EBNF Precedence and Associativity Cheat Sheet

EBNF Precedence and Associativity Cheat Sheet.md

EBNF Precedence and Associativity Cheat Sheet

These are the standard patterns for encoding precedence and associativity into an expresion grammar in (E)BNF.

View in EBNF playground.

<ADD_OP>   ::= "+" | "-" 
<MUL_OP>   ::= "*" | "/"
<POWER_OP> ::= "^"
<NUMBER>   ::= [0-9]+

/* Just for illustrative purposes, as this production can be left out. */
<expr> ::= <term>

/* A term is composed of a factor, so factor is parsed/produced first */
<term> ::= <term> <ADD_OP> <factor>
    | <factor>
    
/* Left associative, so written as left recursive */
<factor> ::= <factor> <MUL_OP> <power> 
    | <power>
    
/* Right associative, so written as right recursive */
<power> ::= <unary> <POWER_OP> <power>
    | <unary>
    
<unary> ::= "-" <primary>
	| <primary>
    
/* The leaf nodes……or parenthesized expressions. */
<primary> ::= <NUMBER>
    | "(" <expr> ")"