Syntax diagram

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Syntax diagrams (or railroad diagrams) are a way to represent a large thing context-free grammar. They represent a graphical alternative to Backus–Naur Form or to EBNF. Early books using syntax diagrams include the "Pascal User Manual" written by Niklaus Wirth ^[1] (diagrams start at page 47) and the Burroughs CANDE manual ^[2]. In the compilation field, textual representations like BNF or its variants are usually preferred. BNF is well understood by compiler writers and compilers, but is not well understood by most users of languages. Railroad diagrams are more readily understood by most people. Some of the popularity of the JSON data interchange format is due to its representation in railroad diagrams.^{[citation needed]}

[edit] Principle of syntax diagrams

The representation of a grammar is made of a set of syntax diagrams. Each diagram defines a non-terminal. There is a main diagram which defines the language in the following way: to belong to the language, a word must describe a path in the main diagram.

Each diagram has an entry point and an end point. The diagram describes possible paths between these two points by going through other nonterminals and terminals. Terminals are represented by round boxes while nonterminals are represented by square boxes.

[edit] Example

We use arithmetic expressions as an example. First we provide a simplified BNF grammar:

<expression> ::= <term> | <term> "+" <expression>
<term>       ::= <factor> | <factor> "*" <term>
<factor>     ::= <constant> | <variable> | "(" <expression> ")"
<variable>   ::= "x" | "y" | "z" 
<constant>   ::= <digit> | <digit> <constant>
<digit>      ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

This grammar can also be expressed in EBNF:

expression = term , {"+" , term};
term       = factor , {"*" , factor};
factor     = constant | variable | "(" , expression , ")";
variable   = "x" | "y" | "z"; 
constant   = digit , {digit};
digit      = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9";