3.7.3 Operator Precedence

Use the %left, %right or %nonassoc declaration to declare a token and specify its precedence and associativity, all at once. These are called precedence declarations. See section Operator Precedence, for general information on operator precedence.

The syntax of a precedence declaration is nearly the same as that of %token: either

%left symbols…

or

%left <type> symbols…

And indeed any of these declarations serves the purposes of %token. But in addition, they specify the associativity and relative precedence for all the symbols:

• The associativity of an operator op determines how repeated uses of the operator nest: whether ‘x op y op z’ is parsed by grouping x with y first or by grouping y with z first. %left specifies left-associativity (grouping x with y first) and %right specifies right-associativity (grouping y with z first). %nonassoc specifies no associativity, which means that ‘x op y op z’ is considered a syntax error.
• The precedence of an operator determines how it nests with other operators. All the tokens declared in a single precedence declaration have equal precedence and nest together according to their associativity. When two tokens declared in different precedence declarations associate, the one declared later has the higher precedence and is grouped first.

For backward compatibility, there is a confusing difference between the argument lists of %token and precedence declarations. Only a %token can associate a literal string with a token type name. A precedence declaration always interprets a literal string as a reference to a separate token. For example:

%left  OR "<="         // Does not declare an alias.
%left  OR 134 "<=" 135 // Declares 134 for OR and 135 for "<=".