Left-associativity

[ghost]

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[bd82]

Have a look at this calculator example grammar it handles operator precedence.
https://github.com/SAP/chevrotain/blob/master/examples/grammars/calculator/calculator.js

Its the same pattern as used in Antlr3 and most Top Down parsers which do not support Left recursion.
Antlr3 Java Grammar expressions Example

You can also consider to not embed precedence into the grammar.
The disadvantage of this pattern is that it creates some fairly deep parse trees.

Alternative

The Swift programing language takes an interesting approach to solve this complexity
by removing the operator precedence logic from the grammar altogether.
See:
https://developer.apple.com/library/prerelease/content/documentation/Swift/Conceptual/Swift_Programming_Language/Expressions.html#//apple_ref/doc/uid/TP40014097-CH32-ID383

Note
At parse time, an expression made up of binary operators is represented as a flat list. This list is transformed into a tree by applying operator precedence. For example, the expression 2 + 3 * 5 is initially understood as a flat list of five items, 2, +, 3, *, and 5. This process transforms it into the tree (2 + (3 * 5)).

[bd82]

Precedence and associativity are two fundamentally different concepts, though, aren't they?

Yes, I'm sometimes a bit too focused on syntax and syntax is sometimes used for Precedence handling.
Associativity is more about what you do with the syntax you parsed.