-Step

Load a preset grammar or write your own:

A simple integer: an optional sign followed by one or more digits.

BNF Rules (one rule per line):

4 rules parsed · Non-terminals: <integer>, <sign>, <digits>, <digit>

Start symbol:

BNF syntax:

<name> — non-terminal (variable)

::= — "is defined as"

| — separates alternatives ("or")

Anything not in angle brackets is a terminal (literal character)

Test Strings

✅"42"VALID

✅"-7"VALID

✅"+100"VALID

✅"0"VALID

❌"abc"INVALID

❌"12.5"INVALID

❌ε (empty)INVALID

❌"-"INVALID

BNF / Context-Free Grammar Practice Questions

Given the BNF rule <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9, how many alternatives does this rule have?

0/1 mark

Show your working:

Answer:

The grammar is: <S> ::= a<S>b | ab. What is the length of the shortest string that can be derived from <S>?

0/1 mark

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Answer:

Using the grammar <S> ::= a<S>b | ab, how many derivation steps are needed to produce the string "aaabbb"?

0/2 marks

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Answer:

A grammar has: <expr> ::= <term> | <expr>+<term>, <term> ::= <digit>, <digit> ::= 0|1|...|9. How many non-terminal symbols are in this grammar?

0/1 mark

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Answer:

A BNF grammar generates the language {aⁿbⁿ | n ≥ 1}. Using the rule <S> ::= a<S>b | ab, what is the length of the string generated after exactly 5 derivation steps?

0/2 marks

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Answer:

Quick reference — BNF & Context-Free Grammars

What is BNF?

Backus–Naur Form (BNF) is a notation for describing the syntax of context-free grammars. Each rule defines how a non-terminal can be expanded into a sequence of terminals and/or non-terminals.

BNF notation

<name>	Non-terminal (a variable that can be expanded)
::=	"Is defined as"
\|	Separates alternatives
terminals	Literal characters that appear in the final string

Context-free vs regular

Context-free grammars (CFGs) are more powerful than regular expressions. CFGs can describe languages like aⁿbⁿ (matched parentheses) which regular expressions cannot. However, CFGs cannot describe all possible languages — for example, aⁿbⁿcⁿ requires a context-sensitive grammar.

Derivation

A derivation shows how a string is produced from the start symbol by repeatedly replacing non-terminals using the production rules. A leftmost derivation always expands the leftmost non-terminal first.

AQA exam tips

Be able to read BNF and determine if a string is valid
Be able to write BNF rules for a given language
Show derivations step by step
Know the difference between BNF and EBNF (Extended BNF uses { } for repetition and [ ] for optional)