📐 How Do Computers Understand Grammar?

BNF & Syntax Diagrams

Programming languages have strict grammar rules — just like English. BNF is how we write those rules down, and syntax diagrams (railroad diagrams) show them visually.

CS A-Level Unit 3

🤔 What is BNF?

BNF (Backus-Naur Form) is a way of writing the grammar rules of a programming language. Just like English has rules ("a sentence needs a subject and a verb"), programming languages have rules about what code looks like.

🍕 Analogy: Think of ordering pizza. The "grammar" might be:

<order> ::= <size> <topping> "pizza"
<size> ::= "small" | "medium" | "large"
<topping> ::= "pepperoni" | "margherita" | "Hawaiian"

✅ "large pepperoni pizza" — valid!
❌ "pepperoni large pizza" — wrong order!
❌ "huge pepperoni pizza" — "huge" isn't a valid size!

📂

Choose a grammar

BNF Rules:

Format: <name> ::= option1 | option2 · Terminals in "quotes" · Non-terminals in <angle brackets>

🚂

Syntax Diagrams (railroad diagrams)

Follow the track from left to right. Each path through the diagram is a valid option. It's like a train track — you can only go where the rails take you.

🧪

Test a string

Type something and see if it follows the grammar rules. The validator will show you step by step whether it's valid.

📖

BNF Cheat Sheet

Symbol	Meaning	Example
::=	"is defined as"	<digit> ::= "0" \| "1"
\|	"or" — choose one option	"a" \| "b" \| "c"
< >	Non-terminal — a rule name (gets expanded)	<expression>
" "	Terminal — an actual character/word (stays as-is)	"hello"
<empty>	Nothing — the rule can produce an empty string	<list> ::= <item> <list> \| <empty>

📝 Exam tip: In the exam, you might be asked to write BNF rules for a simple language, or trace through rules to check if a string is valid. Practice by changing the rules above and testing different strings!